C:/Dokumente und Einstellungen/Volker/Desktop/BeautyThesis/Thesis.dvi Measurement of Beauty Production in Deep Inelastic Scattering at HERA Volker Michels Measurement of Beauty Production in Deep Inelastic Scattering at HERA Dissertation zur Erlangung des Doktorgrades des Departments Physik der Universität Hamburg vorgelegt von Volker Michels aus Lüneburg 2008 korrigierte Fassung (30.08.2008) Gutachter der Dissertation: Dr. B. List Prof. Dr. R. Klanner Gutachter der Disputation: Prof. Dr. P. Schleper Dr. H. Jung Datum der Disputation: 28.08.2008 Vorsitzender des Prüfungsausschusses: Dr. M. Martins Vorsitzender des Promotionsausschusses: Prof. Dr. J. Bartels Dekan der Fakultät Mathematik, Informatik, Naturwissenschaften: Prof. Dr. A. Frühwald Abstract A measurement of the beauty production cross section in ep collisions at a centre-of-mass energy of 319 GeV is presented. The data was collected with the H1 detector at the HERA collider in the years 2005-2007 and corresponds to an integrated luminosity of 285 pb−1. Events are selected by requiring the presence of at least one jet together with a muon in the final state. The large mass of b-flavoured hadrons is exploited to identify events containing beauty quarks on a statistical basis. Single and double differential cross sections are measured in deep inelastic scattering, with photon virtualities 3.5 < Q2 < 100 GeV2. The results are compared to perturbative QCD calculations. The next-to-leading order prediction is 1.8σ below the measurement. The deficiencies of the pre- diction are found in the forward direction of the muon, which is defined by the direction of the proton beam, and at low transverse momenta of the muon and jet. The leading-order predictions, which are augmented by parton showers, describe the shape of the measurements very well, but not the normalization. The predictions are about a factor two too low, which is compatible with the next-to-leading order prediction. Kurzfassung Eine Messung des Wirkungsquerschnittes für beauty-Quark Produktion in ep-Kollisionen bei einer Schwerpunktsenergie von 319 GeV wird vorgestellt. Die Daten wurden mit dem H1-Detektor am HERA-Beschleuniger in den Jahren 2005-2007 aufgezeichnet und entsprechen einer integrierten Luminosität von 285 pb−1. Für die Auswahl der Ereignisse wird mindestens ein Jet zusammen mit einem Myon verlangt. Die große Masse von Hadronen mit beauty-Quarks wird ausgenutzt, um Ereignisse mit beauty-Quarks auf einer statistischen Weise zu identifizieren. Einfach- und doppelt-differentielle Wirkungsquerschnitte wer- den in tief-inelastischer Streuung gemessen, mit Photonvirtualitäten 3, 5 < Q2 < 100 GeV2. Die Ergebnisse werden mit perturbativen QCD Berechnungen ver- glichen. Die Vorhersage in nächst führender Ordnung ist 1, 8σ niedriger als die Messung. Die niedrigeren Werte der Vorhersage werden in Vorwärtsrichtung für das Myon, welche gegeben ist durch die Richtung des Protonstrahls, und bei niedrigen Transversalimpulsen für das Myon und den Jet gemessen. Die Vorher- sagen in führender Ordnung, ergänzt durch Partonenschauer, beschreiben die Form der Messungen sehr gut, nicht jedoch die Normierung. Die Vorhersagen sind ungefähr einen Faktor zwei zu niedrig, was kompatibel ist mit der Vorher- sage in nächst führender Ordnung. Contents Contents 6 1 Heavy Flavour Production at HERA 13 1.1 Kinematics of High-Energy ep Scattering . . . . . . . . . . . . . . . 13 1.2 Quark Parton Model and Proton Structure Functions . . . . . . . . 14 1.3 Quantum Chromo Dynamics (QCD) . . . . . . . . . . . . . . . . . . 15 1.4 QCD Improved Parton Model . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 Parton Evolution Models . . . . . . . . . . . . . . . . . . . . 20 1.5 Heavy Quark Production . . . . . . . . . . . . . . . . . . . . . . . . 22 1.6 Parton Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.7 Charm and Beauty Hadrons . . . . . . . . . . . . . . . . . . . . . . . 25 1.8 Monte Carlo Event Generators . . . . . . . . . . . . . . . . . . . . . 26 1.9 NLO Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2 The Experiment 29 2.1 HERA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 H1 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3 Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.1 Central Silicon Tracker (CST) . . . . . . . . . . . . . . . . . . 35 2.3.2 Central Proportional Chamber (CIP) . . . . . . . . . . . . . 35 2.3.3 Central Jet Chamber (CJC) . . . . . . . . . . . . . . . . . . . 36 2.3.4 Outer Z Chamber . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3.5 Forward Tracker . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.4.1 Liquid Argon Calorimeter (LAr) . . . . . . . . . . . . . . . . 37 2.4.2 SpaCal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5 Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.6 Luminosity Measurement . . . . . . . . . . . . . . . . . . . . . . . . 41 2.7 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.7.1 Level 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.7.2 Level 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6 2.7.3 Level 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.7.4 Level 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3 Previous Experimental Results 45 3.1 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Measurements at HERA . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.1 Photoproduction . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.2 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . 50 3.2.3 Fixed Target . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3 Measurements at Other Colliders . . . . . . . . . . . . . . . . . . . . 54 3.3.1 pp̄ Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.3.2 γγ Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4 Event Reconstruction 59 4.1 Identification and Reconstruction of the Scattered Lepton . . . . . . 59 4.2 Identification and Reconstruction of the Muon . . . . . . . . . . . . 60 4.2.1 Track Reconstruction in the Inner Drift Chambers . . . . . . 60 4.2.2 Track Reconstruction in the Instrumented Iron . . . . . . . . 60 4.3 Reconstruction of the Hadronic Final State . . . . . . . . . . . . . . 61 4.3.1 Selection of Input Objects . . . . . . . . . . . . . . . . . . . . 61 4.3.2 Hadroo2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 62 4.3.3 Treatment of Calorimetric Energy Deposition for Muons . . . 62 4.4 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4.1 Longitudinally Invariant kT -Clustering Algorithm . . . . . . . 64 4.4.2 Jets in the Breit Frame . . . . . . . . . . . . . . . . . . . . . 65 4.5 Kinematic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5 Event Selection 69 5.1 Data Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.1.1 Run Selection and Detector Status . . . . . . . . . . . . . . . 70 5.1.2 Trigger selection . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.2 Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.2.1 Background Sources . . . . . . . . . . . . . . . . . . . . . . . 72 5.3 Z Vertex Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.4 Selection of DIS Events . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5 Selection of Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.5.1 Muon Identification Efficiency . . . . . . . . . . . . . . . . . . 86 5.6 Selection of Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.7 Summary of the Selection . . . . . . . . . . . . . . . . . . . . . . . . 89 6 Measurement 93 6.1 Cross Section Definition . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.2 Cross Section Determination . . . . . . . . . . . . . . . . . . . . . . 93 6.3 Measurement of Beauty Fractions . . . . . . . . . . . . . . . . . . . . 94 6.3.1 Relative Transverse Momentum . . . . . . . . . . . . . . . . . 95 6.3.2 Binned Likelihood Fit . . . . . . . . . . . . . . . . . . . . . . 96 6.3.3 Fit Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.4 Efficiency and Acceptance Corrections . . . . . . . . . . . . . . . . . 103 6.5 QED Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.6 Systematic Uncertainties and Cross Checks . . . . . . . . . . . . . . 106 6.6.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . 106 6.6.2 Cross Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7 Results 115 7.1 Theoretical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.2 Total Visible Cross Section . . . . . . . . . . . . . . . . . . . . . . . 116 7.3 Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . 117 7.3.1 Comparison to NLO Prediction . . . . . . . . . . . . . . . . . 117 7.3.2 Comparison to Monte Carlo Prediction . . . . . . . . . . . . 121 7.4 Double Differential Cross Sections . . . . . . . . . . . . . . . . . . . 124 7.4.1 Comparison to NLO Predictions . . . . . . . . . . . . . . . . 124 7.4.2 Comparison to Monte Carlo Predictions . . . . . . . . . . . . 127 7.5 Analysis in the Breit Frame . . . . . . . . . . . . . . . . . . . . . . . 129 8 Summary and Discussion of the Results 133 9 Outlook 139 A Run Selection 141 B Transformation to the Breit Frame 143 C Cross Section Tables 145 D Level 1 Z-Vertex Trigger 155 D.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 D.1.1 Fast Track Trigger . . . . . . . . . . . . . . . . . . . . . . . . 156 D.1.2 Z Vertex Trigger . . . . . . . . . . . . . . . . . . . . . . . . . 159 D.2 Data Flow and Hardware . . . . . . . . . . . . . . . . . . . . . . . . 161 D.2.1 Front End Modules and Multipurpose Processing Boards . . 162 D.2.2 Key Technologies . . . . . . . . . . . . . . . . . . . . . . . . . 163 D.3 Implementation of the Z Vertex Trigger . . . . . . . . . . . . . . . . 167 D.3.1 VHDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 D.3.2 Hit finding and Z Measurement . . . . . . . . . . . . . . . . . 167 D.3.3 Segment Finding . . . . . . . . . . . . . . . . . . . . . . . . . 170 D.3.4 Merging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 D.3.5 Linking and Trigger Decision . . . . . . . . . . . . . . . . . . 174 D.3.6 Trigger Element Generator Unit . . . . . . . . . . . . . . . . 177 D.3.7 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 D.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 D.4.1 Cosmic Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 D.4.2 Luminosity Runs . . . . . . . . . . . . . . . . . . . . . . . . . 178 List of Figures 185 List of Tables 189 References 191 Danksagung 199 9 10 Introduction Quantum Chromo Dynamics (QCD) describes one of the fundamental forces of na- ture, the strong force. The study of the production of heavy quarks at the electron proton collider HERA gives insight into various aspects of QCD, both at the short distances where perturbative calculations are possible (perturbative regime), and at larger distances where only phenomenological approaches exist (non-perturbative regime). The large masses of heavy quarks set an energy scale, where perturbative QCD is expected to give reliable predictions. This holds true in particular for the production of beauty quarks which have a mass of about 5 GeV. In this thesis open beauty production is studied in the region of deep inelastic scat- tering (DIS) in the range 3.5 < Q2 < 100 GeV2, where Q2 is the virtuality of the exchanged photon. A muon from a semi leptonic heavy quark decay and a jet are required in the final state. The momentum of the original quark, which is not visible in the final state directly, can be approximated by the energy and direction of the observed jet. The fraction of beauty events of the data sample is determined on a statistical basis, using the large momentum of the muon with respect to the jet axis (prelt ) for beauty quarks. In comparison to the photoproduction regime (Q2 ≈ 0 GeV2), the cross section and therefore the statistics of the data sample is small in the DIS regime. On the other hand the structure of the photon is not important for the DIS regime, which helps to reduce the uncertainties of theoretical predictions. Q2 provides an additional hard scale apart from the jet transverse momentum and the quark mass. This allows a study of the multiscale problem: the QCD predictions may become unreliable if several hard scales are present due to large coefficients in the perturbation series. In this thesis differential cross sections as a function of different observables are compared to theory predictions. These are available in the form of next-to-leading order calculations of the hard matrix element with respect to αs, the coupling con- stant of the strong interaction. Full event generators perform the calculation in leading order, and the long distance, non perturbative regime is modelled using phenomenological approaches. For a further investigation of the interesting regions of phase space where deviations to the predicitons are observed double-differential cross sections are determined. In the region of phase space investigated in this analysis, both the transverse mo- mentum of the jet and √ Q2 are comparable to the beauty quark mass. Therefore the calculations in the massive scheme are expected to give reliable results. In this 11 scheme the beauty and charm quark are not treated as active flavours inside the proton, but are produced in the hard interaction process (boson-gluon fusion). This process is sensitive to the gluon density of the proton which can be determined from the scaling violations of the inclusive cross sections. Using information gained on the gluon density, predictions of heavy quark production become possible. In this thesis direct measurements of heavy quark production are made thus providing a test of such predictions. This thesis is organized as follows: Chapter 1 gives a theoretical introduction to heavy quark production at HERA. In Chapter 2 the H1 detector and the relevant subdetectors are introduced. In Chapter 3 an overview of experimental methods and previous measurements at HERA and elsewhere is given. The explanation if the experimental work of this thesis starts with Chapter 4, where the event reconstruction is discussed in detail. In Chapter 5 the selection of the event samples, in both data and Monte Carlo, is presented, followed by a discussion of the beauty quark measurement in Chapter 6. Here the prelt method, which is used to obtain the beauty fraction of the data sample together with all correction factors applied to the data to obtain the cross sections as well as systematic studies are discussed in detail. In Chapter 7 the results are presented: the total visible cross section for beauty quark production, differential and double differential cross sections as a function of different observables compared to next-to-leading order calculations and two differ- ent Monte Carlo predictions. In Chapter 8 the summary of the results is given. Some results are compared to other measurements and discussed in a more general context. The presentation of the analysis is concluded with Chapter 9 where an outlook is given and some potential improvements of the measurement are discussed. In Appendix D a topic not related to the analysis but part of the work done for this thesis is discussed. A z vertex trigger based on drift chamber signals was implemented as a part of the Fast Track Trigger (FTT) upgrade project of the H1 experiment. The principle and implementation of this trigger and the results thereof are discussed. 12 Chapter 1 Heavy Flavour Production at HERA 1.1 Kinematics of High-Energy ep Scattering The scattering process ep → lX (1.1) is described by the exchange of a virtual gauge boson as illustrated in figure 1.1. For this thesis only the neutral current process ep → eX is relevant where a virtual photon or Z boson is exchanged. The exchange of virtual W bosons leads to the charged current process ep → νeX with a neutrino in the final state. The photon virtuality Q2 is given by the squared momentum transfer Q2 = −q2 = −(k − k′)2, (1.2) the squared centre-of-mass energy of the reaction is s = (p + k)2. (1.3) The relative energy transfer at the electron-boson vertex in the proton rest frame is given by y = p · q p · k , 0 ≤ y ≤ 1, (1.4) the Bjorken scaling variable as x = Q2 2p · q , 0 ≤ x ≤ 1. (1.5) The Bjorken scaling variable can be interpreted as the fraction of the proton’s mo- mentum carried by the interacting quark in the infinite momentum frame. Neglect- ing the lepton and proton masses, these variables are related by the equation Q2 = x · y · s. (1.6) The phase space region of small momentum transfers (Q2 ≈ 0) is called photopro- duction, at H1 usually selected by the condition Q2 < 1 GeV2. The region of larger Q2 is referred to as deep inelastic scattering (DIS). 13 � ��� � ��� � ��� � � ���� Figure 1.1: Deep inelastic electron-proton scattering at HERA in the single boson exchange picture. For the neutral current process a photon or Z0 boson is exchanged, resulting in an final state electron. In the case of a charged current process a W boson is exchanged, resulting in an outgoing antineutrino. The four momenta are denoted in parantheses. 1.2 Quark Parton Model and Proton Structure Func- tions In the Quark Parton Model (QPM) picture [39, 61] the proton is made of quasi- free, non interacting particles, called partons, which can be identified as quarks. The double differential cross-section for electron proton scattering can then be de- scribed by the incoherent sum of electron parton scatterings d2σ dxdQ2 = 2πα2 xQ4 ( 1 + (1 − y)2 ) ∑ i e2i xqi(x). (1.7) The distribution function qi(x) gives the probability that the struck quark i carries the momentum fraction x of the proton. The momentum distribution xq(x) is called parton distribution function (PDF). The inelastic electron proton scattering cross-section is given by the general formula dσ ∼ Leμν W μν , (1.8) where Leμν is the tensor describing the leptonic current and W μν is the tensor de- scribing the hadronic current. For unpolarized neutral current scattering, neglecting parity violating effects due to the weak interaction, the hadronic tensor has the form W μν = W1 (−gμν ) + gμgν q2 + W2 m2 ( pμ − p · q q2 qμ ) ( pν − p · q q2 qν ) , (1.9) where W1 and W2 are structure functions and m is the proton mass. When ignoring mass terms and redefining the structure functions as F1 = W1 and F2 = (p · q)W2/m2, the double differential cross-section can be expressed as d2σ dx dQ2 = 4πα2s xQ4 ( xy2F1(x, Q 2) + (1 − y)F2(x, Q2) ) . (1.10) 14 In terms of F2 and the longitudinal structure function FL = F2 − 2xF1 the cross- section may also be written as d2σ dx dQ2 = 4πα2s xQ4 ( Y+F2(x, Q 2) − y2FL(x, Q2) ) , (1.11) where Y+ = 1 + (1 − y)2. The longitudinal structure function FL is related to the exchange of a longitudinally polarised photon. This contribution is kinematically suppressed due to the factor y2 and leads to sizeable effects only for large inelastic- ities. When compared to equation (1.7), the quark parton model predicts that the struc- ture function depends only on x and not on Q2: F2(x, Q 2) = F2(x) = ∑ i e2i xqi(x). (1.12) This effect, known as scaling, can be seen for x ∼ 0.1 for HERA and fixed target data, as shown in figure 1.2. Scaling violations become visible at low x, where F2 rises with increasing Q2. This can be interpreted by QCD (see section 1.3) due to the parton dynamics and the corresponding rise of the gluon density towards small x. 1.3 Quantum Chromo Dynamics (QCD) Quantum Chromo Dynamics is a non-Abelian gauge theory that describes the in- teractions between quarks and gluons. Quarks are spin-1/2 color charged particles building the hadronic matter. Massless spin-1 gluons are the mediators of the strong force between quarks. The interaction is based on a SU (3)c color symmetry group and three-fold color charges. The symmetry group allows for a rich interaction structure. The exchange quanta itself carry charge, which is the main difference to Quantum Electrodynamics (QED). Loop graphs (see figure 1.3), contributing to higher orders of the expansion of scattering amplitudes in αs, are divergent. QCD is a renormalizable field theory: to ensure finite results in all orders of the expansion in αs, a renormalized (redefined) coupling αs(μr) is defined, that depends on the renormalization scale μr. The leading order equation for the running coupling is αs(μr) = ( b0 ln( μ2r Λ2QCD ) )−1 , with b0 = 33 − 2nf 12π , (1.13) where nf is the number of active flavours. The scale parameter ΛQCD depends on the renormalization scheme and on the number of active flavours. It was determined experimentally for the M S scheme (see section 1.4) to be about 215 MeV [58]. The running coupling is shown in figure 1.4. For μr much larger than ΛQCD, the effective coupling is small and a perturbative description is applicable. This region of asymptotic freedom corresponds to the quark parton model picture of quasi-free quarks. For μr of the order of ΛQCD the strong binding force becomes important, which confines the quarks within hadrons (confinement). 15 HERA F2 0 1 2 3 4 5 1 10 10 2 10 3 10 4 10 5 F 2 em -l og 10 (x ) Q2(GeV2) ZEUS NLO QCD fit H1 PDF 2000 fit H1 94-00 H1 (prel.) 99/00 ZEUS 96/97 BCDMS E665 NMC x=6.32E-5 x=0.000102 x=0.000161 x=0.000253 x=0.0004 x=0.0005 x=0.000632 x=0.0008 x=0.0013 x=0.0021 x=0.0032 x=0.005 x=0.008 x=0.013 x=0.021 x=0.032 x=0.05 x=0.08 x=0.13 x=0.18 x=0.25 x=0.4 x=0.65 Figure 1.2: Proton structure function F2 for various fixed values of x, measured by H1, ZEUS and different fixed target experiments together with DGLAP-based fits. For better visibility an offset (− log x) is applied to each data point. 16 Figure 1.3: Virtual corrections to the gluon propagator: gluon loop (left) and fermion loop (right). 0.1 0.15 0.2 0.25 QCD αs(MZ) = 0.118 ± 0.003 HERA 10 100 ET jet (GeV) α s Figure 1.4: Running of the effective coupling constant αs as a function of the transverse jet energy. Shown is the combined H1 and ZEUS measurement and the QCD prediction [51]. 17 Figure 1.5: Diagrams contributing to O(αs) correction to the quark parton model by emission of gluons from the quark line (γ∗q → gg). For QCD Compton processes the gluon can either be emitted from the initial or final state quark. Figure 1.6: O(αs) boson gluon fusion process γ∗g → qq (BGF). 1.4 QCD Improved Parton Model In QCD the scaling of the structure functions is broken due to O(αs) corrections to the parton model result. Diagrams contributing to this corrections by emission of gluons from the quark line (γ∗q → qg) are shown in figure 1.5. Therefore in QCD the structure function is Q2 dependent and given by [59] F2(x, Q 2) = x ∑ q,q̄ e2q [ q0(x) + αs 2π ∫ 1 x dξ ξ q0(ξ) { Pqq ( x ξ ) ln Q2 κ2 + C ( x ξ )} + ... ] , (1.14) where C(x) is a calculable function and the splitting function Pqq is given in leading order by the equation1 Pqq(x) = 4 3 ( 1 + x2 (1 − x)+ + 3 2 δ(1 − x) ) . (1.15) 1This splitting function is always used inside an integral and is therefore a distribution. The plus description is used, the integral with any sufficiently smooth function f is ∫ 1 0 dx f (x) (1−x)+ =∫ 1 0 dx f (x)−f (1) 1−x and 1 (1−x)+ = 1 1−x for 0 ≤ x ≤ 1. The singularity for x → 1 is due to emissions of soft gluons. 18 The scaling is broken by logarithms of Q2/κ2, where κ is a cut-off that has to be introduced due to collinear divergencies, which arise when the gluon is emitted parallel to the quark. This problem is solved by absorbing these singularities into the quark distribution, which now becomes scale dependent: q(x, μ2f ) =q0(x) + αs 2π ∫ 1 x dξ ξ q0(ξ) ( Pqq( x ξ ) ln μ2f κ2 − Cq( x ξ ) ) + αs 2π ∫ 1 x dξ ξ g0(ξ) ( Pqg( x ξ ) ln μ2f κ2 + Cg( x ξ ) ) + ... (1.16) In this formula, O(αs) contributions from the process γ∗g → qq (see figure 1.6) are included and folded with the bare gluon distribution g0(x), where the corre- sponding splitting function is Pqg(x) = 1 2 ( x2 + (1 − x)2 + (1 − x)2 ) . (1.17) The factorization scale μf defines the scale where the singularities are contributed to the quark density which cannot be calculated perturbatively. The Wilson coeffi- cient functions Cq and Cg depend on the factorization and renormalization schemes, as the amount of finite contributions to the quark density is arbitrary. For the DIS factorization scheme the structure function F2 has the simple form F2(x, Q 2) = x ∑ q,q̄ e2q q(x, Q 2). (1.18) For the M S factorization scheme, where not all the gluon contribution is absorbed into the quark distribution, the structure function has the form F2(x, Q 2) =x ∑ q,q̄ e2q ∫ 1 x dξ ξ q(ξ, Q2) ( δ(1 − x ξ ) + αs 2π CM Sq ( x ξ ) + ... ) + x ∑ q,q̄ e2q ∫ 1 x dξ ξ g(ξ, Q2) ( αs 2π CM Sg ( x ξ ) + ... ) . (1.19) The coefficient functions are CM Sq (z) = δ(1 − z) + αs 2π C1q + ... (1.20) CM Sg (z) = αs 2π C1g (z) + ... , (1.21) with C1q (z) = 4 3 ( 4 ln(1 − z) − 3 2(1 − z)+ − (1 + z) ln(1 − z) − 1 + z2 1 − z ln z + 3 + 2z − ( π2 3 + 9 2 )δ(1 − z) ) , (1.22) 19 Figure 1.7: Gluon and valence quark densities of the proton as obtained from H1 and ZEUS fits. C1g (z) = 1 2 ( (z2 + (1 − z)2) ln( 1 − z z ) + 8z(1 − z) − 1 ) . (1.23) Equations (1.18) and (1.19) are based on the factorization theorem [52] which states that the cross-section for DIS may be written as the convolution of a hard scattering cross-section and a non-perturbative parton density. From fits to the measured F2 structure functions the parton density functions can be determined. The gluon and valence quark distributions as determined from H1 and ZEUS fits are shown in figure 1.7. The gluon density becomes important and exceeds the quark densities by far for the small x region. This is the reason for the observed scaling violations of the structure functions at low x. To compare the data measured in this analysis with theory predictions, sets of parton density functions are used that are based on global fits, provided by the CTEQ [89] group. 1.4.1 Parton Evolution Models The scale dependent parton densities discussed in the previous section include soft processes up to the factorization scale μf . They are not calculable by perturbative QCD, nevertheless QCD predicts the scale dependence. If the densities are measured at a scale μ0, an evolution to a scale μ > μ0 is possible. The variations of q(x, μ2) and g(x, μ2) with respect to ln μ2 are given by the DGLAP2 equations [25,57,67,68,91] ∂qi(x, μ2) ∂ ln μ2 = αs 2π ∫ 1 x dξ ξ ( qi(ξ, μ 2)Pqq(x/ξ) + g(ξ, μ 2)Pqg(x/ξ) ) (1.24) 2Dokshitzer, Gribov, Lipatov, Altarelli, Parisi 20 Figure 1.8: Illustration of the four different splitting functions used for the DGLAP equations. z denotes the longitudinal momentum fraction. and ∂g(x, μ2) ∂ ln μ2 = αs 2π ∫ 1 x dξ ξ (∑ i qi(ξ, μ 2)Pgq(x/ξ) + g(ξ, μ 2)Pgg(x/ξ) ) . (1.25) These equations depend on the splitting functions Pqq, Pgq, Pqg and Pgg, which are illustrated in figure 1.8. They give the probability for a parton j to emit a parton i with momentum pi = zpj. The DGLAP approach is based on resumming the leading αs ln(Q2/μ2) terms.3 This leading log approximation (LLA) requires a strong ordering in the transverse momenta of the emitted partons (see figure 1.9): μ2 < p2t,1 < p 2 t,2 < ... < p 2 t,n < Q 2. (1.26) This approach describes successfully the scaling violations of the structure functions observed at HERA down to the smallest accessible x. The DGLAP evolution is used to model parton showers for Monte Carlo programs (see section 1.8). The probability for evolving from a virtual mass scale t1 to t2 without resolvable branching is given by the ratio Δ(t2)/Δ(t1), where Δ(t) is the Sudakov form factor (for a deeper discussion see e.g. [54]). The CCFM4 approach [45, 46, 48, 95] is an alternative to the DGLAP approach. It is based on the angular ordering constraint, which is a property of QCD: in a cascade of gluon and quark emissions the angles of the emitted particles decrease when proceeding down one branch. An unintegrated kt dependent gluon density 3This resumming is achieved by replacing αs by the running coupling. 4Ciafaloni, Catani, Fiorani, Marchesini 21 Figure 1.9: Subsequently emitted gluons build a gluon ladder. For the DGLAP approach the emitted gluons are ordered in transverse momenta kt. A(xg, k2t , μ2F ) is used, allowing the partons entering the hard matrix element to be off-shell. The CCFM approach, also called kt factorization, is equivalent to the DGLAP approach, also called collinear factorization, for large Q2 and moderate x. This scheme avoids the problem of αs ln(1/x) terms of the DGLAP solution which becomes important for small x and might spoil the convergence of the perturbation series. 1.5 Heavy Quark Production The production of charm and beauty quark pairs at HERA is an ideal testing ground for QCD as the masses of these heavy quarks set a hard scale which allows the mea- surements to be compared to perturbative calculations. At scales of the charm mass mc ≈ 1.5 GeV and beauty mass mb ≈ 4.75 GeV the strong coupling constant αs gets so small that processes with further gluons involved are expected to be sufficiently suppressed. In the model described so far, only light quarks are considered. Several approaches exist to introduce beauty and charm quarks, they treat these quarks either as massless or massive: Massive Scheme As no charm or beauty density for the proton is assumed, this scheme is also called fixed flavour number scheme (FFNS). Heavy quarks are only produced per- turbatively in the hard interaction. The leading order (O(αs)) boson-gluon-fusion process and some next to leading order (O(α2s)) processes are shown in figure 1.10. The corresponding beauty structure function (the formalism is similar for charm quarks) is given by F b2 (x, Q 2) = 2 ∫ 1 x dz z xg3(x/z, μ 2)CF Fg (z, m 2 b /Q 2, μ2), (1.27) 22 Figure 1.10: Leading order (outer left) and next-to-leading order diagrams for heavy quark production in the massive scheme. where g3 is the gluon density for three light flavours, μ2 is the used scale (e.g. μ2 = m2b + p 2 tbb̄ ), and the massive fixed flavour coefficient function is given by CF Fg (z, m 2 b /Q 2, μ2) = αs(μ2) 2π e2b C 1,F F g (z, m 2 b /Q 2) + ... (1.28) For Q2 � m2b the gluon coefficient function is given by C1,F Fg (z, m 2 b /Q 2) = C1g + 1 2 ( z2 + (1 − z)2 ) ln( Q2 m2b ), (1.29) where C1g is the gluon coefficient function from the massless DGLAP formalism (equation (1.23)) and an additional term proportional to ln( Q 2 m2 b ) appears, represent- ing collinear gluon emissions from the heavy quarks. For Q2 � m2b , terms proportional to ( αs ln( Q2 m2 b ) )n , which are considered up to the order O(α2s), might spoil the convergence of the perturbation series. The same holds for terms proportional to ( αs ln( p2t m2 b ) )n for p2t � m2b . If p 2 t and Q 2 are not too large compared to m2b , this method is reliably applicable. This scheme is used for the theory predictions for this analyis. Massless Scheme In this scheme heavy quarks are considered as massless active flavours of the pro- ton by introducing heavy quark structure functions for scales larger than the heavy quark mass. Therefore this scheme is called zero-mass variable flavour num- ber scheme (ZM-VFNS). This results in a resummation of the terms representing collinear gluon radiations. The parton dynamics of heavy quarks can then be de- scribed by the DGLAP approach in a similar way as for the light quarks. The disadvantage is that the threshold behaviour for low Q2 can not be described prop- erly by this scheme. Some leading and next to leading order diagrams for this scheme are shown in figure 1.11. The variable flavour number scheme (VFNS) is a mixed scheme that interpo- lates between the VFNS and the FFNS approach with a correct threshold behaviour at low Q2 and heavy quark densities for large Q2. 23 Figure 1.11: Leading order (outer left) and next-to-leading order diagrams for heavy quark production in the massless scheme. 1.6 Parton Hadronization As a consequence of the colour confinement (see section 1.3), all experimental re- sults are derived from the observation of hadrons. The hadronization, also called fragmentation process, has to be modelled to allow the comparison to theoretical predictions. This process can be calculated perturbatively above a scale of ≈ 1 GeV. The evolution of a heavy quark from the factorization scale μf to this scale via sub- sequent gluon emissions and splittings is described in Monte Carlo simulations by the parton shower approach. The scale dependence of this evolution is described by the DGLAP evolution (see section 1.4). For the long distance, non perturbative part of the hadronization process different phenomenological models exist. For this analysis the string fragmentation model [28] is used. In this model strings are formed by qq̄ pairs and the colour field between them (see figure 1.12, left). The stored potential energy is proportional to the separation distance of the quarks. When this energy is large enough, the string breaks up and a new qq̄ pair is produced out of the vacuum. Gluons are incorporated into this mechanism by kinks in the strings. Finally the string fragments are combined to hadrons. The transverse momentum distribution is assumed to be Gaussian, the longitudinal momentum frac- tion z is given by the fragmentation function DhQ(z). The Lund fragmentation function [28], defined as DhQ(z) ∼ 1 z (1 − z)a exp(−bm2t /z), (1.30) is used as default for the Monte Carlo simulation for this analysis. Here mt is the transverse mass m2 + p2x + p 2 y of the hadron, and a and b are free parameters. For heavy quarks the Lund-Bowler [40] fragmentation function is used, which is a modification of equation (1.30). Another widely used fragmentation function is the Peterson fragmentation function [101], given by DhQ(z) ∼ 1/z (1 − 1/z − �Q/(1 − z))2 , (1.31) where �Q is a free parameter which is different for charm and beauty quarks, resulting in a harder fragmentation for beauty quarks. This means that beauty hadrons get 24 Mesons q q d is ta n c e time c d s u d u s D∗+ Κ0 Κ− Εc (1-z)z’Ec zEc (1-z)(1-z’)z’’Ec vacuum fluctuation until cut-off energy Figure 1.12: Illustration of the String Fragmentation model (left) and the Inde- pendent Fragmentation (right). on average a larger longitudinal momentum fraction of the initial parton. In this analysis this function is used for the systematic study of the fragmentation of heavy hadrons. A further fragmentation function is the Kartvelishvili fragmentation function [84], defined as DhQ(z) ∼ z α(1 − z). (1.32) The string fragmentation model is similar to the independent fragmentation [62] which is not used anymore. In this model the partons hadronize individually (see figure 1.12, right). For each transition the initial parton is combined with a quark from a vacuum fluctuation. The other quark pair continues the fragmentation process. This cascade is stopped when all the energy is used up. Another model which is not used for this analysis but mentioned for completeness is the cluster fragmentation model [116] where clusters form colour singlets which decay isotropically into hadron pairs. 1.7 Charm and Beauty Hadrons The most important properties of charm and beauty hadrons that can be exploited as experimental signatures on a statistical basis for heavy quark production are their large mass and lifetime (see section 3.1). The main properties of heavy hadrons are listed in table 1.1. The much smaller CKM (Cabbibo-Kobayashi-Maskawa) matrix element |Vcb| responsible for the decay b → cW − compared to the matrix element |Vcs| responsible for the decay c → sW + is the reason for the longer lifetime of beauty hadrons, which is about 1.6 ps, compared to 0.4-1 ps for charm hadrons [58]: |Vcb| = 0.0412 ± 0.0020 (1.33) |Vcs| = 0.224 ± 0.016 (1.34) This results in a larger decay length for beauty hadrons, where the lifetime effect is partially compensated by the larger Lorentz-boost of charm hadrons. Due to the 25 Hadron quark content lifetime [ps] cτ [μm] mass [GeV] D+ cd 1.051 ± 0.013 315 1869.3 ± 0.5 D0 cū 0.412 ± 0.003 123 1864.5 ± 0.5 D1s + cs̄ 0.490 ± 0.009 147 1968.5 ± 0.6 Λ+c ucd 0.200 ± 0.006 60 2284.9 ± 0.6 B+ ub 1.674 ± 0.018 502 5279.0 ± 0.5 D0 db̄ 1.542 ± 0.016 462 5279.4 ± 0.5 B0s sb̄ 1.461 ± 0.057 438 5369.6 ± 2.4 Λ0b udb 1.229 ± 0.080 368 5624 ± 9 Table 1.1: Lifetime, decay length and mass of some selected charm and beauty hadrons. � � � � � � � � � � � � � �� Figure 1.13: Diagrams for semi-leptonic decays of beauty quarks: direct (left) and the cascade decay via a charm quark (right). large beauty quark mass the semi-leptonic decay of beauty hadrons can be described by the spectator model [73,74], where the beauty quark decay is not affected by the light quarks (see figure 1.13). One can distinguish two modes for the decay B → μ X: for the direct process the beauty quark decays into cW and the W subsequently into a muon and neutrino. The branching ratio for this direct decay is about 10.6% [58]. For the indirect decay the charm quark decays further into sW , where the W decays into a muon and neutrino. In rare cases two muons can be produced as two W bosons appear in this indirect decay chain. The branching ratio for this indirect decay is about 8% [58]. Other decay chains as B → J/Ψ → μμ or B → τ X → μX′ have much smaller branching ratios. 1.8 Monte Carlo Event Generators Monte Carlo Generators provide an event-by-event prediction of the full hadronic final state. This is the input of detector simluations needed to study detector effects and to determine detector acceptances and efficiencies. Event generators model the underlying physics using several steps, based on the factorization theorem (see sec- tion 1.4). In figure 1.14 the different parts of an event generator are shown. All generators available at present calculate the hard matrix element in leading order αs. Higher order QCD effects are modelled by the simulation of parton showers before and after the hard interaction. These parton showers are based on parton evolution equations (see section 1.4.1), where a backward evolution from the hard 26 PS PS h a d ro n is a ti o n h a d ro n s ME p e Figure 1.14: Illustration of the perturbative and non perturbative processes imple- mented in Monte Calo generators: hard matrix element (ME), parton showers (PS) and the hadronization. matrix element to the proton is used for performance reasons. As the multi gluon emissions result in observable objects, event generators are in this sense superior to NLO predictions. For the hadronization part of the generators phenomenological fragmentation models (see section 1.6) are implemented. In addition hadron decays are modelled, e.g. semi-leptonic decays of heavy hadrons. After running the jet algo- rithm this hadron level prediction can be compared to data. For the determination of detector corrections this hadron level information is fed into detector simulations, usually based on the GEANT package [42], which provides particle tracking through the different subdetectors. Decays of long lived particles are simulated at this step. This simulation step is not part of the Monte Carlo generators and not discussed further. Finally the simulated data is subject to the same reconstruction as the data (see section 4). For this analysis the default event generator is RAPGAP [82], used for a full simu- lation and in a separate mode to produce beauty events via boson gluon fusion. In both cases the leading order calculation is performed in the massive scheme. The in- clusive mode includes a full simulation, including quark parton model and processes of the order αs, like boson gluon fusion and QCD Compton. Higher order QCD effects are modelled using the DGLAP approach for the initial and final state par- ton showers. Hadronization and particle decays are implemented using the JETSET part of the PYTHIA code [109–112]. The hadronization is modelled using the Lund string fragmentation, where for heavy quarks the Peterson fragmentation function can be used. RAPGAP is interfaced to the HERACLES program [88], which simu- 27 lates QED radiative corrections. It generates the eγ∗e vertex, including real photon emission from the incoming and outgoing electron and virtual corrections. By in- corporating these corrections at this level large correction factors on reconstruction level for the DIS kinematic variables x, Q2 and y can be avoided. As an alternative, the Monte Carlo generator CASCADE [81, 83] is used. This pro- gram generates the boson gluon fusion process γ∗g∗ → qq̄ for light and heavy quarks using an unintegrated gluon density which is obtained from the measured structure function F2. This model has the advantage that the gluon entering the hard subpro- cess is allowed to carry a non zero transverse momentum. The backward evolution of the gluon density is based on the CCFM model, final state parton showers are modelled based on the DGLAP approach (see section 1.4.1). The hadronization pro- cess is again modelled by the JETSET routine. QED radiation is not implemented in CASCADE. Details about the Monte Carlo parameters used for the simulated samples and for the samples used for the comparison to the data can be found in section 5.2 and 7.1, respectively. 1.9 NLO Calculation The Monte Carlo integration program HVQDIS [69] provides the total and differ- ential cross sections for a number of variables for heavy quark production in deep inelastic scattering. The matrix element is calculated in next-to-leading order using the massive approach (see section 1.5) in the M S scheme (see section 1.4). The program provides two or three partons for the final state. To allow a comparison to data, an extended version of this program is used. The hadronization of beauty hadrons into beauty flavoured hadrons is modelled by rescaling the three-momentum of the quark using the Peterson fragmentation function. Semileptonic decays into a final state with a muon are modelled using the muon decay spectrum taken from JETSET [109–112]. Parton level jets are reconstructed by applying the kt algorithm (section 4.4.1) to the outgoing partons. A comparison to data at hadron level re- quires a correction to the hadron level using a Monte Carlo generator like RAPGAP. This is explained in section 7. The main theoretical uncertainties of the NLO calcu- lation arise from the uncertainty of the beauty quark mass and the renormalization and factorization scales (see section 7). 28 Chapter 2 The Experiment 2.1 HERA Two accelerators, one for electrons or positrons and one for protons, are housed in a common ring tunnel of 6.3 km circumference. This HERA collider, the preaccel- erators and the location of the four interaction regions are illustrated in figure 2.1, left. The proton ring is equipped with 422 dipole magnets, 224 main quadrupole magnets, 400 correction quadrupoles, 200 correction dipoles, all superconducting. About 100 mA of protons were injected at an energy of 40 GeV and accelerated up to 920 GeV. The magnetic field for the proton ring was 5.1 Tesla for the nominal beam energy produced by a current of 5500 A for the dipoles. The electron ring consists of more than 1000 normal conducting dipole magnets. The injection energy was 12 GeV, the lumi energy 27.5 GeV. The usual beam current was about 45 mA. A maximal longitudinal polarisation of 45% was achieved for the lepton beam using three spin rotator pairs. The lepton beam and proton beam consisted of up to 180 bunches, where each bunch contained about 1010 particles. The bunch length was about 8 mm for the leptons and, much longer, up to 20 − 30 cm for the protons. The revolution frequency was 47.3 kHz. Whereas the HERA B and HERMES experiments were using only the proton and lepton beam, respectively, the beams were brought to collison at the collider ex- periments H1 and ZEUS. Every 96 ns an intersection happened, which defined the HERA bunch crossing rate of 10.4 MHz. The luminosity is given by L = 1 4πe2f0nb IeIp σxσy , (2.1) where f0 is the revolution frequency, nb is the number of bunches, Ie and Ip are the electron and proton currents, and σx · σy is the spot size at the interaction point, with typical values of 118 μm · 31 μm. Typical parameters of the lepton and proton beams are summarized in table 2.1. After a shutdown and upgrade program to increase the luminosity, which included the installation of focussing magnets within the H1 and ZEUS detectors, luminosity 29 Hall North H1 Hall East HERMES Hall South ZEUS HERA Hall West HERA-B e p Volkspark Stadion 360m 360m R= 79 7m Trab rennb ahn day A c c u m u la te d b y H 1 [ p b -1 ] 0 100 200 300 0 40 80 120 160 2004 2005 2006 2007 Figure 2.1: HERA accelerator, preaccelerators and the four experiments H1, ZEUS, HERMES and HERA B and accumulated lumi for the H1 experiment for the years 2004-2007 1. Electron-Proton Positron-Proton Proton/Electron beam energy 920 GeV/27.6 GeV Proton/Electron beam currents 108 mA/41 mA 110 mA/44 mA Luminosity [cm−2s−1] 4.9 · 1031 4.0 · 1031 Specific luminosity [mA−2cm−2s−1] 2.4 · 1030 1.7 · 1030 Spot size σx × σy [μm2] 118 × 32 Table 2.1: Parameters of HERA II [53, 107] operation resumed in 2002 in the electron-proton mode. In July 2006 the operation switched to positron-proton mode. The accumulated luminosities for the different years are shown in figure 2.1, right. After dedicated low energy runs with a reduced proton beam energy to measure the longitudinal structure function FL, the HERA operation ended at the end of June 2007. 2.2 H1 Detector The H1 detector [11], which is currently being dismantled after the shutdown of HERA, was a complex detector consisting of several subdetectors which were ar- ranged in a shell structure around the interaction point at the center of the detector. It was optimized for new particle production, neutral current inclusive measurements 30 Detector Component Abbreviation Tracking Detectors 1 Forward Silicon Detector FST 2 Central Silicon Detector CST 3 Backward Silicon Detector BST 4 Central inner proportional chamber CIP 5 Central outer z drift chamber COZ 6 Inner central jet chamber CJC1 7 Outer central jet chamber CJC2 8 Backward proportional chamber BPC Calorimeters 9 Electromagnetic spaghetti calorimeter SpaCal em. 10 hadronic spaghetti calorimeter SpaCal hadr. 11 Liquid argon calorimeter (electromagnetic) LAr em. 12 Liquid argon calorimeter (hadronic) LAr hadr. Muon Detectors 13 Instrumented iron: Central Muon Detector CMD 14 Forward Muon Detector FMD Table 2.2: List of the main detector components of H1 (legend to figure 2.2). and charged current interactions. Therefore the detector covered the whole 4π solid angle with a higher instrumentation in the proton direction to account for the asym- metric beam energies. The main design decisions were the use of liquid argon as detector medium and lead/copper as absorber for the calorimeters and a coil outside the calorimeters. A drawing of the detector is shown in figure 2.2, the inner part is shown in figure 2.3. The proton beam direction defines the positive z-axis, the x − y plane is per- pendicular to this axis, with the x-axis pointing to the center of the ring and the y-axis downward. The nominal interaction point defines the origin of the coordinate system. The polar angle φ of a particle trajectory is defined in the x−y plane where φ = 0 defines the x-axis, the azimutal angle θ is defined with respect to the z-axis. The most inner detectors are tracking detectors used for identifying decay vertices, triggering and reconstruction of tracks. They are surrounded by calorimeters using liquid argon as active material for the measurements of particle energies. A lead- scintillator-fibre detector was used to identify the scattered electron in the backward direction. The superconducting magnet, which was outside the calorimeters, gener- ated a magnetic field of 1.15 Tesla which was needed for the momentum measurement of charged particles. The return yoke of the magnet was instrumented with limited streamer tubes used to detect muons that penetrate the calorimeters. In the forward direction the detector was instrumented with a forward muon detector, which is not used for this analysis. As part of the HERA II upgrade program many subdetectors and trigger systems were improved, this includes the Fast Track Trigger (FTT), which is used to trigger 31 Detector Component Abbreviation Tracking Detectors 2 Central Silicon Tracker CST 3 Central inner proportional chamber CIP 4 Inner central jet chamber CJC1 5 Central outer z drift chamber COZ 6 Central outer proportional chamber COP 7 Outer central jet chamber CJC2 8 CJC electronics 9 Forward tracking detector FTD 10 Superconducting quadrupole magnet GO 11 Forward tracker cables 12 Inner wall of LAr vacuum tank 13 Backward proportional chamber BPC 14 Electromagnetic spaghetti calorimeter SpaCal em. 15 Photomultipliers for SpaCal em. 16 Hadronic spaghetti calorimeter SpaCal hadr. 17 Photomultipliers for SpaCal hadr. 18 Superconducting quadrupole magnet GG Table 2.3: The main component of the central H1 tracker and backward calorime- ters (legend to figure 2.3). Shown is the 2005 configuration without forward and backward silicon detectors (FST, BST). In figure 2.3 ’1’ denotes the nominal inter- action point. events based on drift chamber information and a combination with other subdetec- tors. The FTT is discussed in more detail in section D. 2.3 Tracking System A radial view of the central tracking system is shown in figure 2.4. The sub-detector closest to the interaction region is the Central Silicon Tracker (CST) used for precise measurements of charged particle tracks close to the event vertex. This detector is surrounded by the Central Inner Proportional Chamber (CIP) used for triggering. The most important tracking detectors are the inner and outer Central Jet cham- bers, CJC 1 and CJC 2, with the central outer z-chamber between them. They cover the angular range in 20◦ < θ < 160◦. In the forward direction the Forward Tracking Detector FTD delivers track infor- mation in the angular range 5◦ < θ < 25◦. The CST is supplemented by silicon detectors in the forward and backward region, the FST and BST, which were only operational for a fraction of the HERA II period due to repair work. The Backward Proportional Chamber BPC refines the measurement of the scattered electron of the backward calorimeter. 32 52 02 5 3 4 1 2 7 1 4 0 1 5 1 1 6 0 1 7 1 1 1 5 63 2 1 7 4 5 8 e le c tr o n s p ro to n s 9 1 2 1 3 1 4 1 0 Figure 2.2: Technical drawing of the H1 detector after the luminosity upgrade. For the different subdetectors see table 2.2. 33 1 2 3 4 5 6 7 1 m 9 8 11 12 13 8 14 15 16 17 10 18 Figure 2.3: The inner part of the H1 detector, consisting of the central tracking system, the forward tracking system and backward calorimeter. The legend to the subdetectors is given in table 2.3. Not shown in this drawing are the forward and backward silicon detectors. 1 2 4 3 5 Figure 2.4: Radial view of the central tracking system at H1. Shown are from the inside to outside: CST (1), CIP (2), CJC1 (3), COZ (4), CJC2 (5). 34 rf -strips 25 µ m implant pitch 50 µ m readout pitch aluminium wire bonds carbon fiber rail APC128 amplifier and pipeline chip Ceramic Hybrid 221 mm 34 mm 4.4 mm 640 readout lines on 2nd metal layer z-strips 88 µ m pitch vias metal-1 to metal-2 n-side:p-side: Decoder chip CST Half Ladder Kapton cable Figure 2.5: Central silicon detector: elliptical arrangement of the two layers of strip sensors (left) and detailed view of the n and p side of the strip sensors (right). 2.3.1 Central Silicon Tracker (CST) The CST delivers precise vertex and track information by refining tracks recon- structed in CJC1 and CJC2. Several analyses use this data and exploit lifetime effects of heavy quarks (see section 3.1). For the analysis presented in this thesis this information is not used. This detector consists of double-sided strip sensors which are arranged in two layers around the beam pipe at a distance between 4 and 13 cm due to the elliptical beam pipe in this region for HERA II (see figure 2.3.1, left). The p side of the sensors has strips parallel to the z-axis and delivers information in the rφ plane, the n side measures the z coordinate. The p and n side of the ladders, made of six sensors each, are illustrated in figure 2.3.1, right. More detailed information on the CST and the two endcap parts (FST, BST) of the H1 silicon tracker can be found in [92]. 2.3.2 Central Proportional Chamber (CIP) The Central Inner Proportional Chamber (CIP) installed for HERA II is a multi- wire proportional chamber with wires parallel to the beam. 5 detector layers enclose the CST at radii between 15 and 20 cm. The chamber covers a range −112.7 < z < +104.3 cm and 11◦ < θ < 169◦. The 9600 readout pads are arranged in a projective geometry which results in the same pattern for tracks that origin from the same z position. The CIP2000 trigger searches for track patterns, builds a z-vertex histogram from the number of tracks pointing to the bins along the beamline, and evaluates the histogram. A fast trigger decision on Level 1 (see section 2.7) allows an early rejection of background events without introducing dead time for data taking. The trigger decision is based on the total number of entries in the histogram and the fraction of central to backward entries (CIP significance). A similar condition is used for the FTT z-vertex trigger (see section D). The fast response time of the detector also allows for a determination of time of the interaction (event t0). Details on the detector and the trigger can be found in [115]. 35 2.3.3 Central Jet Chamber (CJC) The Central Jet Chamber is a drift chamber made of two parts, the inner chamber CJC1 that encloses the CIP at an inner radius of 20.3 cm and the outer chamber CJC2 with an outer radius of 84.4 cm. An angular range 20◦ < θ < 160◦ is covered, defined by the acceptance of the CJC2. The inner (outer) chamber is divided in 30 (60) cells, which are tilted with respect to the radial direction. This ensures that high momentum tracks cross the cell boundaries and can be measured within 2 cells. Each cell of CJC1 (CJC2) contains 24 (32) sense wires. The actual positions of these wires are shifted by an amount of ±150 μm (staggering). The hit position is measured using the drift time of charges to these signal wires (determined in a Qt-analysis of the pulse shape, see section D.3.2), drift velocity and the exact wire position. An ambiguity appears as it is not known from which side the charges drift to the wire resulting in the reconstruction of mirror hits. This left-right ambiguity can be resolved due to the crossing of cell boundaries and the staggering of the sense wires. The single hit resolution in the rφ-plane is about 140 μm, in the z plane only about 22 mm are achieved. The CJC is the main detector component that provides the data (hit information) used for the reconstruction of tracks in the central detector region. The reconstruc- tion algorithm delivers helix parameters of bent tracks due to the magnetic field, which is a measurement of the transverse momentum of the corresponding particle. The principle is described in some more detail in section 4.2 in the context of the muon track reconstruction. A fraction of the signal wires deliver information for the Fast Track Trigger (FTT), which is described in some more detail in section D. 2.3.4 Outer Z Chamber The Central Outer Z Chamber (COZ) is a drift chamber with wires strung perpen- dicular to the z-axis. It is used to improve the poor z measurement of the CJC and achieved a resolution of about 350 μm. This chamber is installed between the inner and outer jet chambers CJC1 and CJC2 and covers the angular range 25◦ < θ < 155◦. The thickness of the chamber is 1.5% X0, where X0 is the radiation length. Energy losses and photon conversions between the jet chambers have to be taken into account for the track reconstruction algorithm. 2.3.5 Forward Tracker An additional tracking system (Forward Tracking Detector, FTD) to identify charged particles is installed in the forward direction. This allows the measurement of heavy quark production for large Q2 and x, where the hadronic final state is produced in the forward direction. The detector is designed to detect tracks in the angular range 5◦ < θ < 25◦ from the interaction point and was upgraded for HERA II. It consists of three supermodules, where the inner two supermodules (with respect to the interaction point) contain five planar chambers (the three inner denoted as P type, the two outer as Q type). 36 Figure 2.6: r-z view of the upper half of the Liquid Argon Calorimeter. The parts denoted with “E“ belong to the electromagnetic section, the parts denoted with “H” belong to the hadronic section. The different orientation of the absorber plates for the different wheels is visible. The outer supermodule has only one module of type Q. The drift cells for the P chambers have four wires each, which are rotated with respect to the y-axis for an amount of 0◦, +60◦ and −60◦. The cells for the Q type have 8 wires each at angles of +30◦ and +90◦. The identification of tracks in the FTD starts with a search for clusters, which are groups of three or four hits consistent with a straight line, in each of the planar chambers. A cluster defines a plane in space containing the path of the particle. The combination of two planes defines a line segment on the particle’s path. A third plane is required to resolve ambiguities due to many different com- binations of two planes if several particles pass the chamber. These segments from different submodules are combined to forward tracks. It is also possible to combine these forward tracks with tracks from the central drift chamber CJC for the overlap region. 2.4 Calorimetry 2.4.1 Liquid Argon Calorimeter (LAr) The Liquid Argon Calorimeter (LAr) (figure 2.6) covers the forward and central region of the H1 Detector in the angular range 4◦ < θ < 153◦. The electromagnetic section (ECAL) measures electromagnetic showers using lead absorbers. Hadronic showers which penetrate into the hadronic part (HCAL) are measured using steel absorbers. In both cases the active material is liquid argon, therefore the whole calorimeter is contained in a cryostat. The calorimeter is divided into eight wheels made of eight octants each. The orientation of the absorber plates is such that par- ticles from the interaction point impinge with an angle larger than 45◦. The electro- magnetic section of the calorimeter has a resolution of σE /E ≈ 11% √ E/GeV ⊕ 1%, the hadronic section has a resolution of σE/E ≈ 50% √ E/GeV ⊕ 2%. The calorime- 37 Figure 2.7: Illustation of the electromagnetic SpaCal: each module, indicated by the thick lines, consists of eight submodules (thin lines). ter is of non compensating type, which means that the response for electromagnetic particles is higher than for hadrons. The compensation is obtained using offline algorithms. 2.4.2 SpaCal The backward region of H1 is instrumented with a lead-scintillating fibre Spaghetti Calorimeter (SpaCal). It has a diameter of 160 cm and consists of an electromag- netic (see figure 2.7) and a hadronic section. The electromagnetic section consists of about 1150 quadratic lead absorber cells with scintillating fibres, pairwise arranged in submodules, where eight submodules build a module. The cells have an active volume of 4 × 4 × 25 cm3. The thick- ness corresponds to 27.5 radiation lengths which ensures an only small leakage of the deposited electromagnetic energy to the hadronic section. The fibres with 0.5 mm diameter direct the light through light mixers to photomultiplier tubes (PMT), where the scintillation light is converted into an electrical pulse and amplified. This calorimeter is used to measure the scattered electron in the backward direction, with an energy resolution σE/E ≈ 7% √ E/GeV ⊕ 1%, and the polar angle of the scat- tered electron can be measured with a resolution of about 2 mrad. In addition this detector is used to trigger on the scattered electron and as a veto to suppress beam gas due to the precise timing information with a resolution of 1 ns. 38 604 606 10 c m 2 cm 404 405 504 605 506406 40.5 mm 81 m m Figure 2.8: Inner SpaCal region: the circle shows the new SpaCal hole, which has a radius of 10 cm. The origin is shifted with respect to the origin of the H1 coordinate system. The hadronic section of the SpaCal has a similar structure with larger cells of di- mension 12 × 12 × 25 cm3. The cell depth corresponds to one interaction length. This calorimeter is used as a veto against hadrons. The installation of the focussing at H1 for the HERA II upgrade required modi- fications of the inner spacal region. In order to have space for the new elliptical beam pipe, the radius of the spacal hole was extended 10 cm, where the center is shifted with respect to the center of the H1 coordinate system (see figure 2.8). The angular coverage is reduced to 153◦ < θ < 173◦, the acceptance in Q2 is reduced to ≈ 4 < Q2 < 100 GeV2. 2.5 Muon System The return yoke of the solenoid magnet is instrumented with limited streamer tubes to measure tracks of muons that penetrate the calorimeters. This Central Muon Detector (CMD) is divided into four parts: forward endcap (4◦ < θ < 35◦), backward endcap (130◦ < θ < 171◦), and the barrel region (35◦ < θ < 130◦), made of the backward and forward barrel. The backward barrel region is not used for the analysis presented in this thesis. Each of these parts consists of 16 modules (see figure 2.9). About 103 000 limited streamer tubes with a cross section of 1 × 1 cm2 are mounted in the slits between the ten iron plates with a thickness of 7.5 cm, where the slits are on average 2.5 cm wide. Three additional layers of streamer tubes are mounted on the inner and outer surface of the return yoke. The wires are strung parallel (perpendicular) to the beam axis for the barrel (endcap) region. Influence charges 39 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6362 X Y Z 32 33 34 3536 37 38 39 40 41 42 43 44 45 46 47 X Y Z 16 17 18 1920 21 22 23 24 25 26 27 28 29 30 31 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1514 magnet coil backward endcap forward endcapbackward barrel forward barrel Figure 2.9: Illustration of the four parts of the Central Muon Detector. Each part consists of 16 modules. ��� ��� ��� ��� �������� ������������������������������ ���� ���� ���� ���� z y x h i �������������� 23 24 28 27 2629 30 25 31 g 16 17 18 21 19 20 22 Strips Strips and Pads Pads Iron ds layers with pads layers with pads layers with strips layers with strips layers with strips 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 50 mm 25 mm 75 mm Figure 2.10: Cross section view of an instrumented iron module. 40 are induced and measured at electrodes mounted at the top side of the chambers. These electrodes are either strips with a width of 17 mm and 3 mm spacing or pads with a size of 25 × 25 cm2 in the endcaps and 50 × 40 cm2 in the barrel. The instrumentation of the different layers of a module is shown in figure 2.10. Wires and strips are read out digitally and allow for a two-dimensional space measurement. Five layers (3,4,5,8 and 12) are used in addition for trigger purposes. The momentum resolution of the CMD is only about 30%. Therefore for this analysis the muon system is only used to identify muons, the momentum measurement is provided by the tracking system. The tracks from the muon system (iron tracks) are combined with the inner tracks from the tracking system (see section 4.2). 2.6 Luminosity Measurement The rate at which the Bethe-Heitler process ep → epγ [37] occurs, is used to measure the luminosity. This process has a large and well known cross section, calculable in Quantum Electro Dynamics (QED). The photons of this process are detected at small angles by a quartz-fibre calorimeter with tungsten absorber located at z=-103 m. A beryllium filter shields the detector against synchrotron radiation background induced by the focusing magnets. The main uncertainty of the measurement is the acceptance of the photon detector. The offline measurement for the HERA II running period is not fully understood when writing this thesis. Therefore an averaged uncertainty of about 4% is assumed for the data period analysed in this thesis, which is higher than the uncertainty for HERA I, which is about 2%. 2.7 Trigger At the nominal bunch crossing rate of 10 MHz at HERA, electron proton scattering is expected to appear at a rate of several kHz. As the rate of background events (e.g. beam gas and beam wall events) is three orders of magnitude higher and the detector can only be read out at a rate of 50 Hz, a trigger system with a high selectivity is required which selects interesting physics events and rejects background event efficiently. At H1 a four level trigger system was used: the algorithms of the first three levels were running on custom made hardware. The readout of one event takes about 1.4 ms, during which the data taking is stopped. The optimisation goal to keep this dead time reasonably low (about 10%) defined the maximum rate at which the detector can be read out. The computing farm of standard PCs at level four reduced the rate further to about ten events per second which were fully reconstructed and written to tape. 2.7.1 Level 1 The first level trigger is the only trigger level that does not induce deadtime itself, as the data from the subdetectors is written to pipelines and the data taking continues during the calculation of the trigger decision. In total 256 Trigger Elements (TEs) 41 are formed, based on track signals of the muon system and the central tracker and energy depositions in the calorimeters. These TEs are forwarded to the Central Trigger Logic (CTL) where they are combined to up to 192 Subtriggers (STs). Only if a subtrigger condition is fulfilled, the pipelines are stopped and the dead time starts. In order to limit the output rate of this trigger level to the predefined target rate and to make best use of the available bandwidth, subtriggers are prescaled, i.e. scaled down.2 Therefore some subtriggers “see” only a fraction of the luminosity. This is not the case for the subtrigger relevant for the analysis presented in this thesis. Subdetectors with precise timing information (SpaCal and CIP) deliver t0 trigger signals, which define the bunch crossing of the triggered interaction and mark there- fore the positions in the pipelines that has to be read out by the subdetectors. 2.7.2 Level 2 After a positive level 1 decision dead time is accumulated as the pipelines are stopped. The level 1 decision is validated using three trigger systems: the topo- logical trigger and the neural network trigger combine information from trackers, calorimeters and the muon system. The FTT refines the level decision and reaches a track resolution comparable to the offline reconstruction. The total time available for the level 2 decision is 20 μs. 96 trigger elements are forwarded to the Central Trigger Logic and combined. If no level one trigger could be validated by level two, the data taking resumes, otherwise the readout of the detector begins. Many level one triggers did not have level two conditions and were validated by default. 2.7.3 Level 3 The readout started after a positive level two decision with an average readout time of 1.3 ms per event. This time could be much larger, depending on the event size. The level 3 trigger, which was part of the FTT system (see section D), could stop the readout after 100 μs and therefore reduce the deadtime of the detector. The level 3 system performed a partial event reconstruction based on level two track information on commercial processors. In addition information from the muon system and calorimeter information is used. 48 trigger elements are provided to the Central Trigger Logic, which rejects the event if no trigger element could be validated, where some subtriggers with no level 3 condition are validated by default. The level 3 system must ensure a maximum output rate of about 50 Hz. 2.7.4 Level 4 After readout the full event information was assembled at the event builder. The full event reconstruction was performed at a PC farm, followed by an event classification. 2Events are rejected in a deterministic way: for subtriggers with prescale factor n only each n-th positive decision is taken into account. 42 Based on this decision events which fall into one of the event classes and in addition a fraction of rejected events were stored with a rate of about 10-20 Hz. 43 44 Chapter 3 Previous Experimental Results In this section an experimental review about beauty quark production at HERA and elsewhere is given. After a short introduction of the experimental methods used for the measurements at the HERA experiments, the results are discussed for the photoproduction and the DIS region. This is complemented by a discussion of measurements at other colliders. A discussion of charm quark production can be found in [33]. 3.1 Experimental Methods The different taggig methods used at H1 and ZEUS to select heavy flavour enriched samples are illustrated in figure 3.1. A full reconstruction of heavy flavoured hadrons is only done for charmed hadrons, where e.g. the golden decay channel (D∗+ → D0π+s → (K−π+)π+s ) is used. For beauty hadrons, no similar decay channel without neutral particles and large enough branching ratios exists. Instead usually a lepton tag is used. The muons and electrons from semileptonic decays of beauty hadrons have large enough momenta and can therefore be well reconstructed. For the muon+jet analyses, jets are required in addition to the lepton (dijets for the photoproduction region and only one jets due to the lower statistics for the DIS region). The jets estimate the quark direction. This information is needed to determine the fraction of beauty events on a statistical basis using the prelt tag. prelt is the relative transverse momentum of the lepton with respect to the jet axis. The large mass of beauty hadrons is exploited which results in large values of prelt . An event display of a dijet event with an identified muon is shown in figure 3.2. Figure 3.3 shows the prelt distributions used for the first H1 measurement [10], the H1 measurement using the full HERA 1 statistics [8], and for the analysis presented in this thesis. In [8] the prelt tag is combined with a lifetime tag which exploits the long lifetime of beauty hadrons. The signed impact parameter distribution δ of a track is defined as the shortest distance to the primary event vertex. To define a signed impact parameter the jet axis is needed. In figure 3.4 the δ distribution for the muon track is shown. The position of the muon track at the primary vertex is measured 45 Figure 3.1: Tagging methods used at H1 and ZEUS to select heavy flavour enriched samples (from [33]). Figure 3.2: Event display of a dijet event with an muon identified in the Central Muon Detector. 46 0 1 2 3 4 5 0 40 80 120 160 H1 Data Fit b contrib. c contrib. fake muons M uo ns / 0 .2 G eV pμ [GeV] T,rel 20 40 60 80 100 120 0 1 2 3 p rel t [ GeV ] E n tr ie s Data bb − cc − uds Sum H1 2 < Q2 < 100 GeV2 rel t p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 0 200 400 600 800 1000 1200 1400 1600 b MC c+uds MC sum MC Data [GeV] Figure 3.3: P relt distribution from the first H1 measurement [10] based on 7 pb −1 from 1996 photoproduction data (upper left plot), from the measurement [8], based on about 50 pb−1 of DIS data recorded in 1999/2000 (upper right plot) and from the measurement presented in this thesis, based on about 285 pb−1 HERA II data (lower plot). The upper right and lower plot show the distribution for electroproduction data. The increased statistics of the 1999/2000 data and the HERA II data allow the measurement of differential cross sections and double differential cross sections, respectively. 47 1 10 10 2 -0.05 0 0.05 0.1 Impact Parameter δ [ cm ] E n tr ie s Data bb − cc − uds Sum H1 2 < Q2 < 100 GeV2 Figure 3.4: δ distribution of the muon track, which is defined as the distance to the primary vertex, for the DIS sample of the H1 muon+jet analysis [8]. using the innermost tracking detector, the Central Silicon Tracker (see section 2.3.1). This additional information allows a separation of light flavour, charm and beauty events on a statistical basis. This is not possible when using prelt alone, as the light flavour and charm quark distributions are very similar. The main disadvantage of methods using jets is the lower energy cut at about 5 GeV, which is necessary to reconstruct a stable jet axis. This cut limits the measured range of the beauty quark transverse momentum. A measurement at threshold is possible when requiring a second heavy quark tag besides the muon, either a D∗ or a second muon. For the D∗ analyses [9, 18] the charm and beauty content of the sample can be disentangled on a statistical basis using charge and angular correlations (see figure 3.5). For the dimuon analyses [50] it is exploited that for the beauty signal there are significantly more muon pairs with unlike-sign charges. This method has the advantage that low beauty quark momenta can be measured but the disadvantage of a low statistics data sample compared to other methods. An alternative method is the inclusive lifetime tagging method, based on the displaced impact parameter of tracks in dijet events [7, 63]. This method has the advantage that highest transverse jet momenta up to 35 GeV can be reached, because of the larger available statistics. 48 Figure 3.5: Possible production of a muon and a D∗ meson in a beauty quark event (from [33]). 3.2 Measurements at HERA Beauty production is measured at HERA in photoproduction and deep inelastic scattering by the collider experiments H1 and ZEUS using the different methods explained in the previous section and covering different kinematic regions. The largest statistics is available for the photoproduction region. In addition, beauty production was measured at the fixed target experiment HERA B. 3.2.1 Photoproduction In figure 3.6 a summary of ZEUS results, based on HERA I data, is shown. This includes the very recent results from the analysis using decays into electrons [17], an older measurement using the same method [22], the measurement using decays into muons [16, 19] and the D∗ muon measurement [18]. The measured cross sections with respect to the beauty quark momentum are compared to the NLO prediction. For the jet measurements the transverse quark momentum is given by the transverse jet momentum, the lowest momentum is accessible for the D∗ muon measurement. In [17] it is stated that “the measurements agree well with the previous values, giving a consistent picture of b-quark production in ep collisions in the photoproduction regime and are well reproduced by the NLO calculations”. The interesting region of low transverse momenta will be further explored by an H1 measurement at threshold using electrons and muons triggered by the Fast Track Trigger [103]. The NLO prediction predicts a less steep behaviour than the H1 HERA I analysis based on events with muon and jets, which combines prelt tag and the lifetime tag [8] (see figure 3.7). The prediction “is lower than the data in the lowest momentum bin by roughly a factor of 2.5”. When extrapolated to the inclusive beauty quark cross 49 (GeV)b T p 0 5 10 15 20 25 ( p b /G e V ) b T /d p σ d 1 10 210 e→ b -1ZEUS 120 pb μ D* → b ZEUS 96-00 μ → b ZEUS 96-00 e→ b ZEUS 96-97 NLO QCD | < 2 b η| ebX)→ (ep b T /dpσd 2 < 1 GeV2Q 0.2 < y < 0.8 ZEUS Figure 3.6: Summary of ZEUS photoproduction results, obtained from HERA I data. Besides the latest results using decays into electrons [17], the results from [22], [16, 19] and [18] are given. section, the result is 2.3 standard deviations below the result obtained in the first H1 measurement using the prelt tag [10]. The analogue ZEUS measurement [16] did not verify this result and agrees with the NLO prediction (see figure 3.7). The higher statistics of the HERA II data and the better understood CST detector allows a measurement of higher precision [85]. Also for the dijet analysis based on the inclusive lifetime tag [7] the data is above the NLO prediction (see figure 3.8). 3.2.2 Deep Inelastic Scattering The beauty production cross section at a median transverse momentum value for the b-quark of 6.5 GeV was measured as well for deep inelastic scattering in [18]. It is concluded that “[...] the measured cross sections exceed the NLO predictions, but they are compatible within errors.” Some results of the ZEUS HERA I measurement at higher transverse momenta using the prelt tag are shown in figure 3.10. The jet selection is performed in the Breit frame (see section 4.4.2). It is concluded that “the differential cross sections are in general consistent with the NLO QCD predictions; however at low values of Q2, Bjorken x, and muon transverse momentum, and high values of jet transverse energy and muon pseudorapidity, the prediction is about two standard deviations below the data.” A similar measurement was performed at H1 for HERA I data, in a more restricted phase space. Also for this measurement jets are selected in the Breit frame, and in addition to the prelt tag the lifetime tag is used. For this measurement it is concluded that also for DIS “the total cross section measurements are somewhat higher than the predictions.[...]the observed excess is pronounced at large muon pseudo-rapidities.” Preliminary results for a ZEUS measurement using a fraction of the HERA II statistics, again using only the prelt tag, are shown in figure 3.11. This time the jet selection is done in the laboratory 50 1 10 10 15 20 25 Data NLO QCD ⊗ Had NLO QCD Cascade Pythia H1ep → ebb − X → ejjμX Q2 < 1 GeV2 1p jet t [ GeV ] d σ /d p je t t [ p b /G e V ] 1 Figure 3.7: Differential photoproduction cross section as a function of the jet trans- verse momentum for the highest transverse momentum jet for the H1 muon+jets HERA I measurement [8] (left) and the ZEUS muon+jets HERA I measurement [16] (right). / GeV1 jet t p 15 20 25 30 35 [ p b /G eV ] 1 je t t /d p σ d -110 1 10 210 Data Pythia Cascade had⊗NLO QCD ejjX→X b eb→ep / GeV1 jet t p 15 20 25 30 35 [ p b /G eV ] 1 je t t /d p σ d -110 1 10 210 Data Pythia Cascade had⊗NLO QCD ejjX→X b eb→ep / GeV1 jet t p 15 20 25 30 35 [ p b /G eV ] 1 je t t /d p σ d -110 1 10 210 Data Pythia Cascade had⊗NLO QCD ejjX→X b eb→ep / GeV1 jet t p 15 20 25 30 35 [ p b /G eV ] 1 je t t /d p σ d -110 1 10 210 Data Pythia Cascade had⊗NLO QCD ejjX→X b eb→ep H1 / GeV1 jet t p 15 20 25 30 35 [ p b /G eV ] 1 je t t /d p σ d -110 1 10 210 Data Pythia Cascade had⊗NLO QCD ejjX→X b eb→ep H1 / GeV1 jet t p 15 20 25 30 35 [ p b /G eV ] 1 je t t /d p σ d -110 1 10 210 Figure 3.8: Differential photoproduction cross section as a function of the jet transverse momentum for the highest transverse momentum jet for the H1 HERA I dijet analysis using the inclusive lifetime tag [7]. 51 10 -1 1 10 15 20 25 30 Data NLO QCD ⊗ Had NLO QCD Cascade Rapgap H1ep → ebb − X → ejμX 2 < Q2 < 100 GeV2 p Breit t,jet [GeV] d σ /d p B re it t, je t [p b /G e V ] 10 20 -0.5 0 0.5 1 Data NLO QCD ⊗ Had NLO QCD Cascade Rapgap H1ep → ebb − X → ejμX 2 < Q2 < 100 GeV2 ημ d σ /d η μ [ p b ] Figure 3.9: Differential cross sections as a function of the jet transverse momen- tum and the muon pseudorapidity for the H1 HERA I DIS analysis [8] using a combination of the prelt tag and the lifetime tag. frame and the measurement was extended to the forward region and supplemented by double differential cross sections. It is concluded that “the total visible cross section is 2σ higher than the NLO prediction. [...]In all distributions the data are described in shape by the MC and by the NLO QCD calculation.” For the analysis presented in this thesis the well established prelt method is applied to a large fraction of the HERA II data. In comparison to the H1 HERA-1 analysis, the phase space is extended towards larger pseudorapidities and smaller momenta of the muon and the jet selection is performed in the laboratory frame. As a cross check, the analysis is repeated for the same phase space region as for the HERA I anaysis1, selecting the jets in the Breit frame. 3.2.3 Fixed Target Fixed target beauty production at HERA-B, where the proton beam halo interacts with wires of different materials, allows a measurement at threshold complementary to the collider experiments. The result of a combined measurement based on the decay channels bb̄ → J/ΨX and bb̄ → μμX [5, 6] is shown in figure 3.12. The conclusion is that the combined result “is consistent with the latest QCD predictions [...] based on NLO calculations and resummation of soft gluons.” 1Due to the modified SpaCal detector the lower part of the Q2 phase space is only accessible by an extrapolation based on the Monte Carlo prediction 52 Figure 3.10: Differential cross sections as a function of the jet transverse momen- tum and the muon pseudorapidity for the ZEUS HERA I DIS analysis [21] using the prelt tag. (GeV)jet T p 5 10 15 20 25 30 ( p b /G e V ) je t T /d p σ d -110 1 10 ZEUS -1ZEUS (prel.) 39pb RAPGAP x 2.49 NLO (HVQDIS) ZEUS -1ZEUS (prel.) 39pb RAPGAP x 2.49 NLO (HVQDIS) (GeV)jet T p 5 10 15 20 25 30 ( p b /G e V ) je t T /d p σ d -110 1 10 μη -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 ( p b ) μ η /d σ d 0 5 10 15 20 25 30 35 40 ZEUS -1ZEUS (prel.) 39pb RAPGAP x 2.49 NLO (HVQDIS) ZEUS -1ZEUS (prel.) 39pb RAPGAP x 2.49 NLO (HVQDIS) μη -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 ( p b ) μ η /d σ d 0 5 10 15 20 25 30 35 40 Figure 3.11: Differential cross sections as a function of the jet transverse momen- tum and the muon pseudorapidity for the ZEUS HERA II DIS analysis [20] using the prelt tag. 53 Proton Beam Energy [GeV] 600 700 800 900 1000 [ n b /n u cl eo n ] b b σ 10 10 2 Kidonakis et al. (2004) Bonciani et al. (2002) + X)ψJ/→E789 (b + X)μμ→bE771 (b + X)μμ→b + X and bψJ/→HERA-B (b Figure 3.12: Cross section for bb̄ production as a function of the proton energy in fixed target collisions. Shown is the result of a combined HERA B measurement [5,6], lower energy Fermilab experiments [24, 78] and NLO predictions. 3.3 Measurements at Other Colliders 3.3.1 pp̄ Collisions Beauty production in hadron collisions was first measured at the Spp̄S collider at CERN. In [14, 15] the UA1 collaboration finds “good agreement with an [NLO] QCD prediction over the whole measured transverse-momentum range”(figure 3.13 left). Also this measurement is based on a prelt fit to the muon decay spectrum (see figure 3.13, right). Over the last years the Tevatron collider is the main source for beauty quark production measurements in pp̄ collisions. The measurements were performed at an centre of mass energy of 1800 GeV for Run I and 1960 GeV for Run II. For the final Run I measurements based on beauty hadron decays, both collaborations, D0 and CDF, come to the conclusion that the measurements do not agree very well with NLO predictions (see figure 3.14). For a measurement in the forward region [3], the D0 collaboration states that they “find that next-to-leading order QCD calculations underestimate b quark production by a factor of four in this region.” For the measurement [2] CDF comes to the conclusion that “the differential cross section is measured to be 2.9 [...] times higher than the NLO QCD predictions with agreement in shape.” In contrast, a D0 measurement based on beauty jets [4] is well described by the NLO QCD prediction. The results of a CDF measurement based on Run II data [1] are shown in figure 3.15. The data is in good agreement with QCD predictions using a fixed-order approach with a next-to-leading-log resummation, using updated determinations of proton parton densities and beauty quark fragmentation functions. 54 Figure 3.13: Results from the UA1 measurement at the Spp̄S collider (left) and the prelt distributions used to measure the beauty fraction. Figure 3.14: Tevatron Run I measurements of beauty quark production from D0 (left) [3] and CDF (right) [2]. 55 Figure 3.15: Recent measurement of beauty quark production from CDF for Run II data [1]. The data is compared to improved QCD calculations. 3.3.2 γγ Collisions Beauty quark production in photon-photon collisions was measured at the LEP experiments. The L3 collaboration published final results based on the whole data sample, where events containing b quarks are identified through their semileptonic decay into electrons or muons [13]. The result is shown in figure 3.16 and compared to NLO QCD predictions. The results are ”found to be in significant excess with respect to Monte Carlo predictions and next-to-leading order QCD calculations.” The measurement is a factor of three, and three standard deviations, higher than the prediction. 56 Figure 3.16: Beauty quark production measurement at the LEP collider [13]. The data is compared to NLO QCD calculations. For completeness also measurements of charm quark production are compared to the predictions. 57 58 Chapter 4 Event Reconstruction This analysis is based on the reconstruction of the scattered electron1 and the hadronic final state, in particular muons and jets. This will be discussed in this chapter in detail, focussing on the subdetectors and algorithms involved. 4.1 Identification and Reconstruction of the Scattered Lepton The main detector for measuring the kinematics of the scattered lepton in the kine- matic range of this analysis is the electromagnetic part of the SpaCal calorimeter. Due to the high granularity of the calorimeter, the scattered lepton deposits en- ergy in several neighbouring cells, which comprise a cluster. The cluster having the highest energy is taken as the scattered electron, where only clusters with a minimum energy of 8 GeV and a maximal radius2 of 4 cm are taken into account. The cell energies are calibrated using the double-angle method, which was intro- duced in [71] and [34] and has become the standard method to perform the electron calibration [66]. This method makes use of the fact that the kinematics of the scat- tered lepton is overconstrained and can be determined from the measurement of the hadronic final state. The polar and azimuthal angle of the lepton with respect to the event vertex is determined from the cluster position3 taking into account the position of the event vertex. In addition tracks measured from the BPC detector are extrapolated to the SpaCal. If the distance of the track impact point to the cluster centre is smaller than 4 cm, this extrapolated value is used. Finally beam tilt corrections are applied. This ensures that the angles are measured with respect to the beam axis which is tilted against the nominal axis. 1From now on only the term electron is used for electrons and positrons. 2The radius is defined using logarithmic weighting. 3The z position of the cluster is not measured directly but calculated from the cluster energy Ecl using the formula z = 0.002 · Ecl + 0.853 log(2479 · Ecl). The parameters of this formula are determined from simulations of the longitudinal shower distribution. 59 4.2 Identification and Reconstruction of the Muon The reconstruction of the muon kinematics is done using the information from tracks in the inner tracking chambers. The CMD, which is the outermost part of the H1 detector, is used to identify the muon. Muons in the energy range considered in this analysis are minimal ionising particles. In addition they do not produce electromagnetic or hadronic showers in the calorimeters (The average energy loss in lead is only about 10 MeV per traversed cm). The energy deposits are concentrated within a narrow cone around the muon track. Muons need an energy of about 1.5 GeV to pass the superconducting coil surrounding the calorimeter and reach the CMD. Here they loose an energy of about 90 MeV per iron plate. For this analysis only muons are considered whose inner track fulfills certain quality criteria (”Lee West Tracks”, [117]) and can be extrapolated and linked to the outer track with a minimal link probability. The latter is derived from the χ2 value which is determined from the track parameters of both the inner and outer track and their covariance matrices. Details concerning this procedure as well as the reconstruction of inner tracks (inner chambers) and outer tracks (CMD) can be found e.g. in [106]. The track reconstruction will be outlined briefly in the following. 4.2.1 Track Reconstruction in the Inner Drift Chambers In the Central Jet Chamber a track finding in the plane perpendicular to the beam axis is perfomed. This track finding is based on charge and drift time information of single hits. Triplets of hits are connected to curved tracks using a χ2 fit. The curvature κ allows the determination of the muon momentum since the magnetic field is known. In the r-z-plane the z-position is determined from the charge division between the wire ends. In addition information from the COZ drift chamber is used to increase the resolution. The values determined for the track include the helix parameters κ, θ, φ, and z0. θ and φ denote the track direction and z the position at the DCA, which is the point of closest approach to the event vertex. After the track reconstruction a vertex fit is performed yielding refined helix parameters. This leads to a momentum resolution of σpt /pt = 0.005 pt/GeV ⊕ 0.015. Track segments of the radial and planar drift chambers of the Forward Tracking Detector are combined to tracks and fitted to the reconstructed vertex. In the overlap region (15◦ ≤ θ ≤ 25◦) a combination of forward and central tracks is performed. 4.2.2 Track Reconstruction in the Instrumented Iron Tracks in the Central Muon Detector are searched for using up to 16 wire layers and 3 pad layers (see section 2.5). A pattern matching is performed separately for the forward and central parts. Only patterns with a sufficient hit number and not matching to particle showers are considered as tracks. Inner tracks are extrapolated to the CMD, taking into account energy loss, multiple scattering and variations of the magnetic field. Then the extrapolated parameters are compared to the parameters 60 measured by the CMD using a χ2 method. The following parameters of the iron track (outer track) are used: • the z-coordinate of the first point on the iron track • the azimuthal angle of the connection of the first measured point on the iron track to the event vertex • the azimuthal angle of the reconstructed iron track From the χ2 value a linking probability is determined. Events with a low linking probability are rejected (see section 5.5). 4.3 Reconstruction of the Hadronic Final State The reconstruction of the kinematics of the hadronic final state is based on Hadronic Final State (HFS) Objects. These are also input objects to the jet finding al- gorithm (see section 4.4). The HFS objects are constructed by a energy flow algo- rithm (Hadroo2 [100]) making use of information from charged particle tracks and calorimetric energy clusters. Their respective resolution and overlap are taken into account, while double counting of energy is avoided [70, 99]. In the following the selection of input objects to the algorithm and the basic principles of the algorithm will be described. 4.3.1 Selection of Input Objects Input to the algorithm are tracks and clusters. The tracks have to be well measured with the central detectors, see section 4.2 for the track reconstruction. Tracks are supposed to originate from a pion, the energy is given by E2track = p 2 track + m 2 π, (4.1) the error is obtained from error propagation using the output of the track fit: σEtrack Etrack = 1 Etrack √ P 2t,track sin4 θ cos2 θσ2 θ + σ2Pt,track sin2 θ , (4.2) with σPt and σθ being the corresponding errors on Pt,track and θ. The other input to the algorithm are clusters. They are built by a clustering al- gorithm from neighbouring cells after applying noise reduction and dead material corrections. Clusters can be classified as electromagnetic or hadronic. All clus- ters with at least 95% of their energy in the electromagnetic part of the calorimeter and with also 50% of it in the first two layers are defined as electromagnetic clus- ters [100]. Since the LAr calorimeter is non compensating, a reweighting of the corresponding cells has to be applied to hadronic clusters. Details on the cell selec- tion, clustering and reweighting can be found e.g. in [90]. Finally a noise suppression is applied to the clusters by running several background finders. This includes the suppression of low energy isolated clusters, halo muons, cosmic muons and coherent noise. 61 4.3.2 Hadroo2 Algorithm The Hadroo2 algorithm is a modified energy flow algorithm in the sense that both track and calorimetric information is used without a one-to-one attribution of tracks to individual clusters. The basic idea of the algorithm is to decide whether the track or the calorimeter clusters behind the track are preferred, i.e. better measured. If the track information is preferred, this information is taken to define the HFS object and the clusters are locked to avoid double counting. Tracks are extrapolated to the surface of the calorimeter as a helix, inside the calorimeter a straight line extrapolation is performed. A calorimetric volume is defined by an overlapping volume of a 67.5◦ cone and two cylinders of radius 25 cm for the electromagnetic part and 50 cm for the hadronic part of the calorimeter. A calorimetric energy Ecylinder is defined as the sum of all cluster energies within this volume. The expected relative error on the energy measurement in the calorimeter is estimated, only using the measured track energy, since the contribution of neutral particles to the cluster is not known:( σE E ) LAr,exp. = σE,LAr,expectation Etrack = 0.5√ Etrack . (4.3) The track measurement is preferred either if the track measurement is better com- pared to the expected calorimeter measurement, σE,track Etrack < σE,LAr,expectation Etrack , (4.4) or the calorimetric energy is larger than the energy measured from the track, Etrack < Ecylinder − 1.96 · σEcylinder . (4.5) In the latter case one assumes calorimetric energy from neutral particles, upward calorimetric energy fluctuations are taken into account. If the track measurement is preferred, clusters behind the track are locked to avoid double counting. The maximum locked energy is given by the calorometric energy Ecylinder, also in this case upward energy fluctuations with respect to the track en- ergy are taken into account. If the calorimetric energy is prefered, the HFS object is defined from this energy and the track is locked. The remaining clusters after treating all tracks are considered to be massless. They are assumed to originate from neutral hadrons with no measured track or charged particles with a badly measured track. As discussed in [100], the calorimetric measurement is better than the track mea- surement in the central region for energies larger than 25 GeV. In this detector region the cluster contribution to the total hadronic transverse momentum is about 40%. 4.3.3 Treatment of Calorimetric Energy Deposition for Muons Muons are part of the hadronic final state but as minimal ionizing particles subject to a special treatment. An isolation criterium is applied to the muons. A muon 62 is classified as isolated if the calorimeter energy in a cone around the extrapolated track is less than 5 GeV, but not larger than pμ + 1 GeV. The cone radius is 35 cm in the electromagnetic and 75 cm in the hadronic section of the LAr calorimeter. The muon fourvector is not altered, but depending on the isolation the clusters along the muon track in the calorimeter are treated differently. If the muon is isolated, those clusters are locked and are no longer visible for the HFS algorithm.4 This avoids double counting of energy belonging to the muon. If the muon is not isolated, no locking of clusters is applied. This avoids locking of energy depositions of other particles which would lead to an underestimation of the jet energy. This method results in an overestimation of the jet energy for non isolated muons, which is corrected by applying the same algorithm for the simulated samples. As the calorimetric energy deposition of muons is not described very well the sensitivity of the algorithm to modifications concerning the isolation and locked energy has to be checked. This is described in more detail in section 6.6 where an estimation for the systematic uncertainty is given. 4.4 Jet Reconstruction Jets on detector level are reconstructed by a jet algorithm, using the HFS objects and the muon as input. Jets are complex objects constructed to define and perform the measurement. Therefore the results of the measurement and the definition of the cross sections depend on the used algorithm. To correct detector level jets for detector effects like reconstruction efficiencies and to predict cross sections, the algorithm has to be applied on hadron level as well. It is also possible to apply the algorithm on parton level before hadronization corrections to obtain parton level cross sections. The requirement of a sound definition on these different levels implies that the construction of such an algorithm is a non trivial task. The Snowmass Convention [72] gives some basic properties such an algorithm has to fulfill. The algorithm has to be well defined on each level. From the experimental point of view the jets have to be easily measured from the hadronic final state. From the theoretical point of view this means that the jets have to be easily calculated from the partonic state. Furthermore there has to be a close connection between the jet distributions on detector level and on parton level. The experimental and theoretical requirements the algorithm has to fulfill are closely connected: • The results of the algorithm have to be independent of the detector granularity, this means the angular resolution of the detector. Therefore the results should not depend on resolving two particles which are almost collinear. An analogue requirement has to be fulfilled on parton level, the result should not change when replacing one particle by two almost collinear particles. This reflects the fact that in perturbative QCD collinear divergencies are cancelled by virtual corrections. 4This locking is performed for clusters within a smaller inner cone of radius 25 cm and 50 cm for the electromagnetic and hadronic section, respectively. 63 • The results of the algorithm have to be independent from noise and thresholds of the individual calorimeter cells. The analogue requirement on parton level is the insensitivity to the emission of low energy particles. The resulting infrared divergencies are guaranteed to be cancelled in perturbative QCD by virtual corrections. Two types of algorithms are used: • Cone algorithms define jets on a simple geometric basis by maximizing the energy flow into a cone with a fixed radius R = √ Δη2 + ΔΦ2, where η is the pseudorapidity5 and φ the angle position of the particle. Algorithms of this type are used for hadron-hadron collisions. Despite the advantage of a simple intuitive interpretation and simple implementation, they have several disadvantages. The main problem is the treatment of overlapping jets since the assignment of particles to jets is ambiguous. • Clustering algorithms find pairs of particles based on a closeness criteria and merge them to pseudoparticles in an iterative procedure. These pseudoparticles are the constituents of the jets. Jets created this way have no geometrical definition but the advantage of an unambigous assignment of particles to jets. Algorithms of this type have been used for e+e− collisions and are also used for hadron collisions today after solving problems of the treatment of the hadron remnant and underlying events. The algorithm used for this analysis is the longitudinally invariant kT -clustering algorithm [44], which will be described in the following section in more detail. 4.4.1 Longitudinally Invariant kT -Clustering Algorithm This is the algorithm most frequently used at HERA. It starts with a list of particle fourvectors and proceeds as follows: 1. For each pair of particles a closeness parameter di,j is calculated, where di,j = min[p 2 t,i, p 2 t,j] [ (ηi − ηj )2 + (Φi − Φj)2 ] (4.6) and for each particle a closeness to the beam particles is defined by di = p2t,i. For small opening angles the “distance” di,j is proportional to kt, which is the momentum of the softer particle to the axis of the harder: min[p2t,i, p 2 t,j ](ΔΦ 2 + Δη2) ≈ k2t . (4.7) 2. The minimum dmin of all values di, di,j is determined, if dmin = di,j the two particles are combined to form a new one, if dmin = di then that particle is removed from the list and added to the list of protojets. 3. New values for di, di,j are determined and step 2 is repeated. This iteration continues until all particles are assigned to protojets. 5The pseudorapidity is defined as η = − ln(tan θ 2 ), where θ is the polar angle of the particle. 64 Figure 4.1: Quark Parton Model (left), QCD Compton (middle) and Boson Gluon Fusion (right) processes in the Breit frame (from [47]). The way how two objects are merged is defined by the recombination scheme which is a prescription how to calculate the parameters of the new particle from the two merged particles. For this analysis the pt-weighted recombination scheme is used: ηk = 1 pt,k (pt,iηi + pt,jηj ), (4.8) Φk = 1 pt,k (pt,iΦi + pt,jΦj ), (4.9) with pt,k = pt,i + pt,j. (4.10) 4.4.2 Jets in the Breit Frame In the Breit frame [60] for the lowest order process γ∗q → q′ (Quark Parton Model) there is no energy transfer between the virtual photon and the initial state quark. They collide head on and the quark momentum is reversed (see figure 4.1). If the z-axis is chosen such that q = (0, 0, 0, −Q), the incoming quark has the four momentum p = (Q/2, 0, 0, Q/2) and the outgoing scattered quark has the four momentum p′ = (Q/2, 0, 0, −Q/2). The transformation to the Breit frame requires rotations and a boost and is explained in detail in appendix B. The Breit frame is an appropriate frame for the investigation of leading order QCD processes like boson gluon fusion and QCD Compton. Jets reconstructed from these processes usually have large pt, whereas for quark parton model processes there is no transverse momentum in either the initial or final state on parton level and only limited transverse momentum on hadron level due to fragmentation. Despite the advantage of a better separation of BGF processes from QPM processes, the jet selection is performed in the laboratory frame for this analysis. This selection results in a higher statistics event sample and allows a measurement of the beauty contribution to the proton structure function F2. The selection of jets in the Breit frame is performed as a cross check to compare to published results (see section 6.6). 4.5 Kinematic Variables This measurement is defined in terms of the properties η and pt of the jet and muon and in addition in terms of the event variables x, Q2 and y which are related via 65 Q2 = x · y · s. The quantities Q2 and y can be determined from the kinematics of the scattered electron, this is called the electron method: ye = 1 − E′e(1 − cos θe) 2Ee (4.11) Q2e = 2E ′ eEe(1 + cos θe) = E′2e sin 2 θe 1 − ye . (4.12) Here E′e and θe denote the energy and polar angle of the scattered electron. The resolution of the ye measurement is given by δye ye = ( 1 ye − 1 ) δE′ E′ ⊕ ( 1 ye − 1) cot ( θe 2 ) δθe. (4.13) For y > 0.3 the resolution is dominated by the resolution of the energy measurement (δE′e/E ′ e < 4%). Due to the 1/ye term the resolution gets worse for smaller y. One advantage of the HERA kinematics is that the measurement of the DIS variables is overconstrained and can be performed by using the properties of the hadronic final state alone. When using conservation of energy and longitudinal momentum, (EinP − P in z,P ) + (Ee − Pz,e) = 2Ee = E ′ e(1 − cos θe) + ∑ a Ea(1 − cos θa), (4.14) y can be expressed in terms of the hadronic final state alone: yh = 2Ee − E′e(1 − cos θe) 2Ee = Σ 2Ee , (4.15) where Σ = ∑ a Ea(1 − cos θa) and the sum is performed over all final state particles neglecting their masses. This method is called hadron method, it was introduced by Jacquet and Blondel [76]. The resolution of y reconstructed by the hadron method is given by the hadronic energy resolution: δyh yh = δΣ Σ . (4.16) This method can also be used for lower values of y since the resolution does not diverge at low y. The reconstruction of y can be further improved. Emissions of collinear real photons from the incoming electron before the interaction with the proton (QED initial state radiation) lead to large corrections because in equation (4.15) the electron energy is fixed to Ee. This can be avoided by replacing Ee by the “measured” incoming electron energy using the relation given by (4.14): yΣ = Σ Σ + E′e(1 − cos θe) . (4.17) This sigma method [32] has a similar resolution as the hadron method. 66 yresolution_pfx y gen. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 y re c . / y g e n . 0 0.2 0.4 0.6 0.8 1 yresolution_pfx yresolution q2resolution_pfx Entries 12227 Mean 29.89 Mean y 0.9851 Q 2 gen. [GeV 2 ] 0 10 20 30 40 50 60 70 80 90 100 Q 2 re c ./ Q 2 g e n . 0.92 0.96 1 q2resolution_pfx Entries 12227 Mean 29.89 Mean y 0.9851 q2resolution Figure 4.2: Ratio of reconstructed to generated values as a function of the generated value for yΣ (left) and Q2e (right). To summarize, for this analysis a combination of the electron method and the sigma method is used, Q2 is reconstructed using the electron method and y using the sigma method due to its better resolution at low y and its insensitivity to radiative effects. As a cross check the analysis is repeated using the electron method for the reconstruction of y as well (see section 6.6). The Bjorken scaling variable x is given by x = Q2e yΣ · s . (4.18) The resolution plots for Q2e and yΣ are shown in figure 4.2. 67 68 Chapter 5 Event Selection This measurement is based on the selection of a heavy quark enriched sample where beauty, charm and light quarks contribute with respective fractions of 25%, 55% and 20% [8]. The exact measurement of the beauty fraction and the determina- tion of detector correction factors applied to the data requires a precise description of the data using simulated Monte Carlo samples. In the case of discrepancies addi- tional corrections or the introduction of systematic errors have to be considered. This chapter is organized as follows: first the requirements the analysed data sample has to fulfill are discussed, including the online trigger selection and the correspond- ing correction factors. After this the signal and background Monte Carlo samples are presented. Finally the selection cuts that are applied both to the data and the Monte Carlo samples are discussed in detail, including the selection of DIS events, muon events and jet events. Control distributions are shown for each selection cut. 5.1 Data Sample Data from the years 2005-2007, taken at a center of mass energy of 320 GeV, is analysed. The analysed part of the HERA II data has to fulfill several requirements on the selected runs, the status of subdetectors and the online trigger selection. This will be discussed in the following. The data sample consists of three different run periods, the corresponding run ranges and luminosities are summarized in table 5.1. The total luminosity of the analysed data is 285.1 pb−1. Run Period Run Range Luminosity [pb−1] 2005 e- 401617-436893 101.4 2006 e- 444094-466997 54.3 2006/07 e+ 468531-492541 129.4 Table 5.1: Different run ranges and corresponding luminosities. 69 s 61: ((SPCLe IET>2)||SPCLe IET Cen 3)&&(FTT mul Td>0)&&VETO &&CIPVETO SPCLe IET>2 Spacal inclusive electron trigger, outer part SPCLe IET Cen 3 Spacal inclusive electron trigger, central part FTT mul Td>0 at least one FTT L1 track with pt > 900 MeV VETO Veto wall, Time of flight detectors CIPVETO:(CIP mul>11)&&(CIP sig==0) CIP veto Table 5.2: Trigger elements of subtrigger s61 5.1.1 Run Selection and Detector Status A run selection is applied to the data, taking into account the running conditions of the machine and the detector. Only runs with an assigned quality of good and medium are included in the data sample, in addition several run ranges are excluded due to problems and malfunctions of detector compoments relevant to the analysis. The list of excluded runs is summarized in appendix A. In addition detector status information which is stored every 10 seconds is used. Only events where all relevant subdetectors are fully functional are selected. The high voltage status of the sub detectors has to be controlled since a lower than the nominal value leads to a significant loss of efficiency. The relevant subdetectors are the forward and central tracking chambers, the SpaCal calorimeter, the muon system, the luminosity system, Time of Flight detectors and the Fast Track Trigger. The condition of the CIP detector is not taken into account for the run selection as it is only used as a veto condition. The run ranges and the corresponding corrected luminosites are summarized in table 5.11. 5.1.2 Trigger selection The data sample and its luminosity is defined by the applied online selection crite- rions (trigger condition). The used data sample was triggered by the DIS subtrig- ger s61, which requires a scattered electron detected by the backward calorimeter (SpaCal) and in addition a high momentum track measured by the central drift chambers and found online by the Fast Track Trigger. Background events origi- nating from beam gas events are rejected online using the timing condition of the SpaCal and additional veto conditions from the Veto Wall, different time of flight detectors and CIP trigger elements. The subtrigger elements are summarized in ta- ble 5.2. The online selection of DIS events is only fully efficient for electron energies above 17 GeV. Therefore a correction has to be applied for lower energy electrons. The energy dependence of this subtrigger was measured using a sample of events containing an offline selected scattered electron detected by the SpaCal but trig- gered independently. The fraction of events fulfilling the online SpaCal condition 1The given run range for the 2005 e− does not include the period before the FTT was active. For this period the track trigger condition is not fully efficient and has to be investigated. 70 E’ [GeV] 10 12 14 16 18 20 22 24 26 28 E ff ic ie n c y 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 effSpacal Figure 5.1: Energy dependence of the SpaCal trigger efficiency. as well determines the efficiency as shown in figure 5.1. A Fermi function of the form 1/(1 + exp (−a · E′ + b)), where a and b are free parameters, is fitted to these data points. This additional detector inefficiency was incorporated to the analysis by applying a weight to each simulated event according to the measured electron energy. The online track condition does not lead to an inefficiency. This was checked using an independently triggered data sample. The loss of events due to the additional CIP veto condition, which was applied from run 474479 on, is negligible. 5.2 Monte Carlo Samples The simulated event samples, used to determine detector efficiencies and acceptances and to describe signal and background distributions, are generated using RAPGAP as the default event generator, supplemented by the Heracles program [23] to gen- erate radiative events. The luminosity of the inclusive event samples, generated using the full mode IPRO 1200 [82], including light flavour, charm and beauty events, corresponds to about 6 times the data luminosity (see table 5.3). The kinematic range for the event generation is restricted to Q2 > 1 GeV2 and y > 0.01. Heavy quarks are produced in the massive mode, the decision whether to generate a quark parton model process or a first order αs process is based on the cross section for the particular process at a given x and Q2. The charm and beauty quark masses are set to 1.5 GeV and 4.75 GeV, respectively. The GRV LO [65] sets for the parton density functions are used. The scale is set to Q2 for light flavour events and Q2 + m2Q for heavy quark production, where mQ is the heavy quark mass. Lund String fragmentation is used, with the Peterson fragmentation function for light quarks and the Lund-Bowler frag- 71 MC type runperiod number of events L [pb−1] inclusive 05e− 20.4 · 106 ∼ 500 inclusive 06e− 9.5 · 106 ∼ 220 inclusive 06/07e+ 39.1 · 106 ∼ 970 beauty 05e− 510054 850.8 beauty 06e− 1089269 1701.0 beauty 06/07e+ 254404 425.8 Table 5.3: Monte Carlo sets: given are the number of events that are reconstructed and simulated and the luminosities for the different run periods. mentation function for heavy quarks (see section 1.6). Due to the large cross section only a fraction of the generated events is simulated: events that do not contain at least one jet with a minimum transverse momentum of 4 GeV and a charged parti- cle with transverse momentum of at least 1.9 GeV in the range 10◦ < θ < 165◦ are rejected. In total about 69 Mio. events are simulated. The luminosity of the beauty event samples, generated using mode IPRO 1400 [82], corresponds to about 10 times the data luminosity (see table 5.3), where the kinematic range is again restricted to Q2 > 1 GeV2 and y > 0.01. The MRST 2004FF4lo [96] set of parton density functions is used. The beauty mass is set to 4.75 GeV, the scales are set to Q2 + m2b and the Lund string fragmentation with the Lund-Bowler fragmentation function is used. Also for the beauty sample only a fraction of the generated events is simulated. At least one charged particle with a minimum transverse momentum of 1.9 GeV in the range 10◦ < θ < 165◦ is required. No muon is demanded to allow fake muon studies. In total about 1.9 Mio. events are simulated. 5.2.1 Background Sources Each selected event requires the detection of a muon candidate. If the muon arises from the decay of a hadron or τ -lepton, but no beauty hadron is produced, the event is regarded as a background event. The muon candidate of a background event may either be a real muon or a misidentified hadron. In the case of a real muon this may come from a charm quark decay or from the decay of a light hadron, usually a pion or a kaon, which are predominantly produced. Almost every pion decays into a muon and a neutrino (the branching fraction is almost 100%). The branching fraction the decay of a kaon into a muon and a neutrino is (63.43 ± 0.17)% [58]. Due to the large decay lengths cτ (7.8 m for pions and 3.7 m for kaons), these particles are usually stopped inside the LAr calorimeter before decaying. Because of the abundance of these particles and the large branching fractions, light hadrons that decay during the passage through the detector volume in the inner detector are an important contribution to the background (inflight decays). The other important contribution to the background are misidentified hadrons. This source of background can be further distinguished: 72 • The hadrons that are interacting in the calorimeter do not necessarily deposit their entire energy inside the calorimeter. Energy leakage passing some iron layers may lead to the misidentification of these hadrons (denoted as punch through). • Hadrons may reach the muon detector without strongly interacting inside the calorimeter volume. The maximum probability for this is 0.6%, depending on the polar angle [97]. These hadrons contribute to the background because the muon system in some cases falsely identifies the resulting hadronic showers as muons. This contribution is denoted as sail through background. Misidentified hadrons (punch through, sail through) and inflight decays are summa- rized as fake muons. According to the Monte Carlo simulation, for about 21% of the selected charm events and about 18% of the selected beauty events, the selected muon candidate is a fake muon, and for about 30% of the selected light flavour events the selected muon comes from an inflight decay. 5.3 Z Vertex Distribution A precise measurement of the kinematic variables and modelling of the detector acceptance requires a well described distribution of the z position of the event ver- tex. The longitudinal bunch structure of the protons is reflected in a Gaussian z vertex distribution. A cut on the minimal distance of the z position of the event vertex to the nominal vertex is applied (|zvtx| < 35 cm). Events not fulfilling this cut are most probably background events, e.g. due to beam gas interactions. The z vertex distribution is on purpose simulated broader than the data distribution, and the average z vertex position is different for the simulation. The widths and median values of the z vertex distributions are determined from the simulated dis- tributions and summarized in table 5.4. The simulated distributions are reweighted individually for each run period. The reweight factor is determined from the ratio of the Gaussian functions obtained from the fits which are evaluated for each event. Both the reweighted and non reweighted z vertex distributions are compared to the data distributions in figure 5.2, where all selection cuts as described in the following sections are applied. As for all control plots presented in the following, the beauty fraction is set to 24%, which is the beauty fraction for the total sample as obtained from the measurement (see section 6.3). The reweighting leads to an improvement of the description. 73 z Vertex [cm] -40 -20 0 20 40 N u m b e r o f e v e n ts 0 500 1000 1500 b MC c+uds MC sum MC Data vtxz_xgammabins 0.00 < < 1.00 z Vertex [cm] -40 -20 0 20 40 N u m b e r o f e v e n ts 0 500 1000 1500 vtxz_xgammabins 0.00 < < 1.00 Figure 5.2: Comparison of the simulated z vertex distributions to the data before (left) and after (right) reweighting. Run Period Data Monte Carlo σz [cm] μz [cm] σz [cm] μz [cm] 05e− 10.01 0.57 10.33 1.34 06e− 9.99 0.31 10.10 0.07 06/07e+ 9.20 -0.40 9.49 -0.55 Table 5.4: Parameters of the z vertex distributions for the different run periods for data and Monte Carlo as obtained from a Gaussian fit. The Monte Carlo parameters are determined from the beauty sample which do not differ to the inclusive sample within the errors. 74 5.4 Selection of DIS Events The polar angle of the scattered electron is required to be larger than 155◦, ensuring a reconstruction by the backward calorimeter (SpaCal) and avoiding the overlap region with the LAr calorimeter. For efficient triggering the electron energy has to be larger than 10 GeV. Misidentified electrons, which lead to photoproduction background in the sample, are rejected by requiring a cluster radius smaller than 4 cm because hadronic clusters are usually broader. As shown in figure 5.3 the distri- bution is shifted towards smaller values for the simulation, but otherwise described well in shape. Possible remaining photoproduction background is rejected by a cut E − pz > 45 GeV, with E − pz = ∑ h Ea(1 − cos θa), (5.1) where a summation over the whole final state is done. For photoproduction events, where the scattered electron is not detected but a hadron misidentified as an elec- tron, smaller values of E−pz are measured. The distribution, which peaks at 55 GeV due to momentum conservation, is shown in figure 5.3. A loss of hadrons and of photons from initial final state radiation in the backward direction leads to a broad asymmetric distribution. z E-p 30 35 40 45 50 55 60 65 70 N u m b e r o f e v e n ts 200 600 1000 1400 1800 b MC c+uds MC sum MC Data [GeV] cluster radius [cm] 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 200 600 1000 1400 1800 b MC c+uds MC sum MC Data Figure 5.3: Control distributions for E − pz and the cluster radius. For the Monte Carlo distribution the contribution from beauty quarks is fixed to 24.6%. The E − pz cut applied for the selection is indicated by the dashed line. In addition, several fiducial cuts have to be fulfilled: • In the course of the HERA II upgrade program the beampipe was modified and focussing magnets had to be inserted within the detector region. This implied modifications like a new elliptical shape of the beam pipe and a larger SpaCal hole, where the center is shifted horizontally with respect to the nominal beam axis and the center of the H1 coordinate system. At the SpaCal edge the electron energy and scattering angle cannot be measured correctly since the shower is only partly contained in the SpaCal. Therefore the inner SpaCal region, which 75 ] 2 [GeV2Q 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 1 10 b MC c+uds MC sum MC Data Impact Radius [cm] 0 10 20 30 40 50 60 70 80 N u m b e r o f e v e n ts 0 500 1000 1500 2000 2500 b MC c+uds MC sum MC Data Figure 5.4: Q2 distribution for small values of Q2 and impact parameter distri- bution for the inner SpaCal region, where the contribution from beauty quarks is fixed to 25% for the Monte Carlo distribution. For the Q2 distribution the radial cut is applied, for the impact parameter distribution no lower Q2 cut is applied. The data is compared to the Monte Carlo simulation. The cuts used for the analysis are indicated as dashed lines. corresponds to low Q2 events, is not very well described by the Monte Carlo simulation. The shift of the SpaCal hole leads to an asymmetric acceptance as a function of Q2. To avoid these problems, a radial cut is applied, and only clusters with a minimal radial distance of 16 cm are accepted2. This distance is determined with respect to the intersection of the electron beam with the SpaCal plane, taking into account a possible beam tilt (beam coordinates)3. This ensures a symmetric acceptance and allows for a lower Q2 cut of 3.5 GeV2. The radial cluster distribution and the distribution for low values of Q2 between 2 GeV2 and 5 GeV2 are shown in figure 5.4. Both distributions are well descibed by the Monte Carlo simulation. The loss of acceptance due to the radial cut is clearly visible for the Q2 distribution. No events below 2.5 GeV2 pass the selection. To avoid too large correction factors, a lower Q2 cut of 3.5 GeV2 is applied. For HERA I low Q2 DIS analyses a lower cut of 2 GeV2 was usually applied. The analysis is stable with respect to variations of this cut. The radial cut was modified by an amount of ±0.5 cm, the cross section deviation obtained this way is negligible. • A fraction of the inner SpaCal region is hit by the synchrotron radiation fan of the electron beam. The corresponding cells are taken out of the trigger. Therefore these cells are excluded from the selection by applying a box cut which covers the corresponding SpaCal region. Also in this case the coordinates 2This radial cut is much more conservative than the cut applied in [29], where the distance of the cluster to the SpaCal center has to be larger than 12 cm. For that analysis a larger Q2 cut of 5 GeV2 was chosen to ensure a symmetric acceptance. 3Technically this is done by recalculating the position of the cluster using the angular parameters of the scattered electron which are corrected for beam tilts. 76 x [cm] -40 -30 -20 -10 0 10 20 30 40 y [ c m ] -40 -30 -20 -10 0 10 20 30 40 1 10 210 spacal_selection Figure 5.5: Distribution of the reconstructed impact position of electrons in the SpaCal plane for data events. No fiducial cuts are applied. The circle and box applied in the selection are shown. Additional cell cuts are not shown. Due to reconstruction artefacts the shadow of the BPC is visible. for this cut are defined in beam coordinates. • Additional cell cuts are applied. Some cells do not deliver trigger signals due to electronic problems, others cannot be used for the energy measurement due to a defect photomultiplier. An investigation for these problematic cells for different run periods was done in [29] and [94]. All these cells are excluded from the selection.4 The distribution of impact points for the scattered electron in the SpaCal plane for data events is shown in figure 5.5. The SpaCal hole, the area which is taken out of the trigger and the increase of selected events towards the inner region are clearly visible. The radial and the box cut are also depicted. Control plots for all relevant distributions are shown in figures 5.7 and 5.8. In addition to the DIS selection cuts the muon and jet selection cuts as explained in the following sections are applied as well. For all plots the contribution from beauty quarks is fixed to 24%, as measured from the data (see section 6.3.3). The Monte Carlo distributions are normalized to the number of data events. The polar angle of the scattered electron is reweighted since the distribution does not 4In the case of a defect photomultiplier it is demanded that clusters of neighbouring cells have a minimum distance of 1 cm to the defect cell to achieve a good description of the acceptance by the simulation. 77 θe [deg.] 155 160 165 170 175 C o rr e c ti o n 0.8 0.9 1 1.1 1.2 ScatElecTheta_xgammabins 0.00 < < 1.00 Figure 5.6: Reweight factor applied to the Monte Carlo simulation as a function of θe. cut value Scattering angle θe > 155◦ Electron energy E′ > 10 GeV Cluster radius < 4 cm Impact radius > 16 cm Virtuality 3.5 < Q2 < 100 GeV2 Inelasticity 0.1 < yΣ < 0.7 Table 5.5: DIS selection cuts. The cuts that define the kinematic range of this analyis are in bold letters. describe the data very well. This distribution is reweighted by applying a bin-wise factor that is determined from the comparison of this distribution for data and the inclusive Monte Carlo sample. This reweighting factor as a function of θe is shown in figure 5.6. This reweighting leads to an improvement for Q2 and E′, as shown in figure 5.7, where all distributions are shown before and after reweighting. In figure 5.9 the azimuthal angular distribution of the scattered electron is shown, which is flat and well described by the Monte Carlo simulation. The y distribution is not described very well for low y (see figure 5.9, left). Since this variable is measured from the hadronic final state (see section 4.5), a reweighting of the pseudorapidity distribution of the muon as discussed in section 5.5 leads to a significant improvement (see figure 5.9, right). The log x distribution which is measured from Q2 and y (see section 4.5) is shown in figure 5.10. Also this distribution is well described by the Monte Carlo simulation. All DIS selection cuts are summarized in table 5.5. 78 [GeV2] 2 Q 20 40 60 80 100 120 N u m b e r o f e v e n ts 2 10 3 10 b MC c+uds MC sum MC Data [GeV2]2Q 20 40 60 80 100 120 N u m b e r o f e v e n ts 2 10 3 10 b MC c+uds MC sum MC Data E' [GeV] 5 10 15 20 25 30 N u m b e r o f e v e n ts 200 600 1000 1400 1800 b MC c+uds MC sum MC Data E’ [GeV] 5 10 15 20 25 30 N u m b e r o f e v e n ts 200 600 1000 1400 1800 2200 b MC c+uds MC sum MC Data e [deg.]θ 150 155 160 165 170 175 180 N u m b e r o f e v e n ts 200 600 1000 1400 1800 b MC c+uds MC sum MC Data 150 155 160 165 170 175 180 N u m b e r o f e v e n ts 200 600 1000 1400 1800 2200 b MC c+uds MC sum MC Data e [deg.]θ Figure 5.7: Control distributions for variables determined from the scattered elec- tron. The cuts applied for the selection are indicated as dashed lines. The plots are shown before (left column) and after (right column) reweighting in θe. 79 Σ y 0.1 0.3 0.5 0.7 0.9 N u m b e r o f e v e n ts 0 1000 2000 3000 b MC c+uds MC sum MC Data Σ y0.1 0.3 0.5 0.7 0.9 N u m b e r o f e v e n ts 0 1000 2000 3000 b MC c+uds MC sum MC Data Figure 5.8: Control distribution for the variable y, before (left) and after (right) reweighting in ημ. The cuts applied for the selection are indicated as dashed lines. [deg.]φ -150 -100 -50 0 50 100 150 N u m b e r o f e v e n ts 0 200 400 600 b MC c+uds MC sum MC Data Figure 5.9: φ distribution of the scattered electron. log x -5 -4 -3 -2 -1 0 N u m b e r o f e v e n ts 200 600 1000 1400 1800 2200 b MC c+uds MC sum MC Data Figure 5.10: Distribution of the Bjorken scaling variable. 80 5.5 Selection of Muons As explained in section 4, muons have to be identified as iron muons by the outer central and forward muon detector (outer track). This track has to be linked with a certain probability to an inner track measured by the central and forward track- ing chambers. The muon is required to have a minimum transverse momentum of 2 GeV, the allowed pseudorapidity range is −0.75 ≤ ημ ≤ 2, which corresponds to an angular range 15.4◦ ≤ θμ ≤ 129.4◦ and is an extension in phase space compared to the previous analysis [8]. In the overlap region between the central region (CJC) and the forward region (FTD), a small fraction of the selected muon tracks are re- constructed using information from both detectors (combined tracks) or the FTD alone (forward tracks). This fraction is small (about 8%). In addition, the muon has to be assigned to a jet fulfilling the jet selection criteria as described in the next section. This assignment of muons to jets is an intrinsic property of the used jet algorithm as described in section 4 since every particle is assigned to exactly one jet. In rare cases a second muon is found fulfilling the selec- tion criteria. Then the muon having the highest transverse momentum is selected and required to be assigned to a selected jet. The detector cuts applied to the muon have an influence on the efficiency of the muon selection and the purity of the sample. As the kinematic range of this analysis is extended with respect to the pseudorapidity and momentum range of the muon, the influence of these cuts is studied in detail. The studied cuts are the linking probability of the outer to the inner muon track (see section 4.2) and the number of muon layers having a muon signal separatly for the central and forward region. The linking probability is shown in figure 5.11. For all distributions shown in this section, in addition to the muon selection, the DIS selection and the jet selection, as explained in the following section, are applied to data and Monte Carlo simu- lation. The distribution is flat and increases for small probabilities as expected. The Monte Carlo simulation describes the data reasonably well. In addition the distribution of background events is shown for the simulated samples and compared to data. Background events are defined as misidentified hadrons (fake muons) and real muons coming from inflight decays as defined in section 5.2.1. According to the simulation, the background is dominated by misidentified hadrons both from events with no heavy quark or a charm quark involved. The amount of events with a produced beauty quark and a misidentified hadron or events with a real muon coming from an inflight decay is small. As expected, the fraction of background increases for small linking probabilities. The linking probability cut is scanned, the result for the selection efficiency and the purity of the sample is also shown in figure 5.11. The selection efficiency is defined with respect to a sample with no linking probability cut applied. Whereas the selection efficiency decreases from 85% for a linking probability of 2% to 75% for a linking probability of 20%, the fraction of background events stays constant at 30%. The cut applied for this analysis is at 2%. The influence of this cut on the cross section is studied as a cross check in section 6.6. The same investigation is done for the cut on the number of muon layers with a 81 cut value transverse momentum pμt > 2.0 GeV pseudorapidity −0.75 ≤ ημ ≤ 2.0 linking probability ≥ 2% number of muon layers ≥ 3 Table 5.6: Muon selection cuts. The cuts that define the kinematic range of this analyis are in bold letters. muon signal. The results are shown in figure 5.12 for the central region and figure 5.13 for the forward region. For this study, no other muon detector cut is applied. The maximum number of layers is 10, the inner and outer muon boxes (see section 2.5) are not taken into account. The distributions of the number of layers are not described very well by the simulation because the single hit efficiency is too low for the simulation after a high voltage increase. Therefore only a loose cut of at least three muon layers is possible. As can be seen in the plot comparing the efficiency and purity of the sample, no significant reduction of background is possible by using a harder cut, whereas the efficiency decreases significantly from almost 100% at a cut of at minimum three layers. Again the efficiency is defined with respect to a sample with no cut on the number of muon layers applied. The same holds for the forward region. The distribution of the number of muon layers with a muon signal is not described very well, the fraction of events having a signal from less than six layers is negligible. Applying a cut on the number of layers does not lead to a significant reduction of the background, whereas the efficiency decreases rapidly. For a cut of less than six layers the background fraction is about 35%, which is a bit higher than for the central region. Another quantity for rejecting background is the number of layers between the first and the last muon layer having a muon signal. This distributions are shown in figures 5.15 and 5.14 for the forward and central region. Again, the distribution for the forward region is well described, the distribution for the central region is not described very well. A cut on this distribution does not lead to any additional background rejection, therefore no cut is applied. The pseudorapidity distribution of the muon is shown in figure 5.16. The fraction of events in the forward region (ημ > 0.5) is overestimated by the simulation. A reweighting is applied, where the reweighting factors are determined bin-wise from the ratio of the data to the inclusive Monte Carlo distribution. The reweighting factor as a function of the pseudorapidity is shown in figure 5.17. The polar angle and transverse momentum distributions are shown in figure 5.18. No further reweighting has to be applied, the transverse momentum distribution is well described by the simulation. All cuts concerning the muon selection are summarized in table 5.6. 82 Linking Probability [%] 0 2 4 6 8 10 12 14 16 18 20 N u m b e r o f e v e n ts 0 200 400 600 800 1000 b MC c+uds MC sum MC Data Linking Probability [%] 0 2 4 6 8 10 12 14 16 18 20 N u m b e r o f e v e n ts 0 200 400 600 800 1000 data fake MuonLinkProbFineBinning_xgammabins 0.00 < < 1.00 0 2 4 6 8 10 12 14 16 18 200 0.2 0.4 0.6 0.8 1 efficiency fake fraction Linking Probabiliy [%] Figure 5.11: Linking probability between central track and iron track: in the upper left plot the data distribution is compared to the simulation, in the upper right plot the data distribution and the distribution from background events as determined from the simulation is shown. In the lower plot efficiency and fake fraction are shown as explained in the text. # Muon Layers 0 2 4 6 8 10 12 14 16 N u m b e r o f e v e n ts 0 500 1000 1500 2000 2500 ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ b MC ������ ������ ������ ������ ������ c+uds MC sum MC Data # Muon Layers 0 2 4 6 8 10 12 14 160 0.2 0.4 0.6 0.8 1 efficiency fake fraction Figure 5.12: Distribution of the number of muon layers with a hit for the central region: in the left plot the data distribution is compared to the simulation, in the right plot efficiency and fake fraction are shown as explained in the text. 83 # Muon Layers 0 2 4 6 8 10 12 14 16 N u m b e r o f e v e n ts 0 100 200 300 400 500 ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������ b MC ������� ������� ������� ������� ������� c+uds MC sum MC Data # Muon Layers 0 2 4 6 8 10 12 14 160 0.2 0.4 0.6 0.8 1 efficiency fake fraction NMuonLayersforw_xgammabins_uds 0.00 < < 1.00 Figure 5.13: Distribution of the number of muon layers with a hit for the forward region: on the left plot the data distribution is compared to the simulation, on the right plot efficiency and fake fraction are shown as explained in the text. Distance Muon Layers 0 2 4 6 8 10 12 14 N u m b e r o f e v e n ts 0 500 1000 1500 2000 2500 3000 3500 4000 b MC c+uds MC sum MC Data Distance Muon Layers 0 2 4 6 8 10 12 140 0.2 0.4 0.6 0.8 1 efficiency fake fraction Figure 5.14: Distribution of the distance between first and last hit layer for the central region: on the left plot the data distribution is compared to the simulation, on the right plot efficiency and fake fraction are shown as explained in the text. Distance Muon Layers 0 2 4 6 8 10 12 14 N u m b e r o f e v e n ts 0 200 400 600 800 1000 b MC c+uds MC sum MC Data Distance Muon Layers 0 2 4 6 8 10 12 140 0.2 0.4 0.6 0.8 1 efficiency fake fraction Figure 5.15: Distribution of the distance between first and last hit layer for the forward region: on the left plot the data distribution is compared to the simulation, on the right plot efficiency and fake fraction are shown as explained in the text. 84 η -1 -0.5 0 0.5 1 1.5 2 2.5 N u m b e r o f e v e n ts 0 200 400 600 800 1000 1200 1400 1600 1800 b MC c+uds MC sum MC Data η -1 -0.5 0 0.5 1 1.5 2 2.5 N u m b e r o f e v e n ts 0 200 400 600 800 1000 1200 1400 1600 b MC c+uds MC sum MC Data Figure 5.16: Pseudorapidity distribution for the selected muon, before (left) and after (right) reweighting. μη -0.5 0 0.5 1 1.5 C o rr e c ti o n 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 MuonEta_selection_xgammabins 0.00 < < 1.00 Figure 5.17: Reweight factor applied to the Monte Carlo simulation as a function ημ. φ [deg.] -150 -100 -50 0 50 100 150 N u m b e r o f e v e n ts 0 100 200 300 400 500 600 700 800 b MC c+uds MC sum MC Data tP 0 2 4 6 8 10 12 14 16 18 20 N u m b e r o f e v e n ts 1 10 2 10 3 10 b MC c+uds MC sum MC Data [GeV] Figure 5.18: Azimuthal angle (left) and transverse momentum (right) distribution of the muon. 85 Invariant Mass [GeV] 2.8 3 3.2 3.4 3.6 E v e n ts 0 200 400 600 800 masspeak Figure 5.19: Invariant mass distribution of the elastic J/ψ sample 5.5.1 Muon Identification Efficiency The performance of the muon identification with respect to the efficiency and misiden- tification depends on the detector cuts applied to the event selection. Since the data is corrected for these detector effects using Monte Carlo simulations, the identifica- tion efficiency of muons in the iron implemented in the simulation has to be checked with real data. Correction factors have to be applied to account for a not perfect simulation of the muon identification. A clean sample of muon events is used for this check, the muons origining from decays of elastically produced J/ψ mesons. Exactly two well measured tracks are demanded, their invariant mass has to lie within the J/ψ mass window, which is defined as the mass range from 2.8 GeV to 3.2 GeV. If in addition at least one of these tracks is identified as a muon in the calorimeter, this event sample is almost background free. The sample was triggered by an in- dependent subtrigger which has no iron muon condition and consists of 1321 muon candidates, the invariant mass distribution is shown in figure 5.19. The cuts for se- lecting this sample are summarized in table 5.8. The muon identification efficiency can be checked by considering the second muon. The detector cuts for the iron muon correspond to the final selection cuts discussed in section 5. The pt dependence of the identification is determined for three detector regions: the forward and back- ward of the barrel region and the forward endcap. For each region the efficiency determined from the data is compared to the efficiency determined from a sample of simulated elastic J/ψ events5 where the same selection is applied. The results are shown in figures 5.20 to 5.22. For each efficiency measurement a fit of a Fermi function of the form �(pt) = �max/(1 + exp (−a x + b)) with three free parameters is performed. The important parameter is �max, which denotes the efficiency for the plateau region. Since the Fermi function is not able to describe both the low and 5This sample is generated using the DIFFVM [93] Monte Carlo generator. 86 [GeV] T p 1.5 2 2.5 3 3.5 E ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 efficiency_forwbarrel 30°<θ<80° [GeV] T p 1.5 2 2.5 3 3.5 E ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 efficiency_forwbarrel Figure 5.20: Muon reconstruction and identification efficiency for the forward barrel determined from data (left) and Monte Carlo simulation (right). [GeV] T p 1.5 2 2.5 3 3.5 E ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 efficiency_backwbarrel 80°<θ<135° [GeV] T p 1.5 2 2.5 3 3.5 E ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 efficiency_backwbarrel Figure 5.21: Muon reconstruction and identification efficiency for the backward barrel determined from data (left) and Monte Carlo simulation (right). high pt part, the fit is only performed for the region with pt > 2.0 GeV. Only muons in this region are used for this analysis. In general, the efficiency is overestimated by the simulation. It is assumed that the reconstruction efficiency is the same for muons from elastic J/ψ decays and muons in a jet environment. The pt dependent correction function is given in figure 5.23. The correction factor is in the range from −9% to −5% for the backward part of the barrel region and from −5% to +3% for the forward part of the barrel region. For the forward end- cap a constant correction factor of 20% is used for the region p > 4 GeV which corresponds to pt > 2 GeV. The Monte Carlo simulation is corrected by applying these correction factors. Technically this is done by applying a momentum depen- dent reweighting of the simulated events for each of the three investigated detector regions. The results of this investigation are summarized in table 5.7. The limited statistics of the data sample, especially in the high momentum region, leads to a non negligible systematic uncertainty introduced by this method. This uncertainty is estimated by the relative error of the parameter �max determined from the fit. A conservative overall uncertainty of 3% is estimated for the muon identification. 87 [GeV]p E ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 efficiencyp_forwendcap 2 3 4 5 15°<θ<30° p [GeV] 2 3 4 5 E ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 efficiencyp_forwendcap Figure 5.22: Muon reconstruction and identification efficiency for the forward endcap determined from data (left) and Monte Carlo simulation (right). [GeV] t p 2 2.2 2.4 2.6 2.8 3 3.2 3.4 C o rr e c ti o n fa c to r 0.75 0.8 0.85 0.9 0.95 1 [2]/(1+exp(-[0]*x+[1])) 30°<θ<80° [GeV] t p 2 2.2 2.4 2.6 2.8 3 3.2 3.4 C o rr e c ti o n fa c to r 0.75 0.8 0.85 0.9 0.95 1 [2]/(1+exp(-[0]*x+[1])) 80°<θ<135° Figure 5.23: Correction factors for the muon reconstruction and identification efficiencies for the forward barrel (left) and the backward barrel (right). Detector region Polar angle efficiency rel. correction backward barrel 80◦ ≤ θ ≤ 135◦ 82% −9% to −5% forward barrel 30◦ ≤ θ ≤ 80◦ 75% −5% to +3% forward endcap 15◦ ≤ θ ≤ 30◦ 89% +20% Table 5.7: Muon reconstruction and identification efficiencies as determined from data for the different detector regions. Also given is the range of correction factors. The efficiency denotes the value �max for the plateau region. Elastic J/ψ selection two well measured primary vertex fitted tracks of opposite charge invariant mass 2.8 GeV ≤ mμμ ≤ 3.2 GeV one identified muon in the calorimeter (Quality ≥ 2) 20◦ ≤ θμ ≤ 30◦, 30◦ ≤ θμ ≤ 80◦, 80◦ ≤ θμ ≤ 135◦ |zvtx| < 35 cm Table 5.8: Cuts for the J/ψ selection. 88 cut value transverse momentum pjett > 6.0 GeV pseudorapidity |ηjet| ≤ 2.5 number of associated particles > 2 Table 5.9: Jet selection cuts. The cuts that define the kinematic range of this analyis are in bold letters. 5.6 Selection of Jets Using the output of the jet algorithm, a muon jet association is performed. The selected muon has to be part of a jet that fulfills the jet selection criteria (denoted as muon jet in the following). The minimum transverse momentum of the jet is 6 GeV, the pseudorapidity range is restricted to the detector region |ηjet| ≤ 2.5. To reject possible background from cosmic muons, the number of particles associated to the jet has to be larger than two. The polar angle distribution of the muon jet is shown in figure 5.24, both before and after reweighting of the muon pseudorapidity distribution (see section 5.5). As expected, also this distribution is well described after the reweighting. In addition, in figure 5.25 the transverse momentum distribution, the jet multiplicity distribu- tion and the distribution for the number of associated particles are shown. The transverse momentum distribution is well described, no further reweighting has to be applied. For the jet multiplicity distribution, only jets fulfilling the jet selection criteria (table 5.9) are counted. The distribution is reasonably well described, the majority of events having one or two reconstructed jets, only a small fraction of events having three reconstructed jets. Also the multiplicity distribution of parti- cles belonging to the selected jet is reasonably well described. This measurement relies on a precise understanding of the jet structure. Therefore the energy flow of the jets is studied in more detail. The results are shown in figure 5.26. For all selected events of the heavy quark enriched sample, the aver- age transverse momentum summed over all hadronic final state particles close in azimuthal angle (Δφ < 1) to the jet axis is determined with respect to the distance in pseudorapidity. In an analogous way this is done for all particles close in pseu- dorapidity (Δη < 1) with respect to the azimuthal distance. Both distributions are compared to the Monte Carlo simulation, an excellent agreement for these distribu- tions is achieved. For all the jet control distributions shown, the full event selection including the DIS selection and the muon selection was performed. The jet selection cuts are summarized in table 5.9. 5.7 Summary of the Selection All the cuts defining the kinematic range of this analysis are summarized in table 5.10. In total, 11420 events are selected. The run dependence of the selection (event 89 [deg.]θ 100 140 180 0 200 400 600 800 b MC c+uds MC sum MC Data 6020 N u m b e r o f e v e n ts N u m b e r o f e v e n ts 0 200 400 600 800 b MC c+uds MC sum MC Data [deg.]θ 100 140 1806020 Figure 5.24: Polar angle distribution for the jet selection. The left plot is before, the right plot after reweighting the pseudorapidity distribution of the selected muon. [GeV]tP 5 10 15 20 25 30 35 N u m b e r o f e v e n ts 1 10 210 310 b MC c+uds MC sum MC Data # jets 0 1 2 3 4 N u m b e r o f e v e n ts 0 1000 3000 5000 7000 b MC c+uds MC sum MC Data # objects 0 5 10 15 20 25 30 N u m b e r o f e v e n ts 0 400 800 1200 1600 b MC c+uds MC sum MC Data Figure 5.25: Transverse momentum of the muon jet (upper left), multiplicity for jets fulfilling the jet selection criteria (upper right) and number of particles belonging to the muon jet (bottom). 90 [rad] -3 -2 -1 0 1 2 3 > [G e V ] t < p 0 1 2 Δφ [rad]ηΔ -3 -2 -1 0 1 2 3 > [ G e V ] t < p 0 0.5 1 1.5 2 2.5 jetenergyflow2 Figure 5.26: Energy flow distributions for the selected jet cut value Virtuality 3.5 GeV2 < Q2 < 100 GeV2 Inelasticity 0.1 < ys < 0.7 muon transverse momentum pμt > 2.0 GeV muon pseudorapidity −0.75 ≤ ημ ≤ 2.0 jet transverse momentum pjett > 6.0 GeV jet pseudorapidity |ηjet| ≤ 2.5 Table 5.10: Summary of all selection cuts that define the kinematic range of this analysis. yield) is shown in figure 5.27. No time dependence is observed, the event yield is flat within errors with respect to the run number. On average 40 events are selected per inverse picobarn luminosity. 91 Run Number 420 440 460 480 500 3 10· -1 E v e n ts / p b 0 10 20 30 40 50 60 05e- 06e - 06/07e+ Figure 5.27: Number of selected events per inverse picobarn luminosity. The dif- ferent run periods are indicated. 92 Chapter 6 Measurement In this chapter the measurement of the cross section for beauty quark production in deep inelastic scattering is discussed. The measurement of the beauty content of the event sample is presented, followed by a discussion of correction factors that have to be applied to the measured number of beauty events. Finally the systematic studies are explained in detail. 6.1 Cross Section Definition In this thesis, the cross section is measured for beauty quark production with a muon and a jet in the final state, ep → ebb̄X → ejμX′ in the range 3.5 GeV2 ≤ Q2 ≤ 100 GeV2, 0.1 < y < 0.7 with pμt > 2.0 GeV, −0.75 < ημ < 2 and p jet t > 6.0 GeV. The jets are defined using the kT -algorithm on all final state particles after the decay of charmed or beauty hadrons. Muons coming from both direct and indirect b decays (including τ and J/Ψ decays) are considered to be part of the signal. Muons from decays of light flavoured hadrons (inflight decays, see section 5.2.1) are regarded as background. 6.2 Cross Section Determination In general, the cross section measurement is a counting experiment: the total visible cross section σvisb (ep → ebb̄X → ejμX ′) is determined from the number of measured beauty events for this process, Nb, and the luminosity L, Nb = L · σvisb . (6.1) For the measurement of bin averaged differential cross sections the number of selected events Nb(xi) for each bin xi has to be divided by the bin width Δxi, Nb(xi) Δxi = L · Δσvisb Δx |Bin i. (6.2) The different variables x investigated in this analysis are Q2, the scaling variable x, the transverse momentum of the muon and the jet, and the pseudorapidity of the 93 muon.1 The different binnings for these variables are given in the result tables in appendix C. Double differential cross sections are determined in an analogous way Nb(xi, yi) Δxi · Δyi = L · Δσvisb ΔxΔy |Bin i,j, (6.3) where y is a second variable. In this analysis double differential cross sections are measured as a function of the transverse momentum of the jet for different muon pseudorapidity regions and as a function of log(x) for different Q2. The measured number of beauty events Nb is determined from the number of ob- served beauty events N obsb : Nb = N obs b · � −1, (6.4) where � is the factor that corrects for the limited acceptance, efficiency and resolution of the detector, for events with muons from inflight decays and not direct or indirect decays, and for events that do not carry a muon at all but are selected due to a misidentified hadron. This correction factor is discussed in section 6.4. The number of observed beauty events N obsb is determined from the total number of observed events N obs by measuring the fraction of beauty events fb for the event sample: N obsb = N obs · fb (6.5) This measurement is discussed in the following section. 6.3 Measurement of Beauty Fractions The main experimental challenge of this analysis is the measurement of the fraction of selected events originating from decays of beauty mesons. The cross produc- tion rates of light, charm and beauty quarks at HERA roughly scale like σ(uds) : σ(charm) : σ(beauty) = 2000 : 200 : 1. Beauty production is strongly suppressed due to the limited kinematic phase space and the smaller electric charge of the down type beauty quark compared to the up type charm quark. When requiring a high pt muon, heavy quarks are enriched, the ratio is then about σ(uds) : σ(charm) : σ(beauty) = 2 : 5 : 3.2 Light flavour events still give a large contribution to the sample due to the large cross section for light quarks. To measure the beauty fraction, a statistical method is used, based on a fit of tem- plate distributions derived from Monte Carlo simulations to the data. Only the transverse momentum distribution of the muon with respect to the jet axis prelt as an input for this method. In the following, the definition of the variable used to determine the beauty fraction is presented, the statistical method is discussed and the fit results are presented. 1For the cross section plots the bin averaged cross sections are denoted as dσ dx and shown at the middle of the bin. No bin-centre correction is performed. 2This ratio was determined in [8], where the charm and beauty fractions could be disentangled, which is not possible for this analysis (see section 9). 94 rel t p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 0 200 400 600 800 1000 1200 1400 1600 b MC c+uds MC sum MC Data [GeV] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 1 10 2 10 3 10 b MC c+uds MC sum MC Data rel t p [GeV] Figure 6.1: prelt distribution for the selected events shown in linear (left) and logarithmic (right) scale, compared to the simulation, which is the sum of the two template distributions, weighted according to the fit result. The fraction of the beauty sample as obtained from the fit is 24.6%. [GeV]rel t p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 0 100 200 300 400 500 600 700 ptreltrack_xgammabins 0.00 < < 1.00 [GeV]rel t p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 10 210 ptreltrack_xgammabins 0.00 < < 1.00 Figure 6.2: Shown is the prelt distribution for the highest momentum track with respect to the jet axis for a sample with no muon requirement, compared to the simulation shown in linear (left) and logarithmic (right) scale. 6.3.1 Relative Transverse Momentum The transverse momentum of the muon with respect to the jet axis is determined as follows: prelt = |pμ × (pjet − pμ)| |pjet − pμ| (6.6) Following the procedure adapted in the previous analysis [8], the muon momentum is subtracted from the jet momentum. The alternative definition of this variable where the muon momentum is not subtracted is discussed in section 6.6 in the context of the systematic studies. The difference in the fit results for both methods is the major contribution to the systematic uncertainty of this analysis. The measured distribution of prelt is shown in figure 6.1 together with the Monte Carlo predictions. The beauty fraction is set to 24% which is the result of the fit 95 of the different template distributions to the data. This method is only valid if the contribution from light quark events, which are mainly misidentified hadrons, is well described. This is indeed the case, as shown in figure 6.2. For this check a light quark sample was selected by omitting the muon requirement. In this case prelt is defined as the transverse momentum of the highest momentum track with respect to the jet axis, analogue to (6.16). 6.3.2 Binned Likelihood Fit The prelt distributions for the different Monte Carlo sources are used as templates to determine the fraction of beauty events in the data. Since the shapes of the distributions are not given by a smooth function, the data as predicted from the simulation has to be binned and a binned likelihood fit has to be performed where the distributions for each bin content is assumed to be a Poisson distribution both for data and simulation. For this analysis an extended method is used as proposed in [31] where as an additional degree of freedom for each template component also fluctuations of the number of simulated events are taken into account. This is necessary if the Monte Carlo statistics is limited which is the case for this analysis. In addition, this method is applicable for Monte Carlo templates with empty bins and weighted Monte Carlo templates. The implementation used for this anlysis is provided by the Root analysis package [41] and uses the MINUIT minimization library [77]. In the following a short outline of this fit method is given. When using m templates, the number of events in bin i as predicted from the simulation is fi = m∑ j=1 pjaji, (6.7) where pj are the strength factors3 one is interested in and aji are the number of Monte Carlo events from source j in bin i. Assuming a Poisson distribution for the bin contents, the logarithm of the likelihood is given by ln L = n∑ i=1 di ln fi − fi, (6.8) where di is the number of measured events in bin i, and n is the number of bins. To take into account fluctuations of the number of Monte Carlo events, the number of data events in a bin is not given by equation 6.7, but fi = m∑ j=1 pjAji, (6.9) 3The actual fractions Pj are obtained when considering the normalization of the template samples with Nj events to the data sample with ND events: Pj = pj Nj /ND. 96 where Aji is the unknown expected number of events for source j in bin i. The corresponding likelihood that has to be maximized is ln L = n∑ i=1 (di ln fi − fi) + n∑ i=1 m∑ j=1 (aji ln Aji − Aji). (6.10) This method results in one additional free parameter Aji for each template bin in which one is not interested in. A simplification is possible by solving the m differentials of equation (6.10) with respect to pj in an interative procedure. For each step of the iteration and given values for pj , a set of n equations di 1 − ti = ∑ j pj aij 1 + pjti , (6.11) is solved for ti. The new values of Aji for the next step of the iteration are then given by the relation Aji = aji 1 + pjti . (6.12) This method has the advantage that it can also be used for reweighted Monte Carlo distributions. This is important for this analysis for several reasons, including the study of systematic effects (see section 6.6). In this case eqs. (6.11) and (6.12) have to be modified by di 1 − ti = ∑ j pj wjiaji 1 + pj wjiti (6.13) and Aji = aji 1 + pjwjiti , (6.14) where wji is the average weight for source j in bin i.4 6.3.3 Fit Results The prelt distributions obtained from the beauty Monte Carlo sample and the in- clusive Monte Carlo samples are used as input templates to the fit procedure as described above. Although this method is sensitive to the amount of light quark events, it is not able to distinguish the charm and the light quark fractions. There- fore the fit is performed using two input templates, the beauty template sample and the charm/light quark template. The latter template is based on the inclusive sample where the events originating from beauty quarks are removed. In this way a Monte Carlo dependency is introduced, since it is assumed that the ratio of events originating from light quarks and charm quarks is correctly described. The shapes for the light and charm quark distribution are compared in figure 6.3. The light 4To obtain this average weight for each bin, a template histogram with no weights applied to the events is filled. The average weight for a bin is then given by the ratio of entries for the weighted and unweighted template. 97 [GeV]rel t p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 1 10 210 310 PtRel_xgammabins_cincl 0.00 < < 1.00 uds c Figure 6.3: Comparison of the prelt shape for light and charm quark events. quark distribution has a slightly more pronounced tail for high prelt . The corre- sponding systematic uncertainty, which is of the order of the statistical uncertainty of the fit, is discussed in section 6.6. The fit yields a fraction of 24% beauty events for the selected data sample, which is measured with a statistical relative uncertainty of 4%. The statistical error of the fit is the major contribution to the statistical uncertainty. As expected, the statistical error is larger for the differential measurements. Due to the reduced statistics of both data and simulated samples the error reaches values up to 15%, which is com- parable to the total systematic uncertainty of this measurement (see section 6.6). The fractions and corresponding values for χ2 obtained from the fit for the different binnigs are shown in figures 6.4 and 6.5. For most bins, the χ2 value (per degree of freedom) is between 1 and 2. To check the stability of the fit, the number of bins is modified from 40 bins to 20 and 10 bins. No deviation of the fit result within the errors and the fit quality is observed. The main features of the beauty fraction measurement are as follows: • The dependency on Q2 and log x is flat within the errors. • A strong dependency on the transverse muon momentum is observed, the mea- sured beauty fraction increases towards higher momentum and reaches a maxi- mum value of about 50%. This is expected as the light quark cross section rises very fast towards low jet transverse momenta, whereas the rise is slower for heavy quarks due to their mass. This momentum dependence is reflected in the measurement with respect to the transverse jet momentum. The prelt -spectra for data and Monte Carlo for the different bins of the muon transverse momentum are shown in figure 6.6. • The measurements show a dependency on the polar angle of the muon. The background contribution to the selected sample is highest for the central region 98 of the detector and decreases towards the forward region. This can be explained by the fact that the amount of material the hadrons have to traverse is lowest for the central region. 99 [GeV 2 ]2Q 10 2 10 b e a u ty fr a c ti o n 0 0.1 0.2 0.3 0.4 bfractions_myq2bins ]2 [GeV2Q 10 210 /n d f. 2 χ 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 fitchi2_myq2bins logx -4 -3.5 -3 -2.5 b e a u ty f ra c ti o n 0 0.1 0.2 0.3 0.4 bfractions_mylogxbins logx -4 -3.5 -3 -2.5 /n d f. 2 χ 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 fitchi2_mylogxbins [GeV]μ T p 2 3 4 5 6 7 8 9 10 b e a u ty f ra c ti o n 0.2 0.3 0.4 0.5 bfractions_mymuonptbins [GeV]μ T p 2 3 4 5 6 7 8 9 10 /n d f. 2 χ 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 fitchi2_mymuonptbins Figure 6.4: Results of the prelt fits (left column) and the corresponding χ 2/ndf. (right column) for the different analysis intervals. To summarize, the prelt method gives stable results with small errors and very good χ2 values for the fit. This justifies the use of this variable for a one dimen- sional fit without additional lifetime information. Nevertheless a large dominating systematic error has to be applied due to a possible bias of this method (see section 6.6). 100 μη -0.5 0 0.5 1 1.5 2 b e a u ty f ra c ti o n 0.2 0.25 0.3 0.35 bfractions_mymuonetabins μη -0.5 0 0.5 1 1.5 2 /n d f. 2 χ 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 fitchi2_mymuonetabins [GeV]jet T p 10 15 20 25 30 b e a u ty f ra c ti o n 0 0.1 0.2 0.3 0.4 bfractions_mymuonjetptbins [GeV]jet T p 10 15 20 25 30 /n d f. 2 χ 1.2 1.3 1.4 1.5 1.6 1.7 1.8 fitchi2_mymuonjetptbins Figure 6.5: Results of the prelt fits (left column) and the corresponding χ 2/ndf. (right column) for the different analysis intervals. 101 [GeV]rel t p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N u m b e r o f e v e n ts 1 10 2 10 b MC c+uds MC sum MC Data 2.0

2.0 GeV • −0.75 < ημ < 2 • pjett > 6 GeV • |ηjet| < 2.5 yields a cross section of σvis(ep → ebb̄X → ejμX′) = 29.3 ± 1.3(stat.) ± 4.1(sys.) pb. (7.1) The uncertainty of the measurement is dominated by the systematic uncertainty of about 14% which is approximately three times larger than the statistical uncertainty. This measurement is compared to predictions from the RAPGAP and CASCADE Monte Carlo programs. The prediction from RAPGAP is σRAP GAPvis (ep → ebb̄X → ejμX ′) = 14.0 pb, (7.2) from CASCADE σCASCADEvis (ep → ebb̄X → ejμX ′) = 17.7 pb. (7.3) 116 The RAPGAP Monte Carlo prediction is about 3σ lower than the measurement, the CASCADE Monte Carlo prediction is about 1.8σ lower. The prediction from the NLO calculation, corrected to hadron level, is σN LOvis (ep → ebb̄X → ejμX ′) = 14.4+7.3−1.1 pb. (7.4) This prediction is compatible with both Monte Carlo predictions, but about 1.8σ lower than the data. 7.3 Differential Cross Sections Differential cross sections are determined in bins of the transverse momentum of the muon and jet, pseudorapidity of the muon, Q2 and log x and compared to the NLO and Monte Carlo predictions in the following sections. The measured cross sections and NLO predictions are given in appendix C. 7.3.1 Comparison to NLO Prediction The NLO prediction lies below the data for most of the measured bins, with the difference at most 2 to 3σ. A steep rise towards small Q2 is measured (see figure 7.1). The NLO prediction for the lowest bin is compatible with the data, but the shape of the distribution is not described very well. The deviation of the prediction to the data increases towards higher Q2, with about 2.9σ difference for the highest bin. The differential cross section as a function of the scaling variable x is shown in figure 7.2, the shape of the distribution is described reasonably well, the prediction is below the data for most of the bins. The cross section as a function of the pseudorapidity of the muon is shown in figure 7.3. The cross section rises towards the forward region and falls for the most forward bin. The rise of the cross section is not described by the prediction. The differential cross sections as a function of the muon and jet transverse momentum fall steeply towards higher transverse momenta. The data show a steeper behaviour than the predictions, with a difference of about 2σ for the lowest bins. 117 ]2 [GeV2Q 10 210 ]2 [ p b /G e V 2 /d Q σ d -110 1 HERA II NLO Hadronlevel ]2 [GeV2Q 10 210 ]2 [ p b /G e V 2 /d Q σ d -110 1 xsection_myq2bins Figure 7.1: Differential Born level cross section as a function of Q2. The data is compared to the HVQDIS NLO prediction. log x -4 -3.5 -3 -2.5 /d lo g x [ p b ] σ d 0 5 10 15 20 25 HERA II NLO Hadronlevel log x -4 -3.5 -3 -2.5 /d lo g x [ p b ] σ d 0 5 10 15 20 25 xsection_mylogxbins Figure 7.2: Differential Born level cross section as a function of log x. The data is compared to the HVQDIS NLO prediction. 118 μη -0.5 0 0.5 1 1.5 2 [ p b ] μ η /d σ d 0 2 4 6 8 10 12 14 16 18 HERA II NLO Hadronlevel μη -0.5 0 0.5 1 1.5 2 [ p b ] μ η /d σ d 0 2 4 6 8 10 12 14 16 18 xsection_mymuonetabins Figure 7.3: Differential Born level cross section as a function of ημ. The data is compared to the HVQDIS NLO prediction. [GeV]μ t p 2 3 4 5 6 7 8 9 10 [ p b /G e V ] μ T /d p σ d 1 10 HERA II NLO Hadronlevel [GeV]μ t p 2 3 4 5 6 7 8 9 10 [ p b /G e V ] μ T /d p σ d 1 10 xsection_mymuonptbins Figure 7.4: Differential Born level cross section as a function of pμt . The data is compared to the HVQDIS NLO prediction. 119 [GeV]Jet T p 10 15 20 25 30 [ p b /G e V ] J e t T /d p σ d 1 HERA II NLO Hadronlevel [GeV]Jet T p 10 15 20 25 30 [ p b /G e V ] J e t T /d p σ d 1 xsection_muonjetptbins Figure 7.5: Differential Born level cross section as a function of pjett . The data is compared to the HVQDIS NLO prediction. 120 ]2 [GeV2Q 10 210 ]2 [ p b /G e V 2 /d Q σ d -110 1 HERA II Rapgap x 2.1 Cascade x 1.7 xsection_myq2bins Figure 7.6: Differential Born level cross section as a function of Q2. The data is compared to RAPGAP and CASCADE Monte Carlo predictions. 7.3.2 Comparison to Monte Carlo Prediction The cross section measurements are compared to the predictions of the RAPGAP and CASCADE Monte Carlo generators (see figures 7.6-7.10). The predictions are scaled with a factor 2.1 and 1.7 for RAPGAP and CASCADE respectively. The scaling factors are determined from the predictions and measurements for the total visible range. With exception of the lowest Q2 bin, where the scaled prediction is below the data, all distributions are well described in shape by the predictions. Both RAPGAP and CASCADE describe the steep rise of the cross section towards small transverse momenta (see figure 7.9). The rise of the cross section towards the forward direction of the muon is better described by the CASCADE prediction (see figure 7.8). 121 log x -4 -3.5 -3 -2.5 /d l o g x [ p b ] σ d 0 5 10 15 20 25 HERA II Rapgap x 2.1 Cascade x 1.7 xsection_mylogxbins Figure 7.7: Differential Born level cross section as a function of log x. The data is compared to RAPGAP and CASCADE Monte Carlo predictions. μη -0.5 0 0.5 1 1.5 2 [ p b ] μ η /d σ d 0 2 4 6 8 10 12 14 16 18 HERA II Rapgap x 2.1 Cascade x 1.7 xsection_mymuonetabins Figure 7.8: Differential Born level cross section as a function of η. The data is compared to RAPGAP and CASCADE Monte Carlo predictions. 122 [GeV]μ T p 2 3 4 5 6 7 8 9 10 [ p b /G e V ] μ T /d p σ d 1 10 HERA II Rapgap x 2.1 Cascade x 1.7 xsection_mymuonptbins Figure 7.9: Differential Born level cross section as a function of pμt . The data is compared to RAPGAP and CASCADE Monte Carlo predictions. [GeV]Jet T p 10 15 20 25 30 [ p b /G e V ] J e t T /d p σ d 1 HERA II Rapgap x 2.1 Cascade x 1.7 xsection_mymuonjetptbins Figure 7.10: Differential Born level cross section as a function of pjett . The data is compared to RAPGAP and CASCADE Monte Carlo predictions. 123 7.4 Double Differential Cross Sections To clarify the measurements of the cross sections as a function of the jet transverse momentum, the measurement is performed double differentially for three regions of the muon pseudorapidity: • −0.75 < η < 0 • 0 < η < 0.5 • 0.5 < η < 2 In addition the differential cross sections with respect to log x are measured for five Q2 ranges: • 3.5 < Q2 < 7 GeV2 • 7 < Q2 < 13 GeV2 • 13 < Q2 < 25 GeV2 • 25 < Q2 < 50 GeV2 • 50 < Q2 < 100 GeV2 The results are tabularized in appendix C and compared to the theory predictions in the following sections. 7.4.1 Comparison to NLO Predictions In figure 7.11 the measurements as a function of the jet transverse momentum are compared to the NLO prediction for three different bins of the muon pseudorapidity. Whereas shape and normalization are well described for the central region, the steep rise of the cross section for the forward region is not predicted by the NLO calculation. The prediction lies below the data with a difference of about 3.1σ for the lowest bin of the jet transverse momentum, but agrees within errors for large jet transverse momenta. The measurements as a function of the scaling variable x are compared to the NLO prediction for five different bins of Q2. In general the prediction is too low, with a deviation of at most 2.2σ. 124 [GeV]Jet T p 10 15 20 25 30 [p b /G e V ] η μ d J e t T /d p σ -1 10 1 HERA II NLO Hadronlevel [GeV]Jetp 10 15 20 25 30 [p b /G e V ] d J e t T d 2 -1 10 1 -0.75<η<0 [GeV]Jet T p 10 15 20 25 30 -1 10 1 [GeV]Jetp 10 15 20 25 30 -1 10 1 [p b /G e V ] η μ d J e t T /d p σ [p b /G e V ] d J e t T d 2 0<η<0.5 [GeV]Jet T p 10 15 20 25 30 -1 10 1 [GeV]Jetp 10 15 20 25 30 -1 10 1 [p b /G e V ] η μ d J e t T /d p σ [p b /G e V ] d J e t T d 2 0.5<η<2 Figure 7.11: Double differential Born level cross section as a function of pjett for three different ranges of the muon pseudorapidity. The data is compared to the HVQDIS NLO prediction. 125 log x -4 -3.8 -3.6 -3.4 ] [p b /G e V 2 2 σ /d lo g (x )d Q 2 d 0 1 2 3 HERA II NLO Hadronlevel log x -4 -3.8 -3.6 -3.4 0 1 2 3 3.5 2.5 GeV • −0.75 < ημ < 1.15 • pjet,Breitt > 6 GeV • |ηjet| < 2.5 is σBreitvis (ep → ebb̄X → ejμX ′) = 13.4 ± 0.9(stat.) ± 1.9(sys.) pb. (7.5) Only about half of the events compared to the laboratory frame analysis are selected, leading to a higher statistical uncertainty of 6.7%. The same systematic uncertainty of 14% is assumed. The result of this measurement is 60% higher than the RAPGAP Monte Carlo prediction, corresponding to a deviation of about 3σ. The differential cross sections and the comparison to the RAPGAP Monte Carlo prediction are shown in figure 7.16. The RAPGAP prediction is scaled by a factor of 1.6 to account for the normalization difference. The shapes of all differential distributions are reasonably well described by the Monte Carlo prediction, no significant deviations are observed. This Breit frame measurement is compared to the published H1 measurement by extrapolating the cross sections from the kinematic range Q2 > 3.5 GeV2 to Q2 > 2 GeV2 using the Monte Carlo prediction. The measured total cross section is scaled up by 17%, yielding σBreitvis (ep → ebb̄X → ejμX ′) = 15.7±1.1(stat.)±2.2(sys.)±0.5(extrapol.) pb (7.6) for the kinematic range • 2 < Q2 < 100 GeV2 • 0.1 < y < 0.7 • pμt > 2.5 GeV • −0.75 < ημ < 1.15 • pjet,Breitt > 6 GeV • |ηjet| < 2.5. The statistical error is 6.7% and a systematic uncertainty of 14% as determined in the laboratory frame analysis is assumed. The uncertainty in the extrapolation 129 due to the limited Monte Carlo statistics is taken into account by an additional uncertainty of 3.5% on the measurement. The result quoted in the publication is σ Breit,publication vis (ep → ebb̄X → ejμX ′) = 16.3 ± 2.0(stat.) ± 2.3(sys.) pb. (7.7) This new HERA II measurement is in good agreement with the published result. The systematic uncertainty of this measurement is of comparable size and the statistical uncertainty is reduced due to the larger data sample. The differential cross sections are compared in figure 7.15. Also in this case a scaling factor is applied for each individual bin according to the Monte Carlo prediction. All new HERA II data points agree even within statistical errors with the published results, except for the most forward bin of the muon pseudorapidity. A deviation of about 2σ suggest an upward fluctuation of the HERA I measurement. The lowest bins of the muon and jet transverse momenta are systematically lower for the new measurement but still in agreement within errors. 130 ]2 [GeV2Q 10 2 10 ] 2 [p b /G e V 2 /d Q σ d -1 10 1 HERA 1 HERA 2 log x -4.5 -4 -3.5 -3 -2.5 /d lo g x [p b ] σ d 2 4 6 8 10 12 HERA 1 HERA 2 η μ -0.5 0 0.5 1 [p b ] η /d σ d 0 2 4 6 8 10 12 14 16 HERA 1 HERA 2 [GeV] t p 3 4 5 6 7 8 9 10 11 12 [p b /G e V ] t /d p σ d 1 10 HERA 1 HERA 2 [GeV] jet t p 10 15 20 25 30 [p b /G e V ] je t t /d p σ d 1 HERA 1 HERA 2 Figure 7.15: Comparision of double differential cross sections measured in the Breit frame to the published HERA I measurement. Only the statistical errors are shown. For better visibility, the data points of the HERA I measurement are shifted horizontally. 131 ]2 [GeV2Q 10 210 ]2 [ p b /G e V 2 /d Q σ d -110 1 Data HERA2 Rapgap x 1.6 xsection_myq2bins log x -4 -3.8 -3.6 -3.4 -3.2 -3 -2.8 -2.6 -2.4 -2.2 /d lo g x [ p b ] σ d 0 2 4 6 8 10 12 Data HERA2 Rapgap x 1.6 xsection_mylogxbins μη -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 [ p b ] μ η /d σ d 0 1 2 3 4 5 6 7 8 9 10 Data HERA2 Rapgap x 1.6 xsection_muonetabins [GeV]μ t p 3 4 5 6 7 8 9 10 11 12 [ p b /G e V ] μ t /d p σ d 1 10 Data HERA2 Rapgap x 1.6 xsection_muonptbins [GeV]Jet t p 10 15 20 25 30 [ p b /G e V ] J e t t /d p σ d -110 1 Data HERA2 Rapgap x 1.6 xsection_mymuonjetptbins Figure 7.16: Comparision of double differential cross sections measured in the Breit frame to the RAPGAP Monte Carlo prediction. 132 Chapter 8 Summary and Discussion of the Results In this analysis, open beauty quark production in deep inelastic scattering with a muon and a jet in the final state was measured with the H1 detector using approxi- mately 285 pb−1 of HERA II data taken in the years 2005-2007. The beauty fraction of the event sample was determined on a statistical basis using the prelt method which exploits the large transverse momentum with respect to the jet axis of the muon for beauty quark events. The phase space was extended to the forward region and lower transverse muon momenta compared to the previous H1 analysis [8]. All relevant systematic uncertainties were reevaluated, and the detector cuts of the muon system were optimized to obtain a high selection efficiency and a small background contri- bution to the sample. For the visisble range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2.0 GeV, −0.75 < ημ < 2, pjett > 6 GeV and |ηjet| < 2.5 where the jet is reconstructed us- ing the inclusive kt algorithm and selected in the laboratory frame, the total cross section was measured to be σvis(ep → ebb̄X → ejμX′) = 29.3 ± 1.3(stat) ± 4.1(sys.) pb. (8.1) The total uncertainty of the measurement was reduced compared to the previous measurement from about 19% to 15% due to the higher statistics of the data sample. The statistical uncertainty was reduced from 14% to 4.5%. Therefore it was also possible to obtain the same systematic uncertainty of 14% although no additional lifetime information as in the previous analysis was used. The results are compared to theory predictions. The prediction of the next-to- leading order calculation in the massive scheme, using the program HVQDIS, cor- rected to hadron level, is σNLOvis (ep → ebb̄X → ejμX ′) = 14.4+7.3−1.1 pb, (8.2) with a much larger uncertainty than the measurement, dominated by scale uncer- tainties. This prediction is about 1.8σ below the measurement, which is compatible 133 with the findings of the previous H1 and ZEUS measurements in DIS. Due to the large beauty mass one would expect a much better agreement. The predictions of the Monte Carlo programs RAPGAP and CASCADE, which cal- culate the matrix element in leading order in the massive scheme (augmented by parton showers) and use different parton evolution schemes, are compatible with the NLO prediction. The normalization factors are 2.1 and 1.7 for RAPGAP and CASCADE respectively. Differential cross section measurements are performed as a function of Q2, Bjorken x, the muon pseudorapidity, and the muon and jet transverse momenta. For the for- ward direction, at large pseudorapidities of the muon and large Bjorken x, and small muon and jet transverse momenta, the next-to-leading order prediction is up to 2σ below the data. The rise of the cross section towards small transverse momenta is steeper than that predicted by the calculations. These results are compatible with the H1 and ZEUS HERA I measurements and the latest ZEUS HERA II results (see figures 8.1 and 8.2). The interpretation is not clear: possible explanations for this deficiency being missing higher order effects or insufficient modelling of the frag- mentation process. The next-to-leading order calculation does not describe the shape of the Q2 dis- tribtion very well for the small and medium Q2 region covered in this analysis. The prediction is below the data for all bins of this measurement. This is also ob- served in the latest ZEUS measurement, which covers an extended Q2 region up to 10 000 GeV2 (see figure 8.3). The prediction agrees only for Q2 much larger than m2b and p 2 t . This may indicate that the interplay of the different scales is not fully understood. With exception of the lowest Q2 bin, both Monte Carlo generators describe the shape of all measured distributions very well. The rise of the cross section as a function of the muon pseudorapidity is better described by the CASCADE Monte Carlo. The large statistics of the data sample allowed a measurement of double differ- ential distributions. The measurement of the cross section as a function of the jet transverse momentum for three regions of the muon pseudorapidity confirms that the excess at low transverse momenta is most significant in the forward region, where the next-to-leading order calculation predicts a less steeper rise of the cross section towards small transverse momenta. The prediction is about 3σ below the data. In contrast, both Monte Carlo generators describe the shape of the distributions very well for all detector regions. Additionally a double differential measurement of the cross section as a function of the scaling variable x is performed for different Q2 regions. With exception of the lowest Q2 region (which is compatible with the single differential Q2 measurement), the shape of the distribution is well described by the prediction for all other Q2 ranges. As a cross check, the measurement is repeated with the reconstruction and selec- tion performed in the Breit frame. This allows a direct comparison to the previous 134 [GeV]μ t p 2 3 4 5 6 7 8 9 10 [ p b /G e V ] μ T /d p σ d 1 10 HERA II NLO Hadronlevel [GeV]μ t p 2 3 4 5 6 7 8 9 10 [ p b /G e V ] μ T /d p σ d 1 10 xsection_mymuonptbins 1 10 10 2 2 3 4 5 6 7 8 9 10 ZEUS ep→ ebb – X→ e μ X ZEUS (prel.) HERA II 125 pb-1 HVQDISHVQDIS pT μ (GeV) d σ /d p Tμ ( p b /G e V ) 1 10 10 Data NLO QCD ⊗ Had NLO QCD Cascade Rapgap H1ep → ebb − X → ejμX 2 < Q2 < 100 GeV2 3 5 pμt [GeV] d σ /d p μ t[ p b /G e V ] Figure 8.1: Cross section measurements as a function of the muon transverse momentum. Shown are the results of the analysis presented in this thesis (upper left), of the latest ZEUS HERA II measurement using decays into a muon and a jet [38] (upper right), and of the previous H1 (lower left) [8] and ZEUS (lower right) [21] HERA I measurements. 135 μη -0.5 0 0.5 1 1.5 2 [ p b ] μ η /d σ d 0 2 4 6 8 10 12 14 16 18 HERA II NLO Hadronlevel μη -0.5 0 0.5 1 1.5 2 [ p b ] μ η /d σ d 0 2 4 6 8 10 12 14 16 18 xsection_mymuonetabins 10 20 -0.5 0 0.5 1 Data NLO QCD ⊗ Had NLO QCD Cascade Rapgap H1ep → ebb − X → ejμX 2 < Q2 < 100 GeV2 ημ d σ /d η μ [ p b ] Figure 8.2: Cross section measurements as a function of the muon transverse mo- mentum. Shown are the results of the analysis presented in this thesis (upper) and of the previous H1 (lower left) [8] and ZEUS (lower right) [21] HERA I measurements. 136 ]2 [GeV2Q 10 210 ] 2 [ p b /G e V 2 /d Q σ d -110 1 HERA II NLO Hadronlevel ]2 [GeV2Q 10 210 ] 2 [ p b /G e V 2 /d Q σ d -110 1 xsection_myq2bins 10 -4 10 -3 10 -2 10 -1 1 10 2 10 3 10 4 ZEUS ep→ ebb – X→ e μ Xep→ ebb – X→ e μ X ZEUS (prel.) HERA II 125 pb-1 HVQDISHVQDIS Q2(GeV2) d σ /d Q 2 ( p b /G e V 2 ) Figure 8.3: Cross section measurements as a function of Q2. Shown are the results of the analysis presented in this thesis (left) and of the latest ZEUS HERA II muon+jet measurement. [38] (right), which covers a larger Q2 region. H1 results and requires only an extrapolation to lower Q2. For the total and differ- ential cross section measurements, both analyses agree within the statistical errors. 137 138 Chapter 9 Outlook The measurements presented in this thesis are another step towards a better under- standing of beauty quark production at HERA in deep inelastic scattering. From the experimental point of view, the high statistics and precision of the HERA II data, which will remain the last ep-data for the next few decades, has not yet been fully exploited. Whereas a combination with HERA I data and the inclusion of the 2004 run pe- riod of HERA II will not lead to a significant increase of the statistical precision of the measurement, there is still potential to decrease the systematic uncertainties (compared to the HERA I measurements). The next step in this direction would be the additional use of lifetime information. The CST tracking detector is very well understood and delivered high precision data for a large fraction of the HERA II run period [85, 86]. Although additional sources of systematic uncertainty have to be considered, it is possible to reduce the total systematic uncertainty of the measurement by combining both prelt and lifetime information and perfoming a two- dimensional fit to determine the beauty fraction. As an estimation of the charm and light quark content of the event sample is possible when lifetime information is used, the measurement of the contribution from light quark events is possible which allows a reduction of the model uncertainties. Furthermore, a measurement of charm quark cross sections is possible in parallel. The results of this and other analyses show that the forward region (defined by the proton direction) is the most interesting phase space region to study. Due to the limited acceptance of the CST detector, lifetime information is not available for this region and one has to rely on the prelt information alone. Despite the stability of this method and the good agreement between the results obtained from both meth- ods [85], it is necessary to get an understanding of the remaining deficits in the modelling of the prelt distribution, which were seen in this analysis. A step in this direction would be a detailed study of the jet axis resolution for different detector regions. Besides a reduction of the systematic uncertainties, a further extension of the mea- sured phase space region is possible. By extending the measurement to regions where the scattered electron is located in the central region, the large Q2 domain can be 139 investigated. As the momentum transfer is much larger than the beauty mass and the transverse momentum of the beauty quark, a comparison to the theory predic- tions in this region allows a better understanding of the multi scale problem. It was shown in this analysis that the double differential measurement is possible due to the high statistics of the data sample. It has to be investigated whether the precision is sufficient to contribute to the measurement of the beauty quark structure function F b2 , which depends on the double differential cross sections as a function of the scaling variable x and Q2. As the uncertainties of the theoretical predictions are large compared to the system- atic uncertainties of the measurements, also from the theory side further progress is needed to complete the picture of beauty quark production. It would be interesting to compare the data to next-to-leading order predictions. This MC@NLO [64] is not available at present. Next to next to leading order calculations (NNLO) are available from the MRST [114] group in the mixed flavour number scheme, but there are no programs existing yet for calculating single or double differential cross sections. The focus of interest in High Energy Physics will move to the LHC (Large Hadron Collider) at CERN very soon, which is expected to discover new physics beyond the Standard Model. Nevertheless, the interpretation of the new data relies on a good understanding of standard model processes, in particular the production of heavy quarks. This is where the legacy of HERA, which has delivered the last data on electron-proton scattering for the next decades, will contribute to the exploration of the new energy frontier. 140 Appendix A Run Selection 141 Run range Reason 421402 FTT problem 422787-422790 FTT timing tests 422799-422811 FTT timing tests 445534-445553 FTT wrongly configured 452556-452560 FTT RO problem 458838-459181 FTT level 1 topologies not loaded 466189-466227 FTT problem (CJC2) 475320-476029 FTT level 1 problems 483626-483763 FTT problem (low efficiency) 486648-486672 FTT RO problem 487728-487812 FTT RO problem 496354-496372 FTT problem (low efficiency) 496410-496480 FTT problem (low efficiency) Table A.1: List of excluded runs Mnemonic Detector component FTP forward tracker CJC1 inner jet chamber CJC2 outer jet chamber LAr LAr calorimeter FTT Fast Track Trigger LUMI lumi system SPAC SPACAL calorimeter IronClusters Central Muon Detector TOF Time of flight system Table A.2: List of requested detector components for the run selection. The mnemonics as used for the steering of the executable to perform the run selec- tion [113] are given. 142 Appendix B Transformation to the Breit Frame The transformation from the laboratory frame to the Breit frame requires rotations and a boost. The complete transformation that contains the boost and rotates the z axis from the laboratory frame to the Breit frame can be written in the matrix form L(L → B) = Ry(α′)Λ(β)Ry (α). (B.1) All components can be written in terms of the components of q = (q0, q1, 0, q3) which is the four momentum of the exchanged virtual photon in the laboratory frame. When defining D21 = q 2 1 + ( q3 + Q2 q0 − q3 )2 (B.2) and D22 = Q 2q21 + q 2 0(q0 − q3) 2, (B.3) the Lorentz parameter is given by β = D1 q0 + Q2/(q0 − q3) , (B.4) the rotation about the y-axis in the HERA frame is given by sin α = − q1 D2 , cos α = q3 + Q2/(q0 − q3) D1 (B.5) and the final rotation about the y axis in the Breit frame is given by sin α′ = Qq1 D2 , cos α′ = − q0(q0 − q3) D2 . (B.6) 143 Details can be found in [54]. The overall transformation matrix takes the simple form L(L → B) = ⎛ ⎜⎜⎜⎝ q0 Q + Q q0−q3 − q1 Q 0 − q3 Q − Q q0−q3 − q1 q0−q3 1 0 q1 q0−q3 0 0 1 0 q0 Q − q1 Q 0 − q3 Q ⎞ ⎟⎟⎟⎠ . (B.7) 144 Appendix C Cross Section Tables 145 Measurement Experimental errors Correction factors ημ-range dσ/dημ stat. sys. fb �rec δrad [pb] [pb] [pb] [%] [%] [%] -0.75 -0.1 10.5 1.2 1.5 18.1 ± 2.0 24.1 -1 -0.1 0.3 13.2 1.4 1.9 18.9 ± 2.0 31.1 -1 0.3 0.6 14.1 1.6 2.0 21.3 ± 2.3 34.4 -1 0.6 1.0 15.9 1.3 2.2 32.0 ± 2.5 36.1 +2 1.0 2.1 7.03 0.61 0.98 31.3 ± 2.5 34.2 +1 p μ t -range dσ/dp μ t stat. sys. fb �rec δrad [GeV] [pb/GeV] [pb/GeV] [pb/GeV] [%] [%] [%] 2.0 2.3 23.6 4.0 3.3 20.5 ± 3.4 20.2 +1 2.3 2.7 14.8 2.1 2.1 16.9 ± 2.3 25.0 -2 2.7 3.4 9.11 0.92 1.28 18.3 ± 1.8 30.0 +2 3.4 4.0 5.83 0.72 0.82 24.8 ± 2.9 35.2 -1 4.0 5.0 3.52 0.40 0.49 33.3 ± 3.6 43.6 +2 5.0 10.0 0.706 0.072 0.100 48.5 ± 4.5 50.9 -2 p jet t -range dσ/dp jet t stat. sys. fb �rec δrad [GeV] [pb/GeV] [pb/GeV] [pb/GeV] [%] [%] [%] 6.0 8.5 4.30 0.33 0.60 19.1 ± 1.4 37.4 +2 8.5 12.0 2.80 0.20 0.39 26.0 ± 1.8 32.4 -1 12.0 30.0 0.450 0.038 0.063 32.3 ± 2.6 25.1 +1 Q2-range dσ/dQ2 stat. sys. fb �rec δrad [GeV2] [ pb/GeV2] [ pb/GeV2] [ pb/GeV2] [%] [%] [%] 3.5 8.0 1.28 0.15 0.18 21.5 ± 2.5 21.8 -2 8.0 20.0 0.712 0.054 0.100 26.6 ± 1.9 36.5 -2 20.0 35.0 0.353 0.035 0.050 27.2 ± 2.5 35.4 0 35.0 100.0 0.146 0.012 0.020 21.5 ± 1.7 34.2 +1 log x-range dσ/d log x stat. sys. fb �rec δrad [pb] [pb] [pb] [%] [%] [%] -4.1 -3.8 9.98 1.62 1.40 25.2 ± 3.9 20.8 -1 -3.8 -3.5 13.6 1.8 1.9 21.4 ± 2.7 25.2 0 -3.5 -3.3 21.5 2.7 3.0 29.3 ± 3.5 30.1 +1 -3.3 -3.1 18.8 2.1 2.6 26.4 ± 2.8 35.6 +2 -3.1 -2.9 19.6 2.2 2.7 25.5 ± 2.8 35.3 -1 -2.9 -2.7 20.2 2.4 2.8 25.8 ± 2.9 34.7 +2 -2.7 -2.2 10.6 1.1 1.5 20.2 ± 2.0 40.3 -1 Table C.1: Differential cross sections for the process ep → ebb̄X → ejμX′ in the kinematic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. 146 Measurement Experimental errors Correction factors p jet t -range dσ/(dp jet t dη μ) stat. sys. fb �rec δrad [GeV] [pb/GeV] [pb/GeV] [pb/GeV] [%] [%] [%] 6.0 8.5 1.86 0.30 0.26 14.6 ± 2.3 30.4 +2 8.5 12.0 1.18 0.18 0.17 23.8 ± 3.5 24.6 -4 12.0 30.0 0.147 0.032 0.021 34.3 ± 6.9 15.8 -1 Table C.2: Differential cross sections as a function of the transverse momentum of the jet in the kinematic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ηµ < 0, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. Measurement Experimental errors Correction factors p jet t -range dσ/(dp jet t dη μ) stat. sys. fb �rec δrad [GeV] [pb/GeV] [pb/GeV] [pb/GeV] [%] [%] [%] 6.0 8.5 1.81 0.30 0.25 14.6 ± 2.4 38.1 0 8.5 12.0 1.32 0.21 0.18 22.0 ± 3.3 32.1 -1 12.0 30.0 0.211 0.042 0.030 26.5 ± 4.9 22.3 -2 Table C.3: Differential cross sections as a function of the transverse momentum of the jet in the kinematic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, 0 < ηµ < 0.5, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. Measurement Experimental errors Correction factors p jet t -range dσ/(dp jet t dη μ) stat. sys. fb �rec δrad [GeV] [pb/GeV] [pb/GeV] [pb/GeV] [%] [%] [%] 6.0 8.5 1.35 0.13 0.19 28.4 ± 2.7 41.6 +3 8.5 12.0 0.856 0.082 0.120 28.6 ± 2.6 36.6 +1 12.0 30.0 0.173 0.018 0.024 34.3 ± 3.4 28.5 -2 Table C.4: Differential cross sections as a function of the transverse momentum of the jet in the kinematic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, 0.5 < ηµ < 2, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. 147 Measurement Experimental errors Correction factors log x-range dσ/(d log xdQ2) stat. sys. fb �rec δrad [pb] [pb] [pb] [%] [%] [%] -4.1 -3.95 2.46 0.60 0.34 26.7 ± 6.2 19.8 -2 -3.95 -3.8 2.55 0.62 0.36 23.9 ± 5.6 20.1 -1 -3.8 -3.4 1.01 0.26 0.14 15.1 ± 3.7 16.2 -1 Table C.5: Differential cross sections as a function of the scaling variable x in the kinematic range 3.5 < Q2 < 7.0 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. Measurement Experimental errors Correction factors log x-range dσ/(d log xdQ2) stat. sys. fb �rec δrad [pb/GeV2] [pb] [pb] [%] [%] [%] -3.7 -3.5 1.46 0.25 0.20 24.9 ± 3.9 33.9 -6 -3.5 -3.3 1.29 0.24 0.18 31.3 ± 5.6 39.0 0 -3.3 -3.1 0.658 0.141 0.092 22.3 ± 4.6 45.8 -1 Table C.6: Differential cross sections as a function of the scaling variable x in the kinematic range 7.0 < Q2 < 13.0 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. Measurement Experimental errors Correction factors log x-range dσ/(d log xdQ2) stat. sys. fb �rec δrad [pb/GeV2] [pb] [pb] [%] [%] [%] -3.4 -3.2 0.906 0.140 0.127 32.2 ± 4.7 34.1 0 -3.2 -3.0 0.756 0.116 0.106 29.3 ± 4.2 39.5 -3 -3.0 -2.8 0.538 0.100 0.075 27.8 ± 4.8 44.8 -8 Table C.7: Differential cross sections as a function of the scaling variable x in the kinematic range 13 < Q2 < 25 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. Measurement Experimental errors Correction factors log x-range dσ/(d log xdQ2) stat. sys. fb �rec δrad [pb] [pb] [pb] [%] [%] [%] -3.1 -2.9 0.363 0.062 0.051 27.0 ± 4.3 32.9 -1 -2.9 -2.7 0.389 0.066 0.054 26.6 ± 4.3 38.0 -5 -2.7 -2.5 0.278 0.049 0.039 24.6 ± 4.1 46.5 -9 Table C.8: Differential cross sections as a function of the scaling variable x in the kinematic range 25 < Q2 < 50 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. 148 Measurement Experimental errors Correction factors log x-range dσ/(d log xdQ2) stat. sys. fb �rec δrad [pb] [pb] [pb] [%] [%] [%] -2.8 -2.6 0.182 0.037 0.025 27.1 ± 5.3 28.3 +5 -2.6 -2.4 0.144 0.030 0.020 16.2 ± 3.3 37.1 -2 -2.4 -2.1 0.099 0.019 0.014 19.2 ± 3.5 46.9 -2 Table C.9: Differential cross sections as a function of the scaling variable x in the kinematic range 50 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. Also given are correction factors as obtained from the Monte Carlo simulation and the beauty fractions of the event sample. 149 NLO prediction Theor. uncertainty Correction to hadron level ημ-range dσ/dημ Sys. Ch − 1 [pb] [pb] [%] -0.75 -0.1 5.61 +2.69−3.81 -10.0 -0.1 0.3 7.72 +2.94−1.47 -9.2 0.3 0.6 7.31 +3.56−1.07 -8.6 0.6 1.0 6.21 +3.20−1.04 -8.0 1.0 2.1 2.97 +0.97−0.42 -8.2 p μ t -range dσ/dp μ t Sys. Ch − 1 [GeV] [pb/GeV] [pb/GeV] [%] 2.0 2.3 9.00 +4.30−1.63 -11.5 2.3 2.7 7.12 +2.89−1.22 -11.0 2.7 3.4 5.05 +2.15−1.02 -10.5 3.4 4.0 3.13 +1.43−0.38 -8.5 4.0 5.0 1.88 +0.76−0.28 -6.0 5.0 10.0 0.36 +0.15−0.05 -0.5 p jet t -range dσ/dp jet t Sys. Ch − 1 [GeV] [pb/GeV] [pb/GeV] [%] 6.0 8.5 1.96 +0.76−0.00 -17.0 8.5 12.0 1.37 +0.65−0.22 -10.5 12.0 30.0 0.29 +0.14−0.05 +10.0 Table C.10: Predictions from next-to-leading order QCD calculations in the kine- matic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. 150 NLO prediction Theor. uncertainty Correction to hadron level Q2-range dσ/dQ2 Sys. Ch − 1 [GeV2] [ pb/GeV2] [ pb/GeV2] [%] 3.5 8.0 0.82 +0.25−0.15 -9.0 8.0 20.0 0.34 +0.15−0.06 -10.0 20.0 35.0 0.16 +0.07−0.02 -9.5 35.0 100.0 0.06 +0.02−0.01 -7.5 log x-range dσ/d log x Sys. Ch − 1 [pb] [pb] [%] -4.1 -3.8 5.26 +2.74−0.93 -7.2 -3.8 -3.5 8.61 +3.87−0.77 -9.4 -3.5 -3.3 10.17 +5.45−2.03 -9.6 -3.3 -3.1 10.01 +4.53−1.82 -9.0 -3.1 -2.9 9.90 +3.85−1.80 -10.0 -2.9 -2.7 8.95 +4.22−1.34 -8.2 -2.7 -2.2 4.55 +1.72−0.64 -9.0 Table C.11: Predictions from next-to-leading order QCD calculations in the kine- matic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. 151 NLO prediction Theor. uncertainty Correction to hadron level p jet t -range dσ/(dp jet t dη μ) sys. Ch − 1 [GeV] [pb/GeV] [pb/GeV] [%] 6.0 8.5 0.95 +0.47−0.15 -17 8.5 12.0 0.60 +0.22−0.11 -9 12.0 30.0 0.09 +0.04−0.02 +13 Table C.12: Predictions from next-to-leading order QCD calculations in the kinematic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ηµ < 0, pjett > 6 GeV and |ηjet| ≤ 2.5. NLO prediction Theor. uncertainty Correction to hadron level p jet t -range dσ/(dp jet t dη μ) sys. Ch − 1 [GeV] [pb/GeV] [pb/GeV] [%] 6.0 8.5 1.00 +0.45−0.13 -17 8.5 12.0 0.72 +0.40−0.08 -11 12.0 30.0 0.14 +0.09−0.02 +11 Table C.13: Predictions from next-to-leading order QCD calculations in the kinematic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, 0 < ηµ < 0.5, pjett > 6 GeV and |ηjet| ≤ 2.5. NLO prediction Theor. uncertainty Correction to hadron level p jet t -range dσ/(dp jet t dη μ) sys. Ch − 1 [GeV] [pb/GeV] [pb/GeV] [%] 6.0 8.5 0.49 +0.16−0.10 -17 8.5 12.0 0.40 +0.16−0.07 -11 12.0 30.0 0.10 +0.04−0.01 +8 Table C.14: Predictions from next-to-leading order QCD calculations in the kinematic range 3.5 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, 0.5 < ηµ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. 152 NLO prediction Theor. uncertainty Correction to hadron level log x-range dσ/d log x Sys. Ch − 1 [pb] [pb] [%] -4.1 -3.95 1.20 +0.67−0.18 -7 -3.95 -3.8 1.30 +0.73−0.25 -8 -3.8 -3.4 0.93 +0.53−0.20 -12 Table C.15: Predictions from next-to-leading order QCD calculations in the kine- matic range 3.5 < Q2 < 7.0 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. NLO prediction Theor. uncertainty Correction to hadron level log x-range dσ/d log x Sys. Ch − 1 [pb] [pb] [%] -3.7 -3.5 0.66 +0.38−0.13 -9 -3.5 -3.3 0.62 +0.29−0.15 -9 -3.3 -3.1 0.40 +0.19−0.08 -13 Table C.16: Predictions from next-to-leading order QCD calculations in the kine- matic range 7 < Q2 < 13 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. NLO prediction Theor. uncertainty Correction to hadron level log x-range dσ/d log x Sys. Ch − 1 [pb] [pb] [%] -3.4 -3.2 0.35 +0.17−0.07 -8 -3.2 -3.0 0.30 +0.15−0.05 -10 -3.0 -2.8 0.21 +0.10−0.04 -13 Table C.17: Predictions from next-to-leading order QCD calculations in the kine- matic range 13 < Q2 < 25 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. 153 NLO prediction Theor. uncertainty Correction to hadron level log x-range dσ/d log x Sys. Ch − 1 [pb] [pb] [%] -3.1 -2.9 0.17 +0.11−0.03 -9 -2.9 -2.7 0.15 +0.07−0.02 -10 -2.7 -2.5 0.11 +0.04−0.02 -11 Table C.18: Predictions from next-to-leading order QCD calculations in the kine- matic range 25 < Q2 < 50 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. NLO prediction Theor. uncertainty Correction to hadron level log x-range dσ/d log x Sys. Ch − 1 [pb] [pb] [%] -2.8 -2.6 0.08 +0.03−0.01 -7 -2.6 -2.4 0.07 +0.03−0.01 -8 -2.4 -2.1 0.04 +0.02−0.01 -9 Table C.19: Predictions from next-to-leading order QCD calculations in the kine- matic range 50 < Q2 < 100 GeV2, 0.1 < y < 0.7, pμt > 2 GeV, −0.75 < ημ < 2.0, pjett > 6 GeV and |ηjet| ≤ 2.5. 154 Appendix D Level 1 Z-Vertex Trigger D.1 Overview The successfull HERA II physics program is based on the four to five times higher instantaneous luminosity that was delivered to the experiments. The upgrade of the storage ring required an upgrade of the detectors. For the H1 detector it was decided to keep the reliable data acquisition electronics and to increase the sensitivity of the experiment to interesting events instead. Therefore new trigger electronics and algorithms were developed, based on signals from different subdetectors. The jet trigger was designed to recognise local energy depositions in the liquid argon calorimeter. The DCRPhi trigger [119] was replaced by the Fast Track Trigger (FTT) [30, 49], both processing drift chamber information. One important part of the trigger upgrade was the replacement of the CIP detector by an improved detector consisting of five instead of three layers and new trigger electronics [115]. Only by rejecting beam induced background, like beam gas and beam wall events (see figure D.1), at an early stage at level 1, an efficient use of the trigger bandwith for all other physics triggers was possible. Nevertheless, at the beginning of the HERA II data taking the CIP was still in the commissioning phase Figure D.1: Event display of a beam gas induced background event. 155 CJC2 21 3 4 CJC1 Figure D.2: A radial view of the FTT, the CJC wires used by the FTT are indicated as dashed lines. Only the three inner FTT layers of CJC1 are used for the z vertex trigger. and only three out of five layers were operational. This was accompanied by very high beam induced backgrounds. It was highly desirable to have a backup solution for the CIP trigger, therefore studies were conducted that demonstrated the feasibility of a z vertex trigger based on drift chamber signals at level 1 by extending the FTT functionality [36]. For this only a minimum of additional hardware was necessary. The corresponding interfaces for this upgrade were introduced from the beginning in the design of the FTT data flow and the algorithms were finally implemented within the work of this thesis. In the following a brief overview of the FTT is given followed by a discussion of the z vertex trigger algorithm. D.1.1 Fast Track Trigger In order to cope with the higher rates after the HERA II upgrade and to increase the selectivity, the Fast Track Trigger was built to replace the DCRPhi trigger. Of special interest is a high selectivity in the photoproduction region where the rate of signal and background events is high and no suppression based on triggering on the scattered electron is possible. Therefore a purely track based trigger is necessary, using information from the central drift chambers. The drift chamber signals allow for a standalone track reconstruction, the achieved resolution of 2% pt/ GeV is com- parable to the offline resolution. The FTT allows for a low momentum threshold of 100 MeV, compared to a threshold of 400 MeV for the DCRPhi trigger. This is of special interest for the study of soft physics, e.g. production of mesons at the production threshold (very low transverse momenta). The large dynamic range of track momenta and the pattern recognition on a short timescale within 500 ns are a major challenge. In addition the algorithms had to be designed to deal with the large drift times of 10-12 bunchcrossings within the drift chambers. 156 CJC1 cell In-cell wires neighbour Upper left Lower right neighbour La ye r 1 La ye r 3 La ye r 2 Figure D.3: Geometry of the CJC with wires marked used for the FTT (from [36]). Each group consists of three wires, the upper left and lower right neighbour wire are included in the processing of each group. 157 The FTT uses only a fraction of 450 from 2440 wires of the drift chambers. A radial slice of the drift chambers is shown in figure D.2. As indicated, the FTT wires are arranged in four trigger layers, three for the inner chamber and one for the outer chamber. The inner and outer layers consist of 30 and 60 trigger cells, respectively. Each trigger group is made of three FTT wires. The cell geometry for the inner layers is depicted in figure D.3. The local pattern matching is performed within these trigger cells. The FTT provides trigger information on all three trigger levels, where the first two levels are solely based on drift chamber signals. At level 1 track segments are linked in the transverse plane, yielding coarse track parameters. Finally the trigger decision is determined, in total a set of 32 trigger elements (TEs) is forwarded to the Central Trigger Logic. These trigger elements are based on the number of tracks above a certain momentum threshold, the total charge of the tracks and the arrangement of tracks in the r − φ plane. All these calculations have to be performed within the level 1 latency of 2.3 μs (24 bunch crossings). Details can be found in [35]. The z vertex trigger, that is described in this thesis, is part of level 1. At level 2 track segments are linked based on refined segment information. A 3- dimensional primary vertex constrained fit is performed. This consists of a circle fit in the transverse plane, which is able to fit four track segments within 2.25 μs. In the longitudinal plane a straight line fit is performed, combining up to 12 hits and the z vertex position. This fit can be performed within 1.12 μs. The level 2-linker algorithm is described in detail in [35], the 3-dimensional fit in [118]. The vertex position in z that is used for the fit in the longitudinal plane is determined by the FTT on an event-by-event basis [35]. In addition it was possible to perform an invariant mass reconstruction already on Level 2 using the parameters determined by the track fits [35]. Finally 64 internal FTT trigger elements [105] are generated making use of the higher precision and resolution at level 2. These trigger elements are combined to 24 physics triggers that are sent to the central trigger logic. The internal trigger elements are based on track multiplicities above a certain threshold, track topologies in the transverse plane and the total charge in the event. Level 2 does not only verify and refine level 1 information but also delivers information based on the z vertex and additional kinematic quantities like the Et and pt, which is the scalar and vectorial sum of charged particle momenta, Vp and Vap, which is the amount of momentum parallel and antiparallel to the direction of missing mo- mentum, and the invariant mass of two track combinations. The total time available on level 2 is 20 μs. At level 3 a partial event reconstruction is performed by determining invariant masses based on the high precision tracks delivered from level 2. For this purpose physics algorithms like the selection of D∗ candidates run on commercial proces- sors [79, 80, 98]. At level 3 it is possible to combine track information with in- formation from other detectors, like the muon system [103] and the liquid argon calorimeter. The latter allows the search for electronic decays of beauty mesons at low momenta [43, 103]. The total time available for level 3 is 100 μs. 158 r z Figure D.4: Mutually exclusive valid patterns for the segment finding (from [35]). Each pattern defines a local search neighbourhood, consisting of five hit positions for the outer and inner wire and three hit positions for the middle wire. For the positions marked in black a hit is required, for positions marked in white no hit is allowed. The grey patterns denote “Don’t care” positions. D.1.2 Z Vertex Trigger The z vertex trigger algorithm consists of the following steps: • For each FTT-wire a hit finding algorithm is applied, followed by a calculation of the z-coordinate of the hit. The hit finding is common for the z vertex algorithm and the r-φ part of the FTT. The result of the z measurement is given in two representations, with a resolution of 62 bins for the level 2 system and a resolution of 40 bins (11 cm per bin) for the level 1 z vertex part due to bandwith limitations1. The hit finding and the z measurement are explained in more detail in section D.3.2. • For each of the 90 trigger cells of the inner three FTT layers a search for track segments is performed. The pattern matching algorithm is based on hitpatterns along the z-coordinate, where five bins of each inner and outer wire2 and three bins of the middle wire build a local search neighbourhood. The valid patterns are summarized in figure D.4. All 32 patterns are mutually exclusive and also patterns consisting of only two hits are valid to account for the limited hit finding efficiency. The result of this part of the algorithm are z-segments for each of the trigger cells. • In the linking step all combinations of two segments belonging to different layers are extrapolated to the beamline, and the intercept is entered into a his- togram. This extrapolation is done separately for 10 different φ-sectors (see 1Technically an internal representation of 124 bit is used, which is converted to a 62 and 40 bit representation. 2The hit information of the outer wires is combined with the information from neighbour wires. 159 ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ������������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ����������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� ���������� trigger layer 1 trigger layer 2 36° trigger layer 3 Figure D.5: Illustration of a φ sector. The vertex histogram is calculated for each sector seperately. Within the overlap region cells contribute to both sectors. figure D.5). The final vertex histogram is the sum of these 10 individual his- tograms and consists of 40 bins with a binwidth of 11 cm, covering the range from −2 m to 2 m. This has to be compared to a much coarser binning of about 16 cm for the CIP, where the number of bins is only 15. The extrapolation method is illustrated in figure D.6. • Finally this vertex-histogram is evaluated by counting the histogram entries and performing a peak search. The trigger decision is based on the peak position and the number of entries in the signal region of the histogram compared to the total histogram contents. Several aspects make the implementation of the z vertex algorithm a challenging task: • The algorithm has to account for the large drift times up to 10-12 bunch cross- ings. A hit might constitute a valid segment combined with a hit detected later due to a larger drift time. Therefore hits have to be held in pipelines of sufficient length. A large fraction of the available time at level 1 is spent for waiting for the latest hits. This latency is about five times larger than the hit finding itself. • Due to the limited time available at level one, the z vertex algorithm has to run in parallel to the r-φ-part. Since large parts of the algorithms run in parallel on the same hardware, a large fraction of the resources for the individual FPGAs has to be shared. This implies complications concerning the timing constraints of the final design at register transfer level. In addition the bandwidth for signal 160 reconstructed tracks tracks hits combinatorial background r axis z axis trigger layer 1 trigger layer 2 trigger layer 3 signal region intersect histogram Figure D.6: Sketch of the z-linking process (from [35]). All combinations of two segments are extrapolated to the beamline, leading to entries in the vertex histogram. The entries are weighted and smeared according to the different precision depending on the layer combination. transmission between the different hardware components is limited. • In comparision to the z vertex algorithm at level 2, not only r-φ linked segments are considered for the extrapolation, but all segments for the inner three layers. Therefore the algorithm suffers from a much larger number of z-segments and z- segment combinations, resulting in a smaller signal to noise ratio. This problem is enhanced by the fact that the outer FTT layer is not used for the algorithm due to hardware limitations. Combining segments from the inner and the outer layer (CJC2), which is possible at level 2, allows for a large lever arm and a much higher precision for the peak measurement. D.2 Data Flow and Hardware The FTT level 1 trigger system is distributed over a large number of hardware boards, most of them are used for level 2 functionality as well. An illustration of the level 1 system is given in figure D.7. The processing of the drift chamber data starts at the Front End Modules (FEM). Each FEM processes the data coming from 5 trigger cells (15 wires times two wire ends). In total the system consists of 30 FEMs, each of the three inner trigger layers is connected to 6 FEMs. The outer layer is not used by the Level 1 z vertex trigger. After digitization the hit finding and z measurement is performed, followed by the segment finding in the r-φ and r − z plane, which is done in parallel. 161 FEM FEM FEM FEM FEM FEM II PB IO PBIO PB II PB L1 Linker Controller LVDS 100 MHz 100 MHz LVDS 100 MHz LVTTL 100 MHz100 MHz Merger Card PB Linker Linker L2 z PB Figure D.7: Overview of the FTT L1 Trigger system, showing the data flow from the FEMs to the various linker cards via the merger cards. In addition, the segment finding at level 2 with a higher resolution is performed on the FEMs. The FEMs transmit the data to the Merger Card at a rate of 100 MHz via LVDS3 channel links. Therefore the Merger Cards are equipped with four Piggy Back Cards that receive the data. Two different types of Piggy Back Cards are used, the II-type has two input channels, the IO-card one input and one output channel. Merger and Piggy Back Cards are operated at a frequency of 100 MHz. The merger collects the r-φ and z data from 6 FEMs and forwards this information to the linker and z linker, respectively (see figure D.7). The z data is organized in 10 sectors (5 or 6 groups each) and sent out in sequence. One of the IO-Piggy Back Cards sends the merged r-φ segments to the linker card via one LVDS Channel Link, the other IO-piggy back card sends r − z segments to the z linker card via a second LVDS channel link. In addition, r-φ segments for level 2 are sent, therefore Merger and Piggy Back Cards switch between level 1 mode and level 2 mode. In level 2 mode, the z linker Piggy Back Card, that is receiving the data from the merger, is forwards the data to the L2 linker card. The Merger card and the different linker cards are Multipurpose Processing Boards (MPBs). Both, the MPBs and the FEM hardware and the used key technologies are presented in more detail in the following subsections. D.2.1 Front End Modules and Multipurpose Processing Boards For the FTT level 1 and level 2 hardware two types of boards are used: 30 Front End Modules (FEMs, figure D.8), built by Rutherford Appleton Laboratory, and several Multipurpose Processing Boards (MBPs, figure D.9), built by Supercomputing Sys- tems (SCS). Each Front End Module is equipped with 15 dual 10 bit Analogue to Digital Converters (ADCs) of type AD9218-80 [55] for sampling the analogue signal 3Low Voltage Differential Signaling [108] 162 of 5 trigger groups at a rate of 80 MHz. The further digital processing is performed on 6 FPGAs of type Altera APEX20K400E [27]. Five of them, the so-called Front FPGAs, perform the hit finding, z measurement and segment finding in the r-φ plane. To include information from neighbour wires, these FPGAs are cross-linked with the neighbour FPGAs. The Front FPGAs are clocked with a frequency of 80 MHz. The sixth FPGA of this type (so called Back FPGA) synchronizes and collects the track segments from the Front FPGAs and forwards them to the Merger system. The five Front FPGAs and the Back FPGA are connected via a 40 bit bus. In level 2 mode a validation of the track segments is performed, using higher granularity masks stored in RAM. (For the level two verification and lookup the board is equipped with a 4 MB Zero Bus Turnaround (ZBT) memory.) The segment finding in the r-z plane at level 1 is an extension of the trigger functionality using the remaining hardware resources. In addition this board is equipped with a FPGA of type ALTERA FLEX which provides a VME4 interface for configuration and readout. Many components of the FTT, including the merger system and different linkers, are implemented on Multiporpose Processing Boards using different firmware imple- mentations. Each MPB hosts up to four Piggy Back cards providing two 5 GBit/s channel links each, controlled by an Altera APEX20K60E FPGA. The correspond- ing buses are collected on the main board by the Data Controler FPGA, which hosts the linker algorithms for the linker cards and the merger algorithm for the merger card. The FPGAs are of type Altera APEX20KC600E for the linker boards and Altera APEX20K400E for the merger boards. A FPGA of type Altera FLEX EPF10K30A is used to control the VME interface. At level 2 fitter boards are used for track fits, which are in addition equipped with four floating point DSPs and a corresponding DSP controller FPGA. D.2.2 Key Technologies The implementation of fast and parallel algorithms and the successful commissioning of the FTT was only possible by the use of fast and flexible programmable hardware on level 1 and level 2. As the FTT is based on pattern matching algorithms a dedicated memory technology is used. Both key technologies are briefly presented in the following. Field Programmable Gate Arrays (FPGAs) FPGAs are programmable integrated circuits (ICs). They are used for complex applications, where flexibility and reprogrammable redesign are important. This is especially important during the commissioning phase. An overview of the APEX20K device is shown in figure D.10. This device incorpo- rates LUT-based logic5, product-term-based logic and memory. These components are organized in groups consisting of logic array blocks (LABs) and embedded sys- 4Vesa Module Europe 5LUT stands for look-up-table, which is a function generator that implements any function of four variables. 163 1 2 3 4 5 6 7 8 9 Figure D.8: Photo of a front end module (from [35]). 1: Connector for analogue signal cables 2: ADCs 3. Front FPGAs 4: Back FPGAs 5: ZBT RAM 6: VME Interface FPGA 7: VME Connector J1 8: Custom backplane connector 9: JTAG Connectors. 164 5 4 3 2 6 1 1 1 1 4 7 8 9 11 10 Figure D.9: Picture of a Multipurpose Processing Board (from [35]). 1: DSPs 2: DSP Controller FPGA 3: Data Controller FPGA 4: Piggy Back connectors 5: VME Interface FPGA 6: VME Connector J1 7: Custom backplane connector 8: Logic analyser connector for Data Controller FPGA 9: Logic analyser connector for DSP Controller FPGA 10: JTAG connectors 11: Status LEDs. For the z linker a simplified version is used without DSPs and DSP Controller FPGA. Not visible are two more Piggy Back connectors, a dual ported RAM and DPRAM Controller FPGA on the back side. 165 Figure D.10: APEX 20K Device Block Diagramm (from [27]). Shown are the logic array blocks, consisting of LUT-based logic, product-term-based logic, and memory. These blocks are connected via fast interconnections (FastTrack Interconnect). tem blocks (ESBs) and connected via fast interconnections. The smallest units of this architecture are logic elements (LEs). Each LE contains a four-input LUT, a programmable register and carry and cascade chains6. Product-term logic is im- plemented using ESBs. In this mode, each ESB contains 16 macrocells consisting of two product terms and a programmable register each. The ESB can implement various types of memory blocks, including dual-port RAM, ROM, FIFO, and CAM blocks. The latter is discussed in the following subsection in more detail due to the importance for the used algorithms. Content Adressable Memories (CAMs) Content Adressable Memories are associative memories based on RAM technology. Instead of receiving the address and supplying the data as in conventional RAM memory, a data word is compared to a list of pre-loaded data words, and the address of the matching data word(s) is signaled. The search through all memory locations is done in parallel. CAMs are used for implementing high-speed search applications, e.g. pattern matching algorithms. The used APEX 20KE device contains on-chip CAM which is built into the ESB blocks [56]. The core task of the z vertex trigger and the FTT in general is a fast pattern matching of drift chamber hits. All valid patterns shown in figure D.4 are used to pre-load the CAMs during configuration. The CAM units allow for a third matching state, the “Don’t care” state (ternary CAM). As all patterns are disjoint, the single match mode can be used. For this mode only one clock cycle is needed to read the stored data. 6Carry chain logic is used to implement counters, adders and comparators. Cascade chain logic is used to implement functions with a very wide fan-in. 166 D.3 Implementation of the Z Vertex Trigger In this chapter the implementation of the z vertex trigger is discussed in detail. Since this is based on the programming of FPGAs using the hardware description language VHDL, this chapter begins with a brief discussion of VHDL and the development process. After this the different steps of the algorithm are presented. D.3.1 VHDL The algorithm is implemented using the hardware description language VHDL7. The use of this high level language allows a high level of abstraction for the system design, including top-down and bottom-up design approaches and reusable components. A common modelling for the simulation and the synthesis of the design can be used. Digital hardware is described in VHDL using concurrent assignments, concurrent processes, and local signals for the communication between them. For processes the use of sequential statements is allowed. This way it is possible to implement not only combinatorical logic but sequential logic using storage components like flip flops. More details can be found e.g. in [75]. For the implementation the Quartus II design software [26] is used. This is an integrated development environment for all design steps, including the compilation, simulation, synthesis, placement and routing. During the synthesis step a netlist is produced. The last step, the mapping of the netlist to the hardware and connecting the components is a very time consuming step. For complex designs this step has to be repeated several times to fulfill the timing requirements. D.3.2 Hit finding and Z Measurement Both hit finding and the z measurement are performed on the Front FPGAs of the Front End Modules. Therefore the digitized signal of 10 channels (both ends of 5 wires, 3 wires of the corresponding cell plus two neighbour wires) is fed into the Front FPGA at a rate of 80 MHz. This results in a total input rate of 720 Gbit/s. The hitfinding and the z measurement, performed by the Qt Algorithm and a charge division algorithm, are described in the following. Qt Algorithm A difference of samples (DOS) method is used to measure the hit timing. Therefore for each time slice n the difference of the digitized wire value to the previous time slice n − 1 is calculated, δn = sn − sn−1, (D.1) where sn is the sum of both wire ends. A hit is found at a time slice n if the following conditions are fulfilled: • The difference δn is above a certain threshold, which implies a minimum slope for the rising edge of the hit. 7Very High Speed Integrated Circuit Hardware Description Language 167 Charge Left Charge Right Sum DOS Threshold Time A D C C o u n ts Figure D.11: Illustration of the Difference of Samples method (from [35]). • The difference δn is larger than the difference for the next time slice δn+1. This DOS technique is illustrated in figure D.11. By applying these conditions a hit finding with high efficiency and purity, high precision of the hit timing measurement and high accuracy of the charge measurement is possible. This step of the algorithm takes only three 80 MHz clock cycles. With the availability of the hit information, the segment finding in r-φ can proceed. Charge Division To determine the z value, a charge integration is performed for both wire ends. The principle of the charge integration is illustrated in figure D.12. The integration is performed for six clock cycles and starts as soon as the difference of samples is above the threshold. A noise substraction is performed, therefore a pedestal integration of six clock cycles is performed eight clock cycles before the hit (in phase with the HERA clock to reduce the influence of correlated noise). For a time period of 20 clock cycles after the hit integration, no pedestal integration is allowed. The values qL and qR for the measured charges are then entered into the simple formula z = Lef f qL − qR qL + qR , (D.2) where Lef f is the effective wire length, which is not only determined by the physical wire length but also by electronics at the wire ends (see figure D.13). If the values for the charges at both wire ends are equal, the formula yields a value z = 0 for the hit position, which is the center of the wire. 168 Time A D C C o u n ts ( o n e w ir e e n d ) H it In te g ra tio n H it In te g ra tio n H it In te g ra tio n P e d e st a l I n te g ra tio n P e d e st a l V e to Figure D.12: Illustration of the charge integration method (from [35]). Shown are the interval for the signal integration, the interval for the background integration (pedestal) and the veto region, where no pedestal integration is allowed. 220 cm ~ 600 Ω 1.5 nF1.5 nF 200 Ω 200 Ω Central Jet Chamber Wire Preamplifier Figure D.13: Illustration of CJC wires (from [35]). For the Qt algorithm an effective wire length is used, which accounts for the impedance due to electronics at both wire ends. 169 Data line L1/Monitor mode 40 80 MHz Clk inverted 39 0 38 κ enable 37 z enable 36 BC half 35 monitor enable 34..19 monitor data 18..17 z(17..16) 16..1 z(15..0)/κ(15..0) Table D.1: Front FPGA to back FPGA protocol. Only the protocol for the level 1 and monitor mode is shown. D.3.3 Segment Finding The segment finding in r − z is performed on the back FPGA. The functional design of the VHDL implementation is shown in figure D.15. The data is processed by three different units: Synchronizer The first step is the synchronization of five 80 MHz 40 bit data streams (one data stream for each trigger cell) to the 100 MHz clock of the back FPGA. For the synchronization the inverted 80 MHz clock is transmitted via the data stream. As a result only 8 of the 10 clock cycles per bunch crossing contain valid data. Three different protocols are used: level 1 mode, level 2 mode and read-out control mode. In level 1 mode, the z data is sent two times per bunch crossing. For each half bunch crossing 5 times 6 bit encoded z data is transmitted, which takes two clock cycles. For these clock cycles the z-enable bit of the data stream is set, the bunch crossing half is indicated by another bit. The front FPGA to back FPGA protocol for level one is shown in table D.1. Pipeline Units To account for the large drift times of the detector, the hit information is fed into five pipeline units, one for each cell, and stored for 10 bunch crossings. Therefore it is possible to form hit patterns consisting of hits detected at different bunch crossings but belonging to the same event. Each pipeline unit contains five counter units, three for the cell wires and two for the left and right neighbour wire. Each counter unit uses 40 counters to model one pipeline per z position. Twice a bunch crossing it is checked whether a hit was detected for each z position. In this case the counter is set to 10 and the bit corresponding to this z position is enabled. The counters are decremented per bunch crossing, and the corresponding bit is disabled if the counter is at zero. 170 10 20 30 40 50 60 0 10 20 30 40 50 0 half bunch crossings e n tr ie s early late 0 10 20 30 40 50 e n tr ie s 10 20 30 40 50 600 half bunch crossings Figure D.14: Drift spectrum for z hits for the innermost layer and the outermost layer. This data was read out from the back FPGA. For each cell 120 bit (40 z positions per wire) are written to a cyclic memory which is used to feed the data to the CAM unit. In addition, the hit information is written to a dedicated cyclic memory twice per bunch crossing for timing studies. This memory has a depth of 31 bunch crossings and can be read out via VME. The number of z hits with respect to the half bunch crossing is shown in figure D.14 for the innermost layer and the outermost layer, ordered from earlier to later bunch crossings. The first hits are written to the memory 20 bunch crossings before the pipelines are stopped by the central trigger decision. The rising edges for all trigger layers show that the pipelines are stopped at the same time with respect to the central trigger signal for each event. The width of this distribution denotes the maximum drift time, which is about 6 bunch crossings for the innermost layer and about 10 bunch crossings for the outermost layer. The latest hits are available only about 10 bunch crossings before the pipelines stop. As all subsequent processing and transmission steps exceed this time constraint, only the fraction of hits that are available early enough is processed and included to the trigger decision. To maximize this fraction, all steps of the algorithm have to be optimized with regard to processing time and parallelism. CAM Unit The CAM Unit performs the search for track segments in a local search neighbour- hood. 10 bit of z-information from three wires is presented to 38 CAMs (one for each z position, omitting the edge positions) in parallel and compared to predefined patterns. This principle and the z-patterns are illustrated in figure D.16 and D.4. The data from five groups has to be processed, but due to limited resources only one CAM unit is available. Therefore the data from each group is presented to the CAM unit in sequence using a state machine. The result of this pattern matching is represented by five 40 bit vectors, where each component represents a z-bin. These vectors become available in sequence for each group. To reduce the amount of data to be transmitted and processed, a reduction to three 40 bit vectors is necessary by merging these vectors. Three groups of 40 bit z data are defined, which belong to 171 FEM PB card PB type group layer 1 layer 2 layer 3 0 1 M1KO 0 0-1 0-1 0-2 1 (5) 1-4 (1) 2-4 (6) 2-4 2 4∗ 1 2 M1II1a 0 5 1 (5) 5-7 (1) 5-7 (6) 5-8 2 7-9 8-9 8-9 2 3 M1II2a 0 10 10 10-11 1 (5) 10-13 (1) 11-13 (6) 11-14 2 13-14 14 14 3 2 M1II1b 0 15-16 15-16 15-17 1 (5) 16-19 (1) 17-19 (6) 17-19 2 19 4 3 M1II2b 0 20 1 (5) 20-22 (1) 20-22 (6) 20-23 2 22-24 23-24 23-24 5 4 M1ZO 0 25 25 25-26 1 (5) 25-28 (1) 26-28 (6) 26-29 2 28-29 29 29 Table D.2: CJC 1 Merger Input. Only the z data is shown, in addition κ informa- tion is sent. The Merger receives three groups of z data for each of the five FEMs for one layer. The data denoted with * is not transmitted due to bandwidth limitations. one sector (see figure D.5). For each group a bitwise or of three or four vectors is performed, depending on the FEM type and layer. This is summarized in table D.2. Finally the z data is sent out to the merger cards in three groups of 40 bit. The sequence of data sent to the merger card is summarized in table D.3. Three cycles are needed for the z data, two cycles for the r-φ data. D.3.4 Merging The amount of data is further reduced by merging the z segments on three merger boards, one for each layer. 10 sectors are defined, with overlap regions between them (figure D.5). As the implementation of the merger algorithms is not part of this thesis, only a brief overview of the merger functionality is given. The merging scheme is complicated because r-φ data and z data are processed on the same merger. A detailed description including the detailed merging scheme and r-φ functionality can be found in [104]. The FEM-Merger channel links are operated at 100 MHz. The protocol is given in table D.4. Five bytes are available for the unencoded z position per group, dedicated header bits are used to denote the group number. In addition r-φ information is sent via these channel links. Control words are used for switching between the level 1 and level 2 mode. For each bunch crossing the BeginTriggerData control word is 172 Step word HClk FEM 1 control word 0 → 1 2 5 lower bytes rφ segments 1 3 5 higher bytes rφ segments 1 4 empty word 1 5 empty word 1 6 40 bits z segments group 0 1 → 0 7 40 bits z segments group 1 0 8 40 bits z segments group 2 0 9 empty word 0 10 empty word 0 Table D.3: Sequence of sending data at 100 MHz (10 cycles per bunchcrossing) from the FEM to the Merger Cards. Synchronizer Pipeline Unit Counter Unit Counter Unit Counter Unit Counter Unit Counter Unit CAM Unit CAM CAM CAM Array State Machine Pipeline Unit Counter Unit Counter Unit Counter Unit Counter Unit Counter Unit Pipeline Unit Counter Unit Counter Unit Counter Unit Counter Unit Counter Unit Pipeline Unit Counter Unit Counter Unit Counter Unit Counter Unit Counter Unit Pipeline Unit Counter Unit Counter Unit Counter Unit Counter Unit Counter Unit Group 1 Group 2 Group 3 Group 4 Group 5 Hits Patterns Wire 1 Wire 2 Wire 3 Wire 4 Wire 5 38 CAMs Figure D.15: Functional design of the segment finding unit of the back FPGA. Hits from each trigger group are fed to the Pipeline Units. Each Pipeline Unit consists of 5 counter units, one for each FTT wire. The CAM Unit consists of 38 CAM memories, one for each z position. 173 wire 0,1 wire 2 wire 3,4 segment Figure D.16: Principle of the pattern matching performed on the back FPGA. For each z position a local pattern matching is performed, resulting in a segment array. Data type byte 5 byte 4 byte 3 byte 2 byte 1 byte 0 Invalid/no data 0 0 0 0 0 X X X load load load load load Track segments cell#(7..3)load(2..0) load load load load load L1 mode header cell 5 cell 4 cell 3 cell 2 cell 1 empty word 0 0 0 0 1 0 0 P ignored ignored ignored ignored ignored rφ segments (low) 0 0 0 0 1 0 1 P lower byte lower byte lower byte lower byte lower byte rφ segments (high) 0 0 0 0 1 1 0 P higher byte higher byte higher byte higher byte higher byte z segment group 0 0 0 0 1 0 0 1 P unencoded z position z segment group 1 0 0 0 1 0 1 0 P unencoded z position z segment group 2 0 0 0 1 1 0 0 P unencoded z position Control words 1 1 1 1 1 X X P BeginTriggerData 1 1 1 1 1 0 0 P FEM# 0x00 #HCLK #HCLK #HCLK SwitchTol2Mode 1 1 1 1 1 0 1 P FEM# 0x00 #L1Keep #L1Keep #L1Keep NoMoreSegments 1 1 1 1 1 1 1 P FEM# 0x00 0x00 0x00 #sent segments SwitchToL1Mode 1 1 1 1 1 1 0 P FEM# 0x00 #L2Keep #L2Keep #L2Keep Table D.4: FEM-Merger Protocol. P stands for parity bit. The control words contain counter information for monitoring purposes. sent along with the actual HERA clock counter. For each of the three trigger layers used by the z-trigger, one merger receives z data data via four Piggy Back cards. One of these cards forwards the data to the z linker. 22 clock cycles after receiving the BeginTriggerData control word, the last z sector is sent to the z linker card. The channel link to the z linker is operated at 100 MHz, the protocol is summarized in table D.5. The sequence of data and control words from the merger to the z linker card is summarized in table D.6. The BeginTriggerData control word is sent only once at the beginning of the level 1 mode. D.3.5 Linking and Trigger Decision The linking of the segments is the essential part of the algorithm. This is performed on a dedicated MPB-board, the z linker, operated at 100 MHz. The z data is received by the z linker via three LVDS channel links, one for each layer. The linking step is followed by the evaluation of the resulting vertex histogram and the generation of trigger elements which are sent to the Central Trigger. The different modules of the implementation are discussed in the following. 174 Data type byte 5 byte 4 byte 3 byte 2 byte 1 byte 0 Invalid/no data (L2 mode) 0 0 0 0 0 0 0 0 Track segments cell#(7..3)load(2..0) load load load load load L1 mode header byte 4 byte 3 byte 2 byte 1 byte 0 z segment 0 sector+1 0 0 S unencoded z position Control words 1 1 1 1 1 X X P BeginTriggerData 1 1 1 1 1 0 0 P FEM# 0x00 #HCLK #HCLK #HCLK SwitchTol2Mode 1 1 1 1 1 0 1 P FEM# 0x00 #L1Keep #L1Keep #L1Keep NoMoreSegments 1 1 1 1 1 1 1 P FEM# 0x00 0x00 0x00 0x00 SwitchToL1Mode 1 1 1 1 1 1 0 P FEM# 0x00 #L2Keep #L2Keep #L2Keep Table D.5: Merger-z-Trigger protocol. P stands for parity bit. The control words contain counter information for debugging purposes. For the sector which is sent first in a sequence (sector 2) the startbit S is set high. In level 2 mode track segments are sent. Step word HClk Merger 1 BeginTriggerData 0 → 1 2 sector 2 z segment 1 3 sector 3 z segment 1 4 sector 4 z segment 1 5 sector 5 z segment 1 6 sector 6 z segment 1 → 0 7 sector 7 z segment 0 8 sector 8 z segment 0 9 sector 9 z segment 0 10 sector 0 z segment 0 11 sector 1 z segment 0 → 1 ... ... ... ... SwitchToL2Mode ... ... ... ... ... L2 track segments ... ... ... ... NoMoreSegments ... ... ... ... ... SwitchToL1Mode ... Table D.6: Sequence of data sent from the merger to the z linker. Signal region: bin 14-30 Backward region: bin 0-13 Forward region: bin 31-39 z Figure D.17: Illustration of the vertex histogram, divided into backward, signal and forward region. 175 Parameter Value length CJC 220 cm centre CJC 110 cm radius inner layer R0 22.0 cm radius middle layer R1 33.0 cm radius outer layer R2 44.0 cm #histogram bins 40 histogram length 440 cm histogram centre 220 cm Table D.7: CJC and vertex histogram parameters used for the extrapolation of z segments. Receiver Unit This unit synchronizes the data from three trigger layers. The incoming data is written to input buffers, implemented as cyclic memories. The synchronization step is performed by a final state machine that writes the data to three z buses, one for each trigger layer. The data of one sector is written per clock cycle to each bus. In total ten clock cycles are needed for all ten sectors. Histogram Unit The Histogram Unit performs the linking step of the algorithm by extrapolating seg- ment pairs linearly to the beam line. It consists of three linking units, corresponding to the three possible combinations of two layers. Each of these linking units fills a 40 bin z vertex histogram with a binwidth of 11 cm. The linear extrapolation of segment pairs to the beamline using the geometric CJC parameters given in table D.78 is performed offline. For each histogram bin all segment combinations, that can be extrapolated to that bin (links) are calculated offline, and the corresponding VHDL code is generated. The algorithm is pipelined, the linking is performed for each of the ten sectors in sequence sharing the same hardware. Each link gives an entry for the corresponding bin. The vertex histogram is calculated by summing up the number of links for each bin. This cannot be done in one clock cycle due to timing constraints. For each bin an adder with a large fan-in would be required. Instead, the addition is done in several steps within five clock cycles using a chain of adders. The sum unit is used to add the individual histograms for each layer combination. The algorithm is pipelined, therefore one tenth of the histogram is processed for each clock cycle. The vertex histograms for all ten sectors become available in sequence and are summed up to the final vertex histogram. After ten clock cycles the data from the next bunch crossing is processed. To take into account the higher resolution for the combina- tion layer 0 - layer 2 due to the longer lever arm, a weighting scheme is applied: 8The radii of the different CJC layers used for the algorithm deviate from the physical parameters and are chosen in a way to avoid binning artefacts (moiré effects). 176 Trigger Element Method Signal region TE 154 Top Peak 40 -40 cm - 100 cm TE 155 Top Peak 50 -50 cm - 100 cm TE 156 Top Peak 60 -60 cm - 100 cm TE 157 Significance -40 cm - 100 cm Table D.8: Trigger elements provided by the z vertex trigger. They correspond to two different methods for evaluating the vertex histogram and different definitions of the signal region. histogram entries from this combination get a weight of three, whereas entries from the other two layer combinations are smeared to the left and right neighbour bin. The Peakfinder Unit analyzes the vertex histogram. A peak search is performed and entries for the central, forward and backward region are counted. An asym- metric signal window is defined from bin 14 to 30 as illustrated in figure D.17. Due to secondary tracks showering in the forward region, the signal window had to be extended to the forward region. D.3.6 Trigger Element Generator Unit This unit processes the results from the Histogram Unit given by the number of entries for the three different histogram regions and a 40 bit array containing the peak information. Two different methods are used: For the Significance Method the number of entries for the signal and background regions are compared. The corresponding trigger element is enabled if the condition 2Nsignal > (Nf orward + Nbackward) (D.3) is fulfilled. A similar method was used for the level 2 z vertex Trigger and the CIP trigger. For the Top Peak Method the peak array is evaluated. The corresponding trigger condition is fulfilled if the position of the top peak is within the signal window. Three different asymmetric signal windows are defined. In total four trigger elements are defined, they are summarized in table D.8. All four trigger elements are sent to the Central Trigger. To fulfill the timing requirements with respect to the central trigger and to synchronize the four trigger elements, additional individual delays are added. D.3.7 Timing The processing and transmission times needed for the individual steps of the algo- rithm are summarized in table D.9. The accumulated time is estimated to 1250 ns. As the maximal level 1 latency is 2100 ns and the maximum drift time is 1056 ns, this results in an implicit cut into the hit distribution for the outermost layer (see figure D.14). The latest hits (about three bunch crossings) for this layer are therefore not included in the processing of the vertex histogram. 177 Delay Clock Cycles time (ns) accumulated (ns) Analogue cable delay - 180 180 FEM: Digitization - 60 240 FEM: Charge Integration (FFPGA) 6 72 312 FEM: Charge Division (FFPGA) 15 180 492 FEM: Data Preparation (FFPGA) 2 24 516 FEM: Segment Finding (BFPGA) 12 120 636 Channel Link: FEM-Merger - 70 706 Merger: Merging 12 120 826 Channel Link: Merger-z Linker - 60 886 z Linker: Receiving, Synchronizing 6 120 1006 z Linker: Linking 6 60 1066 z Linker: Pipelining 10 100 1166 z Linker: Summing histograms 3 30 1196 z Linker: Evaluating histogram 8 80 1276 z Linker: TE Driver, delay 5 50 1326 Transmission of trigger elements to CTL 5 50 1376 Table D.9: Summary of time consumption of the algorithm for the different pro- cessing and transmission steps. D.4 Results D.4.1 Cosmic Runs In the course of the commissioning phase the first test were performed using data from cosmic runs. The cosmic muon events recorded during this runs provide ideal back to back two track events. The functionality of the trigger is documented in figure D.18 where the correlation between z vertex position as determined by the H1 event reconstruction and the position of the top peak is shown. Figure D.19 shows an overlay of many vertex histograms for ideal single track events from cosmic runs. As the vertex position of each event is distributed uniformly, each single histogram is shifted to the central bin. The overlay histogram has a small width and peaks at the central bin. This demonstrates that the FTT is able to reconstruct the vertex position reliably for single track events with small combinatorical background. D.4.2 Luminosity Runs The performance of the trigger with respect to the background rejection and effi- ciency is tested using ep data. For these dedicated test runs the filtering on trigger level 4 was switched off (transparent runs). In figure D.20 the distribution of the offline reconstructed z vertex is shown for an event sample triggered with the level 1 subtrigger s61, which requires a scattered electron (see section 5.1.2 for the trigger conditions). As the veto conditions are switched off for these runs, a background 178 FTT Bin O ff li n e v e rt e x [c m ] -200 -150 -100 -50 50 100 150 200 10 15 20 25 30 35 405 0 Figure D.18: Correlation plot of offline measured z vertex and online measured top peak position for cosmic events. FTT Bin 10 15 20 25 30 35 40 # e v e n ts 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50 Figure D.19: Overlay of vertex histograms for ideal single track cosmic events. Each individual histogram contributing is shifted to the central bin (see text). The binwidth is 11 cm. 179 peak is visible in the backward region of the detector. This peak contains about the same number of events as the signal peak due to the bad background conditions. In the same plot this distribution is shown if the trigger element TE 157 (significance method) is required. A large part of the background peak is rejected (about 65%), whereas only a small fraction of about 5% of the signal peak is rejected. This analysis was preceeded by detailed simulation studies on ep data [36]. The pre- dicted rejection power of the z vertex trigger is shown in figure D.20 for a method very similar to the implemented significance method. A comparison to figure D.20 shows that the predicted background rejection was achieved for the implementation of the algorithm. The implemented methods are compared in figure D.21. The maximum rejection is achieved for the significance method. The width of the signal window influences the rejection for the backward region. As expected, the largest rejection is achieved for the smallest signal window (Top Peak 40 method). For all methods, the signal window is asymmetric and extends to +100 cm in the forward direction. The reason is a secondary vertex peak in the forward direction, which results from secondary tracks induced by particle showers. This peak often exceeds the primary vertex peak which results in a rejection of signal events if the signal window does not cover the forward region. The efficiency for the signal region is comparable for all methods. This was checked using samples of elastic and inelastic J/Ψ events which provide an ideal ep-signal. The selection was performed using the J/Ψ finder algorithm, both tracks belonging to the J/Ψ meson are required to be identified as an electron or muon. For the elastic sample no other tracks are allowed, for the inelastic sample the inelasticity is restricted to the range 0.2 < z < 0.9, the center of mass energy in the photon proton system to the range 50 < Wγp < 250 GeV. In figure D.22 the invariant mass distribution is shown for both samples and compared to the distribution with the requirement of trigger element 157 (significance method). Only minimal losses due to the z vertex condition are desirable, the measured efficiency is about 98%, which is still acceptable. The performance of the FTT z vertex trigger is compared to the CIP z vertex trig- ger, again using the s61 triggered data sample. The result is shown in figure D.23. Whereas the rejection of the FTT is about 65% for the background region, the CIP trigger rejects almost every event for this region. The difference for the signal region is smaller, nevertheless the performance of the CIP z vertex trigger is superior. The FTT has a better rejection power for the forward region. 180 -200 -150 -100 -50 50 100 # e ve n ts 0 100 200 300 400 500 600 700 800 900 with FTT zVtx condition 0 zVtx [cm] z [cm] -200 -150 -100 -50 0 50 100 150 200 0 20 40 60 80 100 120 140 160 180 200 220 Offline reconstructed vertices of: Events with no vertex peak Events triggered by the 3/4 peak method Events vetoed by FTT Figure D.20: Upper plot: z vertex distribution for s61 triggered events and for the additional z vertex trigger requirement. This data sample was taken at the end of a fill using dedicated trigger conditions, avoiding the rejection of background at other trigger levels. Lower plot: z vertex distribution showing the predicted rejection power of the z vertex trigger as result of simulation studies (from [36]). 181 Offline zVtx [cm] -200 -150 -100 -50 50 100 1 -r e je c ti o n 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Toppeak 60 Toppeak 50 Toppeak 40 Significance 0 Figure D.21: Comparison of the rejection power for different z vertex trigger ele- ments. inv. mass [GeV] 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 # e v e n ts 0 200 400 600 800 1000 1200 1400 1600 with FTT zVtx condition inv. mass [GeV] 1.5 2 2.5 3 3.5 4 4.5 5 # e v e n ts 0 50 100 150 200 250 300 350 with FTT zVtx condition Figure D.22: Invariant mass distribution of a elastic (left) and inelastic (right) J/Ψ-sample with and without requiring the z vertex condition. 182 Offline zVtx [cm] -200 -150 -100 -50 100 1 -r e je c ti o n 0 0.2 0.4 0.6 0.8 1 CIP FTT 500 Figure D.23: Comparison of the rejection power for the FTT and the CIP z vertex trigger. 183 184 List of Figures 1.1 Deep inelastic electron-proton scattering at HERA . . . . . . . . . 14 1.2 Proton structure function F2 . . . . . . . . . . . . . . . . . . . . . 16 1.3 Virtual corrections to the gluon propagator . . . . . . . . . . . . . 17 1.4 Running of the effective coupling constant αs . . . . . . . . . . . . 17 1.5 QCD Compton processes . . . . . . . . . . . . . . . . . . . . . . . . 18 1.6 Boson gluon fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.7 Gluon and valence quark densities . . . . . . . . . . . . . . . . . . 20 1.8 Illustration of splitting functions . . . . . . . . . . . . . . . . . . . 21 1.9 Gluon ladder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.10 Diagrams for heavy quark production in the massive scheme . . . . 23 1.11 Diagrams for heavy quark production in the massless scheme . . . 24 1.12 Illustration of fragmentation models . . . . . . . . . . . . . . . . . 25 1.13 Diagrams for semi-leptonic decays of beauty quarks . . . . . . . . . 26 1.14 Illustration processes implemented in Monte Carlo generators . . . 27 2.1 HERA accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2 Technical drawing of the H1 detector . . . . . . . . . . . . . . . . . 33 2.3 Inner part of the H1 detector . . . . . . . . . . . . . . . . . . . . . 34 2.4 Radial view of the central tracking system . . . . . . . . . . . . . . 34 2.5 Central silicon detector . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 r-z view of the upper half of the Liquid Argon Calorimeter . . . . . 37 2.7 Illustration of the electromagnetic SpaCal . . . . . . . . . . . . . . 38 2.8 Inner SpaCal region . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.9 Illustration of the four parts of the Central Muon Detector . . . . . 40 2.10 Cross section view of an instrumented iron module . . . . . . . . . 40 3.1 Tagging methods used at H1 and ZEUS . . . . . . . . . . . . . . . 46 3.2 Event display of a dijet event with a muon identified in the Central Muon Detector . . . . . . . . . . . . . . . . . . . . . . 46 3.4 δ distribution for the DIS sample of the H1 muon+jet analysis . . 48 3.5 Beauty quark event with D∗ and muon . . . . . . . . . . . . . . . . 49 3.6 Summary of ZEUS photoproduction results . . . . . . . . . . . . . 50 3.7 H1 HERA I photoproduction result for the muon+jets analysis . . 51 3.8 H1 HERA I photoproduction result for the dijet analysis . . . . . . 51 185 3.9 Differential cross sections for the H1 HERA I DIS anal- ysis [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.10 Differential cross sections for the ZEUS HERA I DIS analysis [21] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.11 Differential cross sections for the ZEUS HERA II DIS analysis [20] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.13 Results from the UA1 measurement . . . . . . . . . . . . . . . . . . 55 3.14 Tevatron Run 1 measurements . . . . . . . . . . . . . . . . . . . . 55 3.15 Recent measurement of beauty quark production from CDF for Run 2 data . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.16 Beauty quark production measurement at the LEP collider . . . . 57 4.1 Processes in the Breit frame . . . . . . . . . . . . . . . . . . . . . . 65 4.2 Ratio of reconstructed to generated values as a function of the generated value . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 Comparison of the simulated z vertex distributions to the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.3 Control distributions for E − pz and the cluster radius . . . . . . . 75 5.4 Q2 distribution for small values of Q2 and impact pa- rameter distribution for the inner SpaCal region . . . . . . . . . . . 76 5.5 Distribution of the reconstructed impact position of electrons in the SpaCal . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.6 Reweight factor applied to the Monte Carlo simulation as a function of θe. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.7 Control distributions for variables determined from the scattered electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.8 Control distribution for the variable y . . . . . . . . . . . . . . . . 80 5.9 φ distribution of the scattered electron . . . . . . . . . . . . . . . . 80 5.10 Distribution of the Bjorken scaling variable. . . . . . . . . . . . . . 80 5.11 Linking probability between central track and iron track . . . . . . 83 5.12 Distribution of the number of muon layers with a hit for the central region . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.13 Distribution of the number of muon layers with a hit for the forward region . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.14 Distribution of the distance between first and last hit layer for the central region . . . . . . . . . . . . . . . . . . . . . . . 84 5.15 Distribution of the distance between first and last hit layer for the forward region . . . . . . . . . . . . . . . . . . . . . . 84 5.16 Pseudorapidity distribution for the selected muon . . . . . . . . . . 85 5.17 Reweight factor applied to the Monte Carlo simulation as a function of ημ. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.18 Azimuthal angle and transverse momentum distribu- tion of the muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.19 Invariant mass distribution of the elastic J/ψ sample . . . . . . . . 86 186 5.20 Muon reconstruction and identification efficiency for the forward barrel . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.22 Muon reconstruction and identification efficiency for the forward endcap . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.23 Correction factors for the muon reconstruction and iden- tification efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.24 Polar angle distribution for the jet selection . . . . . . . . . . . . . 90 5.25 Transverse momentum of the muon jet, multiplicity for jets fulfilling the jet selection criteria and number of particles belonging to the muon jet . . . . . . . . . . . . . . . . . . 90 5.26 Energy flow distributions for the selected jet . . . . . . . . . . . . . 91 5.27 Number of selected events per inverse picobarn luminosity . . . . . 92 6.1 prelt distribution for the selected events . . . . . . . . . . . . . . . . 95 6.2 prelt distribution for the highest momentum track with respect to the jet axis for a sample with no muon requirement . . . 95 6.3 Comparison of the prelt shape for light and charm quark events . . 98 6.4 Results of the prelt fits . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.5 Results of the prelt fits . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.6 prelt -fits for different bins of the muon transverse momentum . . . . 102 6.7 Resolution of the measured transverse momentum of the jet according to the Monte Carlo simulation . . . . . . . . . . . 104 6.8 Efficiencies and purities for the different analysis bins . . . . . . . . 104 6.9 Efficiencies and purities for the different analysis bins . . . . . . . . 105 6.10 Comparison of prelt and p̃ rel t . . . . . . . . . . . . . . . . . . . . . . 107 6.11 Polar angle resolution of the jet according to the Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.12 Calorimetric energy attributed to muons . . . . . . . . . . . . . . . 110 6.13 Isolation criteria for muons . . . . . . . . . . . . . . . . . . . . . . 112 6.14 Total cross section for four different quadrants of the SpaCal . . . 113 7.1 Differential Born level cross section as a function of Q2 . . . . . . . 118 7.2 Differential Born level cross section as a function of log x . . . . . . 118 7.3 Differential Born level cross section as a function of ημ . . . . . . . 119 7.4 Differential Born level cross section as a function of pμt . . . . . . . 119 7.5 Differential Born level cross section as a function of pjett . . . . . . 120 7.6 Differential Born level cross section as a function of Q2 . . . . . . . 121 7.7 Differential Born level cross section as a function of log x . . . . . . 122 7.8 Differential Born level cross section as a function of η . . . . . . . . 122 7.9 Differential Born level cross section as a function of pμt . . . . . . . 123 7.10 Differential Born level cross section as a function of pjett . . . . . . 123 7.11 Double differential Born level cross section as a function of pjett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.12 Double differential Born level cross section as a function of the scaling variable x . . . . . . . . . . . . . . . . . . . . . . . . 126 187 7.13 Double differential Born level cross section as a function of pjett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.14 Double differential Born level cross sections as a func- tion of log x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.15 Comparision of double differential cross sections mea- sured in the Breit frame to the published HERA I mea- surement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.16 Comparision of double differential cross sections mea- sured in the Breit frame to RAPGAP Monte Carlo pre- diction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8.1 Cross section measurements as a function of the muon transverse momentum . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2 Cross section measurements as a function of the muon pseudorapidity136 8.3 Cross section measurements as a function of Q2 . . . . . . . . . . . 137 D.1 Event display of background event . . . . . . . . . . . . . . . . . . 155 D.2 Radial view of the FTT . . . . . . . . . . . . . . . . . . . . . . . . 156 D.3 Geometry of the CJC . . . . . . . . . . . . . . . . . . . . . . . . . . 157 D.4 z patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 D.5 Illustration of a φ sector . . . . . . . . . . . . . . . . . . . . . . . . 160 D.6 Sketch of the z-linking process . . . . . . . . . . . . . . . . . . . . . 161 D.7 Overview of the FTT L1 Trigger system . . . . . . . . . . . . . . . 162 D.8 Picture of a front end module . . . . . . . . . . . . . . . . . . . . . 164 D.9 Picture of a Multipurpose Processing Board . . . . . . . . . . . . . 165 D.10 APEX 20K Device Block Diagramm . . . . . . . . . . . . . . . . . 166 D.11 Difference of Samples method . . . . . . . . . . . . . . . . . . . . . 168 D.12 Illustration of the charge integration method . . . . . . . . . . . . . 169 D.13 Illustration of FTT wires . . . . . . . . . . . . . . . . . . . . . . . . 169 D.14 Drift spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 D.15 Functional design of the segment finding unit of the back FPGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 D.16 Principle of the pattern . . . . . . . . . . . . . . . . . . . . . . . . 174 D.17 Illustration of the vertex histogram . . . . . . . . . . . . . . . . . . 175 D.18 Correlation plot for cosmic events . . . . . . . . . . . . . . . . . . . 179 D.19 Overlay of vertex histograms for ideal single track cos- mic events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 D.20 Z vertex distribution for s61 triggered events and Pre- dicted rejection power . . . . . . . . . . . . . . . . . . . . . . . . . 181 D.21 Comparison of the rejection power . . . . . . . . . . . . . . . . . . 182 D.22 Invariant mass distribution of an elastic and inelastic J/Ψ-sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 D.23 Comparison of the rejection power for the FTT and the CIP z vertex trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 183 188 List of Tables 1.1 Properties of some heavy hadrons . . . . . . . . . . . . . . . . . . . 26 2.1 Parameters of HERA II . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2 List of the main detector components of H1 . . . . . . . . . . . . . 31 2.3 The main component of the central H1 tracker and backward calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.1 Different run ranges and corresponding luminosities. . . . . . . . . 69 5.2 Trigger elements of subtrigger s61 . . . . . . . . . . . . . . . . . . . 70 5.3 Monte Carlo sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.4 Parameters of the z vertex distributions . . . . . . . . . . . . . . . 74 5.5 DIS selection cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.6 Muon selection cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.7 Muon reconstruction and identification efficiencies . . . . . . . . . 88 5.8 Cuts for the J/ψ selection . . . . . . . . . . . . . . . . . . . . . . . 88 5.9 Jet selection cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.10 Summary of all selection cuts that define the kinematic range of this analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.1 Summary of the different error sources contributing to the systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . 111 7.1 Parameters used for the different theoretical predictions for beauty quark production from LO Monte Carlo gen- erators and a NLO program. . . . . . . . . . . . . . . . . . . . . . . 116 A.1 List of excluded runs . . . . . . . . . . . . . . . . . . . . . . . . . . 142 A.2 List of requested detector components for the run selection . . . . 142 C.1 Differential cross sections for the process . . . . . . . . . . . . . . . 146 C.2 Differential cross sections as a function of the transverse momentum of the jet . . . . . . . . . . . . . . . . . . . . . . . . . . 147 C.3 Differential cross sections as a function of the transverse momentum of the jet . . . . . . . . . . . . . . . . . . . . . . . . . . 147 C.4 Differential cross sections as a function of the transverse momentum of the jet . . . . . . . . . . . . . . . . . . . . . . . . . . 147 189 C.5 Differential cross sections as a function of the scaling variable x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 C.6 Differential cross sections as a function of the scaling variable x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 C.7 Differential cross sections as a function of the scaling variable x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 C.8 Differential cross sections as a function of the scaling variable x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 C.9 Differential cross sections as a function of the scaling variable x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 C.10 Predictions from next-to-leading order QCD calcula- tions as a function of ημ, pμt and p jet t . . . . . . . . . . . . . . . . . 150 C.11 Predictions from next-to-leading order QCD calcula- tions as a function of Q2 and log x . . . . . . . . . . . . . . . . . . 151 C.12 Predictions from next-to-leading order QCD calcula- tions as a function of pjett . . . . . . . . . . . . . . . . . . . . . . . 152 C.13 Predictions from next-to-leading order QCD calcula- tions as a function of pjett . . . . . . . . . . . . . . . . . . . . . . . 152 C.14 Predictions from next-to-leading order QCD calcula- tions as a function of pjett . . . . . . . . . . . . . . . . . . . . . . . 152 C.15 Predictions from next-to-leading order QCD calcula- tions as a function of log x . . . . . . . . . . . . . . . . . . . . . . . 153 C.16 Predictions from next-to-leading order QCD calcula- tions as a function of log x . . . . . . . . . . . . . . . . . . . . . . . 153 C.17 Predictions from next-to-leading order QCD calcula- tions as a function of log x . . . . . . . . . . . . . . . . . . . . . . . 153 C.18 Predictions from next-to-leading order QCD calcula- tions as a function of log x . . . . . . . . . . . . . . . . . . . . . . . 154 C.19 Predictions from next-to-leading order QCD calcula- tions as a 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Wolff, Entwicklung, Bau und erste Ergebnisse eines totzeitfreien Spurfinders als Trigger für das H1-Experiment am HERA Speicherring, PhD thesis, Swiss Federal Institute of Technology Zurich, 1993. 197 198 Danksagung Ich habe vielen Personen zu danken, die einen Beitrag zum Zustandekommen dieser Arbeit geleistet haben. Frau Prof. Dr. B. Naroska, die den Abschluss dieser Arbeit leider nicht mehr er- leben konnte, hat den mit Abstand größten Beitrag geleistet. Ich bedanke mich bei ihr für das Vertrauen und die Möglichkeit, die Promotion am H1 Experiment durchzuführen. Mit ihrem anhaltenden Interesse, unermüdlichen Einsatz und Ver- antwortungsbewusstsein bis zum Schluss wird sie mir als ein großes Vorbild in Erin- nerung bleiben. Dr. Benno List danke ich für die Betreuung der Analyse, das Korrekturlesen der Arbeit und die Übernahme des Gutachtens. Bei Prof. Dr. Klanner bedanke ich mich für seinen Einsatz für die Abschlussfi- nanzierung der Arbeit, das schnelle und gründliche Korrekturlesen der Arbeit und die Übernahme des Gutachtens. Prof. Dr. Schleper und Dr. Hannes Jung danke ich für die bereitwillige Übernahme des Disputationsgutachtens. Bei Dr. Olaf Behnke bedanke ich mich für das Interesse an der Analyse und die beruhigenden, pragmatischen Kommentare. Dr. André Schöning danke ich für die Möglichkeit, am FTT Projekt mitzuarbeiten. Ich konnte in dieser Zeit viel von Dr. Niklaus Berger lernen und habe von seinen Vorarbeiten profitiert. Bei Michael und Mira bedanke ich mich für die gute Zusammenarbeit während der Datenanalyse. Miras positive Einstellung hat zu einer entspannten, positiven Büroatmosphäre beigetragen. Bei Shiraz bedanke ich mich für das Korrekturlesen von Teilen der Arbeit. Besonders wichtig ist es mir, Tobias und den anderen Diplomanden, Doktoranden und Post-Docs der ETH-Zürich-Gruppe in Hamburg, Giom, Lea, Michel, Nik und Ron, für die freundliche Aufnahme während des FTT-Projektes, die gute Zusamme- narbeit auch danach und die vielen privaten Unternehmungen zu danken. 199