() ar X iv :1 40 5. 69 15 v1 [ he p- ex ] 2 7 M ay 2 01 4 DESY–14–083 May 2014 Measurement of beauty and charm production in deep inelastic scattering at HERA and measurement of the beauty-quark mass ZEUS Collaboration Abstract The production of beauty and charm quarks in ep interactions has been studied with the ZEUS detector at HERA for exchanged four-momentum squared 5 < Q2 < 1000 GeV2 using an integrated luminosity of 354 pb−1. The beauty and charm content in events with at least one jet have been extracted using the invariant mass of charged tracks associated with secondary vertices and the decay-length significance of these vertices. Differential cross sections as a function of Q2, Bjorken x, jet transverse energy and pseudorapidity were measured and compared with next-to-leading-order QCD calculations. The beauty and charm contributions to the proton structure functions were extracted from the double-differential cross section as a function of x and Q2. The running beauty-quark mass, mb at the scale mb, was determined from a QCD fit at next-to-leading order to HERA data for the first time and found to be mb(mb) = 4.07 ± 0.14 (fit)+0.01−0.07 (mod.) +0.05 −0.00 (param.) +0.08 −0.05 (theo.) GeV. http://arxiv.org/abs/1405.6915v1 The ZEUS Collaboration H. Abramowicz27,u, I. Abt21, L. Adamczyk8, M. Adamus34, R. Aggarwal4,a, S. Antonelli2, O. Arslan3, V. Aushev16,17,o, Y. Aushev17,o,p, O. Bachynska10, A.N. Barakbaev15, N. Bartosik10, O. Behnke10, J. Behr10, U. Behrens10, A. Bertolin23, S. Bhadra36, I. Bloch11, V. Bokhonov16,o, E.G. Boos15, K. Borras10, I. Brock3, R. Brugnera24, A. Bruni1, B. Brzozowska33, P.J. Bussey12, A. Caldwell21, M. Capua5, C.D. Catterall36, J. Chwastowski7,d, J. Ciborowski33,x, R. Ciesielski10,f , A.M. Cooper-Sarkar22, M. Corradi1, F. Corriveau18, G. D’Agostini26, R.K. Dementiev20, R.C.E. Devenish22, G. Dolinska10, V. Drugakov11, S. Dusini23, J. Ferrando12, J. Figiel7, B. Foster13,l, G. Gach8, A. Garfagnini24, A. Geiser10, A. Gizhko10, L.K. Gladilin20, O. Gogota17, Yu.A. Golubkov20, J. Grebenyuk10, I. Gregor10, G. Grzelak33, O. Gueta27, M. Guzik8, W. Hain10, G. Hartner36, D. Hochman35, R. Hori14, Z.A. Ibrahim6, Y. Iga25, M. Ishitsuka28, A. Iudin17,p, F. Januschek10, I. Kadenko17, S. Kananov27, T. Kanno28, U. Karshon35, M. Kaur4, P. Kaur4,a, L.A. Khein20, D. Kisielewska8, R. Klanner13, U. Klein10,g, N. Kondrashova17,q, O. Kononenko17, Ie. Korol10, I.A. Korzhavina20, A. Kotański9, U. Kötz10, N. Kovalchuk17,r, H. Kowalski10, O. Kuprash10, M. Kuze28, B.B. Levchenko20, A. Levy27, V. Libov10, S. Limentani24, M. Lisovyi10, E. Lobodzinska10, W. Lohmann11, B. Löhr10, E. Lohrmann13, A. Longhin23,t, D. Lontkovskyi10, O.Yu. Lukina20, J. Maeda28,v, I. Makarenko10, J. Malka10, J.F. Martin31, S. Mergelmeyer3, F. Mohamad Idris6,c, K. Mujkic10,h, V. Myronenko10,i, K. Nagano14, A. Nigro26, T. Nobe28, D. Notz10, R.J. Nowak33, K. Olkiewicz7, Yu. Onishchuk17, E. Paul3, W. Perlański33,y, H. Perrey10, N.S. Pokrovskiy15, A.S. Proskuryakov20,ab, M. Przybycień8, A. Raval10, P. Roloff10,j, I. Rubinsky10, M. Ruspa30, V. Samojlov15, D.H. Saxon12, M. Schioppa5, W.B. Schmidke21,s, U. Schneekloth10, T. Schörner-Sadenius10, J. Schwartz18, L.M. Shcheglova20, R. Shehzadi3,aa, R. Shevchenko17,p, O. Shkola17,r, I. Singh4,b, I.O. Skillicorn12, W. Słomiński9,e, V. Sola13, A. Solano29, A. Spiridonov10,k, L. Stanco23, N. Stefaniuk10, A. Stern27, T.P. Stewart31, P. Stopa7, J. Sztuk-Dambietz13, D. Szuba13, J. Szuba10, E. Tassi5, T. Temiraliev15, K. Tokushuku14,m, J. Tomaszewska33,z, A. Trofymov17,r, V. Trusov17, T. Tsurugai19, M. Turcato13, O. Turkot10,i, T. Tymieniecka34, A. Verbytskyi21, O. Viazlo17, R. Walczak22, W.A.T. Wan Abdullah6, K. Wichmann10,i, M. Wing32,w, G. Wolf10, S. Yamada14, Y. Yamazaki14,n, N. Zakharchuk17,r, A.F. Żarnecki33, L. Zawiejski7, O. Zenaiev10, B.O. Zhautykov15, N. Zhmak16,o, D.S. Zotkin20 I 1 INFN Bologna, Bologna, Italy A 2 University and INFN Bologna, Bologna, Italy A 3 Physikalisches Institut der Universität Bonn, Bonn, Germany B 4 Panjab University, Department of Physics, Chandigarh, India 5 Calabria University, Physics Department and INFN, Cosenza, Italy A 6 National Centre for Particle Physics, Universiti Malaya, 50603 Kuala Lumpur, Malaysia C 7 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, Poland D 8 AGH-University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland D 9 Department of Physics, Jagellonian University, Cracow, Poland 10 Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany 11 Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany 12 School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom E 13 Hamburg University, Institute of Experimental Physics, Hamburg, Germany F 14 Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japan G 15 Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan 16 Institute for Nuclear Research, National Academy of Sciences, Kyiv, Ukraine 17 Department of Nuclear Physics, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine 18 Department of Physics, McGill University, Montréal, Québec, Canada H3A 2T8 H 19 Meiji Gakuin University, Faculty of General Education, Yokohama, Japan G 20 Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, Moscow, Russia I 21 Max-Planck-Institut für Physik, München, Germany 22 Department of Physics, University of Oxford, Oxford, United Kingdom E 23 INFN Padova, Padova, Italy A 24 Dipartimento di Fisica dell’ Università and INFN, Padova, Italy A 25 Polytechnic University, Tokyo, Japan G 26 Dipartimento di Fisica, Università ‘La Sapienza’ and INFN, Rome, Italy A 27 Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Tel Aviv, Israel J 28 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan G 29 Università di Torino and INFN, Torino, Italy A 30 Università del Piemonte Orientale, Novara, and INFN, Torino, Italy A II 31 Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 H 32 Physics and Astronomy Department, University College London, London, United Kingdom E 33 Faculty of Physics, University of Warsaw, Warsaw, Poland 34 National Centre for Nuclear Research, Warsaw, Poland 35 Department of Particle Physics and Astrophysics, Weizmann Institute, Rehovot, Israel 36 Department of Physics, York University, Ontario, Canada M3J 1P3 H A supported by the Italian National Institute for Nuclear Physics (INFN) B supported by the German Federal Ministry for Education and Research (BMBF), under contract No. 05 H09PDF C supported by HIR grant UM.C/625/1/HIR/149 and UMRG grants RU006-2013, RP012A-13AFR and RP012B-13AFR from Universiti Malaya, and ERGS grant ER004-2012A from the Ministry of Education, Malaysia D supported by the National Science Centre under contract No. DEC- 2012/06/M/ST2/00428 E supported by the Science and Technology Facilities Council, UK F supported by the German Federal Ministry for Education and Research (BMBF), under contract No. 05h09GUF, and the SFB 676 of the Deutsche Forschungsge- meinschaft (DFG) G supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and its grants for Scientific Research H supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) I supported by RF Presidential grant N 3042.2014.2 for the Leading Scientific Schools and by the Russian Ministry of Education and Science through its grant for Scientific Research on High Energy Physics J supported by the Israel Science Foundation III a also funded by Max Planck Institute for Physics, Munich, Germany b also funded by Max Planck Institute for Physics, Munich, Germany, now at Sri Guru Granth Sahib World University, Fatehgarh Sahib c also at Agensi Nuklear Malaysia, 43000 Kajang, Bangi, Malaysia d also at Cracow University of Technology, Faculty of Physics, Mathematics and Ap- plied Computer Science, Poland e partially supported by the Polish National Science Centre projects DEC- 2011/01/B/ST2/03643 and DEC-2011/03/B/ST2/00220 f now at Rockefeller University, New York, NY 10065, USA g now at University of Liverpool, United Kingdom h also affiliated with University College London, UK i supported by the Alexander von Humboldt Foundation j now at CERN, Geneva, Switzerland k also at Institute of Theoretical and Experimental Physics, Moscow, Russia l Alexander von Humboldt Professor; also at DESY and University of Oxford m also at University of Tokyo, Japan n now at Kobe University, Japan o supported by DESY, Germany p member of National Technical University of Ukraine, Kyiv Polytechnic Institute, Kyiv, Ukraine q now at DESY ATLAS group r member of National University of Kyiv - Mohyla Academy, Kyiv, Ukraine s now at BNL, USA t now at LNF, Frascati, Italy u also at Max Planck Institute for Physics, Munich, Germany, External Scientific Mem- ber v now at Tokyo Metropolitan University, Japan w also supported by DESY x also at Łódź University, Poland y member of Łódź University, Poland z now at Polish Air Force Academy in Deblin aa now at University of the Punjab, Lahore, Pakistan ab deceased IV 1 Introduction The measurement of beauty and charm production in ep collisions at HERA is an im- portant testing ground for perturbative Quantum Chromodynamics (pQCD), since the heavy-quark masses provide a hard scale that allows perturbative calculations to be made. At leading order, the dominant process for heavy-quark production at HERA is boson- gluon fusion (BGF). In this process, a virtual photon emitted by the incoming electron interacts with a gluon from the proton forming a heavy quark–antiquark pair. When the negative squared four-momentum of the virtual photon, Q2, is large compared to the pro- ton mass, the interaction is referred to as deep inelastic scattering (DIS). For heavy-quark transverse momenta comparable to the quark mass, next-to-leading-order (NLO) QCD calculations based on the dynamical generation of the massive quarks [1–5] are expected to provide reliable predictions. Beauty and charm production in DIS has been measured using several methods by the H1 [6–18] and ZEUS [19–33] collaborations. All but the two most recent measurements of charm production [32, 33] and older data [24] have been combined [34]. Predictions from NLO QCD describe all results reasonably well. Inclusive jet cross sections in beauty and charm events are used in the analysis presented here to extract the heavy-quark contribution to the proton structure function F2 with high precision, and to measure related QCD parameters. For this purpose, the long lifetimes of the weakly decaying b and c hadrons, which make the reconstruction of their decay vertices possible, as well as their large masses were exploited. Two discriminating variables, the significance of the reconstructed decay length and the invariant mass of the charged tracks associated with the decay vertex (secondary vertex), were used. This inclusive tagging method leads to a substantial increase in statistics with respect to previous ZEUS measurements. Differential cross sections as a function of Q2, the Bjorken scaling variable, x, jet transverse energy, E jet T , and pseudorapidity, η jet, were measured. They are compared to a leading- order (LO) plus parton-shower (PS) Monte Carlo prediction and to NLO QCD calculations. The beauty and charm contributions to the proton structure function F2, denoted as F bb̄ 2 and F cc̄2 , respectively, as well as beauty and charm reduced cross sections (σ bb̄ r and σ cc̄ r , respectively) were extracted from the double-differential cross section as a function of Q2 and x. The results are compared to previous measurements and to predictions from perturbative QCD. The running MS beauty-quark mass, mb at the scale mb, denoted mb(mb), is measured using σbb̄r , following a procedure similar to that used for a recent extraction of the charm- quark mass [34]. This represents the first measurement of the b-quark mass using HERA or any other hadron collider data. 1 2 Experimental set-up This analysis was performed with data taken with the ZEUS detector from 2004 to 2007, when HERA collided electrons1 with energy Ee = 27.5 GeV with protons of energy 920 GeV, corresponding to a centre-of-mass energy √ s = 318 GeV. This data-taking period is denoted as HERA II. The corresponding integrated luminosity is (354 ± 7) pb−1. A detailed description of the ZEUS detector can be found elsewhere [35]. A brief outline of the components that are most relevant for this analysis is given below. In the kinematic range of the analysis, charged particles were tracked in the central tracking detector (CTD) [36–38] and the microvertex detector (MVD) [39]. These components operated in a magnetic field of 1.43 T provided by a thin superconducting solenoid. The CTD consisted of 72 cylindrical drift-chamber layers, organised in nine superlayers covering the polar-angle2 region 15° < θ < 164°. The MVD silicon tracker consisted of a barrel (BMVD) and a forward (FMVD) section. The BMVD contained three layers and provided polar-angle coverage for tracks from 30° to 150°. The four-layer FMVD extended the polar- angle coverage in the forward region to 7°. After alignment, the single-hit resolution of the MVD was 24 µm. The transverse distance of closest approach (DCA) of tracks to the nominal vertex in X–Y was measured to have a resolution, averaged over the azimuthal angle, of (46 ⊕ 122/pT ) µm, with pT in GeV. For CTD-MVD tracks that pass through all nine CTD superlayers, the momentum resolution was σ(pT )/pT = 0.0029pT ⊕ 0.0081 ⊕ 0.0012/pT , with pT in GeV. The high-resolution uranium–scintillator calorimeter (CAL) [40–43] consisted of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. Each part was subdivided transversely into towers and longitudinally into one electromagnetic section (EMC) and either one (in RCAL) or two (in BCAL and FCAL) hadronic sections (HAC). The smallest subdivision of the calorimeter was called a cell. The CAL energy res- olutions, as measured under test-beam conditions, were σ(E)/E = 0.18/ √ E for electrons and σ(E)/E = 0.35/ √ E for hadrons, with E in GeV. The luminosity was measured using the Bethe-Heitler reaction ep → eγp by a luminosity detector which consisted of independent lead–scintillator calorimeter [44–46] and magnetic spectrometer [47] systems. 1 In this paper “electron” is used to denote both electron and positron. 2 The ZEUS coordinate system is a right-handed Cartesian system, with the Z axis pointing in the nominal proton beam direction, referred to as the “forward direction”, and the X axis pointing towards the centre of HERA. The coordinate origin is at the centre of the CTD. The pseudorapidity is defined as η = − ln ( tan θ 2 ) , where the polar angle, θ, is measured with respect to the Z axis. 2 3 Monte Carlo simulations To evaluate the detector acceptance and to provide predictions of the signal and back- ground distributions, Monte Carlo (MC) samples of beauty, charm and light-flavour events were generated, corresponding to eighteen, three and one times the integrated luminos- ity of the data, respectively. The Rapgap 3.00 MC program [48] in the massive mode (mb = 4.75 GeV, mc = 1.5 GeV) was used to generate the beauty and charm samples, where the CTEQ5L [49] parameterisation for the proton parton density functions (PDFs) was used. In Rapgap, LO matrix elements are combined with higher-order QCD radi- ation simulated in the leading-logarithmic approximation. Higher-order QED effects are included through Heracles 4.6 [50]. Light-flavour MC events were extracted from an inclusive DIS sample generated with Djangoh 1.6 [51] interfaced to Ariadne 4.12 [52]. The CTEQ5D [49] PDFs were used and quarks were taken to be massless. Fragmentation and particle decays were simulated using the Jetset/Pythia model [53, 54]. The Bowler parameterisation [55] of the fragmentation function, as implemented in Pythia [56], was used for the heavy-flavour samples. The generated events were passed through a full simulation of the ZEUS detector based on Geant 3.21 [57]. The final MC events were then subjected to the same trigger requirements and processed by the same reconstruction program as the data. For the acceptance determination, the E jet T and η jet distributions in the charm MC, as well as the Q2 distributions in both the beauty and charm MCs, were reweighted in order to give a good description of the data. The charm branching fractions and fragmentation fractions were adjusted to the world-average values [58, 59]. 4 Theoretical predictions and uncertainties Next-to-leading-order QCD predictions for differential cross sections were obtained from the Hvqdis program [60]. The calculations were used to extrapolate the visible cross sections to extract F bb̄2 , F cc̄ 2 , σ bb̄ r and σ cc̄ r (see Section 9). The calculations are based on the fixed-flavour-number scheme (FFNS) in which only light flavours are present in the proton and heavy quarks are produced in the interaction [61]. Therefore, the 3-flavour (4-flavour) FFNS variant of the ZEUS-S NLO QCD fit [62] was used for the proton PDF for the predictions of the charm (beauty) cross sections. As in the PDF fit, the value of αs(MZ) was set to 0.118 and the heavy-quark masses (pole masses) were set to mb = 4.75 GeV and mc = 1.5 GeV. The renormalisation and factorisation scales, µR and µF , were chosen to be equal and set to µR = µF = √ Q2 + 4m2 b(c) . The systematic uncertainty on the theoretical predictions with the ZEUS-S PDFs were estimated by varying the quark masses and the renormalisation and factorisation scales. 3 Quark masses of mb = 4.5 and 5.0 GeV, mc = 1.3 and 1.7 GeV were used. The scales µR, µF were varied independently by a factor of two up and down. Additionally, the experimental uncertainties of the data used in the PDF fit were propagated to the predicted cross sections. The total uncertainties were obtained by adding positive and negative changes to the cross sections in quadrature. This results in total uncertainties of 10–20 % for beauty and 10–50 % for charm. Predictions were also obtained using the 3- and 4-flavour variants of the ABKM NLO PDFs [63] for the proton. The pole masses of heavy quarks were set to mb = 4.5 GeV and mc = 1.5 GeV, both in the PDF fit and in the Hvqdis calculation. The values of αs(µR) were provided by LHAPDF [64, 65] to ensure that the same function was used as in the PDF fit. The renormalisation and factorisation scales were both set to µR = µF = √ Q2 + 4m2 b(c) . The NLO QCD predictions are given for parton-level jets. These were reconstructed using the kT clustering algorithm [66] with a radius parameter R = 1.0 in the longitudinally invariant mode [67]. The E-recombination scheme, which produces massive jets whose four-momenta are the sum of the four-momenta of the clustered objects, was used. The parton-level cross sections were corrected for jet hadronisation effects to allow a direct comparison with the measured hadron-level cross sections: σhad, NLO = Chadσparton,NLO , (1) where the correction factors, Chad = 1 + ∆had, were derived from the Rapgap MC simu- lation. The factors Chad are defined as the ratio of the hadron-level jet to the parton-level jet cross sections, and the parton level is defined as the result of the parton-showering stage of the simulation. Since Chad were derived from an LO plus parton shower MC, but are applied to an NLO prediction, the uncertainty on Chad cannot be estimated in a straightforward way. Within the framework of parton showering, MC subsets with different numbers of radiated partons were investigated using Rapgap and Pythia samples. These studies indicated that different approaches yield variations of ∆had of typically a factor of two. Since it is not clear if the variations can be interpreted as uncertainties on Chad, no such uncertainties were included in the cross-section (F2) predictions. However, for the extraction of the b-quark mass, such a theoretical uncertainty needs to be included. 5 Data selection Events containing a scattered electron were selected online by means of a three-level trigger system [35, 68]. The trigger [69] did not require the presence of a secondary vertex nor of a jet. 4 Offline, the scattered electron was reconstructed using an electron finder based on a neural network [70]. The hadronic system was reconstructed from energy-flow objects (EFOs) [71, 72] which combine the information from calorimetry and tracking, corrected for energy loss in the detector material. The kinematic variables used in the cross-section measurements, Q2 and x, were reconstructed using the double-angle method [73]. The following cuts were applied to select a clean DIS sample: • the reconstructed scattered electron [70, 74] was required to have an energy E′e > 10 GeV; • the impact position of the scattered electron on the face of the RCAL had to be outside the region 26 × 26 cm2 centred on X = Y = 0; • the primary vertex had to be within ±30 cm in Z of the nominal interaction point; • the photon virtuality, Q2, had to be within 5 < Q2 < 1000 GeV2; • yJB > 0.02, where yJB is the inelasticity reconstructed using the Jacquet-Blondel method [75]; • ye < 0.7, where ye is the inelasticity reconstructed using the electron method [73]; • 44 < (E − pZ) < 65 GeV, where (E − pZ) = ∑ i (Ei − pZ,i) and i runs over all final- state particles with energy Ei and Z-component of momentum pZ,i; this selects fully contained neutral-current ep events for which E − pZ = 2Ee. Jets were reconstructed from EFOs using the kT clustering algorithm [66] as was described for parton-level jets in Section 4. Jets containing the identified scattered electron were not considered further. Events were selected if they contained at least one jet within the pseudorapidity range −1.6 < ηjet < 2.2 and with transverse energy, EjetT , of E jet T = p jet T Ejet pjet > 5 (4.2) GeV for beauty (charm), where Ejet, pjet and p jet T are the jet energy, momentum and transverse momentum. The cut on E jet T was optimised separately for beauty and charm measure- ments. For beauty, a cut of E jet T > 5 GeV ensures a good correlation of reconstructed and hadron-level jets; for charm this cut was 4.2 GeV to reduce the extrapolation uncertainties for the F cc̄2 and σ cc̄ r measurements at low Q 2. In order to reconstruct potential secondary vertices related to b- and c-hadron decays, tracks were selected if: • they had a transverse momentum pT > 0.5 GeV; • the total number of hits3 on the track in the MVD was ≥ 4. 3 Each MVD layer provided two coordinate measurements. 5 • if the track was inside the CTD acceptance, track recognition in the CTD was re- quired; the percentage of the tracks used for vertexing with no CTD hits was 2.5 %. Tracks were associated with the closest jet if they fulfilled the criterion ∆R < 1 with ∆R = √ (ηtrk − ηjet)2 + (φtrk − φjet)2. If two or more of such tracks were associated with the jet, a candidate vertex was fitted from the selected tracks using a deterministic annealing filter [76–78]. This fit provided the vertex position and its error matrix as well as the invariant mass, mvtx, of the charged tracks associated with the reconstructed vertex. The charged-pion mass was assumed for all tracks when calculating the vertex mass. Vertices with χ2/ndf < 6, a distance from the interaction point within ±1 cm in the X–Y plane, ±30 cm in the Z direction, and 1 < mvtx < 6 GeV were kept for further analysis. The MC gives a good description of the track efficiencies, except for a small fraction of tracks that are affected by hadronic interactions in the detector material between the interaction point and the CTD. Efficiency corrections for this effect were determined from a study of exclusive ep → eρ0p events [79], using a special track reconstruction. The number of the pions from the ρ0 decay that were reconstructed in the MVD alone and had no extension in the CTD was measured. The resulting track efficiency correction in the MC was applied by randomly rejecting selected vertex tracks before the vertex fit, with a probability that depends on the track parameters (around 3 % at η = 0 and pT = 1 GeV). 6 Extraction of the heavy-flavour cross sections Using the secondary-vertex candidates associated with jets, the decay length, d, was defined as the vector in X–Y between the secondary vertex and the interaction point4 projected onto the jet axis in the X–Y plane. The sign of the decay length was assigned using the axis of the jet to which the vertex was associated; if the decay-length vector was in the same hemisphere as the jet axis, a positive sign was assigned to it, otherwise the sign of the decay length was negative. Negative decay lengths, which originate from secondary vertices reconstructed on the wrong side of the interaction point with respect to the direction of the associated jets, are unphysical and caused by detector resolution effects. A small smearing correction [79] to the MC decay-length distribution was applied in order to reproduce the data with negative values of decay length. The beauty and charm content in the selected sample was determined using the shape of the decay-length significance distribution together with the secondary-vertex mass dis- tribution, mvtx. The decay-length significance, S, is defined as d/δd, where δd is the uncertainty on d. The invariant mass of the tracks fitted to the secondary vertex provides 4 In the X–Y plane, the interaction point was defined as the centre of the beam ellipse, determined using the average primary vertex position for groups of a few thousand events, taking into account the difference in angle between the beam direction and the Z direction. The Z coordinate was taken as the Z position of the primary vertex of the event. 6 a distinguishing variable for jets from b and c quarks, reflecting the different masses of the b and c hadrons. Figure 1 shows the decay-length significance, S, for E jet T > 4.2 GeV divided into four bins: 1 < mvtx < 1.4 GeV, 1.4 < mvtx < 2 GeV, 2 < mvtx < 6 GeV and no restriction on mvtx. The MC simulation provides a good description of the data. The separation into subsamples is described below. The contents of the negative bins of the significance distribution, N(S−), were subtracted from the contents of the corresponding positive bins, N(S+), yielding a subtracted decay- length significance distribution. In this way, the contribution from light-flavour quarks is minimised. An additional advantage of this subtraction is that symmetric systematic effects, which might arise from discrepancies between the data and the MC, are removed. In order to reduce the contamination of tracks originating from the primary vertex, a cut of |S| > 4 was applied. To extract the contributions from beauty, charm and light flavours in the data sample, a binned χ2 fit of the subtracted significance distribution in the region 4 < |S| < 20 was performed simultaneously for three mass bins [69]: 1 < mvtx < 1.4 GeV; 1.4 < mvtx < 2 GeV; 2 < mvtx < 6 GeV. All MC distributions were normalised to the integrated luminosity of the data before the fit. The overall MC normalisation was constrained by requiring it to be consistent with the normalisation of the data in the significance distribution with |S| < 20 and 1 < mvtx < 6 GeV. The fit yielded scaling factors kb, kc and klf for the beauty, charm and light-flavour contributions, respectively, to obtain the best description of the data. The correlation coefficients were as follows: ρb,c = −0.68(−0.67), ρb,lf = 0.58(0.57) and ρc,lf = −0.98(−0.98) for EjetT > 4.2(5.0) GeV. The subtracted and fitted distributions for E jet T > 4.2 GeV are shown in Fig. 2. A good agreement between data and MC is observed. The first two mass bins corresponding to the region 1 < mvtx < 2 GeV are dominated by charm events. In the third mass bin, beauty events are dominant at high values of significance. The fit procedure was repeated for every bin of a given observable to obtain differential cross sections. For the beauty cross-section extraction, the fit procedure was repeated with the higher cut on E jet T , E jet T > 5 GeV. Control distributions of E jet T , η jet, log10 Q 2 and log10 x are shown in Fig. 3 after beauty enrichment cuts (2 < mvtx < 6 GeV and |S| > 8) for EjetT > 5.0 GeV and in Fig. 4 after charm enrichment cuts (1 < mvtx < 2 GeV and |S| > 4) for EjetT > 4.2 GeV. All data distributions are reasonably well described by the MC. The differential cross sections for jet production in beauty or charm events, q = b, c, corrected to QED Born level, in a bin i of a given observable, Y , are given by: dσjetq dYi = kq(Yi) Nhad,MCq (Yi) L · ∆Yi 1 Crad , (2) where ∆Yi is the width of the bin, kq denotes the scaling factor obtained from the fit, Nhad,MCq is the number of generated jets in beauty or charm events at the MC hadron level, 7 Crad is the QED radiative correction and L is the corresponding integrated luminosity. Hadron-level jets were obtained by running the kT clustering algorithm on all stable final- state particles, in the same mode as for the data. Weakly decaying b and c hadrons were treated as stable particles and were decayed only after the application of the jet algorithm. The predictions from the Hvqdis program are given at the QED Born level with a running coupling, αem. Hence, a correction of the measured cross sections for QED radiative effects is necessary in order to be able to compare them directly to the Hvqdis predictions. The corrections were obtained using the Rapgap Monte Carlo as Crad = σrad/σBorn, where σrad is the cross section with full QED corrections, as used in the standard MC samples, and σBorn was obtained with the QED corrections turned off but keeping αem running. Both cross sections, σrad and σBorn, were obtained at the hadron level. 7 Systematic uncertainties The systematic uncertainties were evaluated by varying the analysis procedure or by chan- ging the selection cuts and repeating the extraction of the cross section. The following sources of experimental systematic uncertainties were identified [69, 79]; the uncertainties on the integrated cross sections determined for each source are summarised in Table 1 to indicate the sizes of the different effects: δ1 DIS selection – the cuts for DIS event selection were varied in both data and MC. The cut on the scattered electron energy was varied between 9 < E′e < 11 GeV (δ Ee 1 ), the cut on the inelasticity was varied between 0.01 < yJB < 0.03 (δ y 1), and the lower cut on E − pZ was changed by ±2 GeV (δE−pZ1 ); δ2 trigger efficiency – the uncertainty on the trigger efficiency was evaluated by comparing events taken with independent triggers; δ3 tracking efficiency correction – the size of the correction was varied by its estimated uncertainty of ±50 %; δ4 decay-length smearing – the fraction of secondary vertices for which the decay length was smeared was varied separately in the core (δcore4 ) and the tails (δ tail 4 ) of the distri- bution such that the agreement between data and MC remained reasonable; δ5 signal extraction procedure – the systematic uncertainty on the signal extraction pro- cedure was estimated by changing the lower |S| cut from |S| > 4 to |S| > 3 and |S| > 5; δ6 jet energy scale – the calorimetric part of the transverse jet energy in the MC was varied by its estimated uncertainty of ±3 %; 8 δ7 electron energy scale – the reconstructed energy of the scattered electron was varied in the MC by its estimated uncertainty of ±2 %; δ8 MC model dependence – the Q 2 (δ Q2 8 ), η jet (δ ηjet 8 ) and E jet T (δ E jet T 8 ) reweighting corrections in the charm MC were varied in a range for which the description of data by MC remained reasonable. The same relative variations were applied to the beauty MC; δ9 light-flavour background – the light-flavour contribution to the subtracted significance distribution includes a contribution from long-lifetime strange-hadron decays. To es- timate the uncertainty due to modelling of this effect, the MC light-flavour distribution of N(S+) − N(S−) was scaled by ±30 % [15] and the fit was repeated; δ10 charm fragmentation function – to estimate the sensitivity to the charm fragmentation function, it was changed in the MC from the Bowler to the Peterson [80] parameterisa- tion with ǫ = 0.062 [81]; δ11 beauty fragmentation function – to estimate the sensitivity to the beauty fragmentation function, it was changed in the MC from the Bowler to the Peterson parameterisation with ǫ = 0.0041 [82]; δ12 charm branching fractions (δ BR 12 ) and fragmentation fractions (δ frag 12 ) – these were varied within the uncertainties of the world-average values [58, 59, 83]; δ13 luminosity measurement – a 1.9 % overall normalisation uncertainty was associated with the luminosity measurement. To evaluate the total systematic uncertainty on the integrated cross sections, the contri- butions from the different systematic uncertainties were added in quadrature, separately for the negative and the positive variations. The same procedure was applied to each bin for the differential cross sections. However, the luminosity measurement uncertainty was not included. In the case of beauty, the dominant effects arise from the uncertainties on the track-finding inefficiencies, the beauty fragmentation function and MC modelling. For charm, the uncertainties on the branching fractions, the light-flavour asymmetry as well as on the MC modelling contribute most to the total systematic uncertainty. 8 Cross sections Cross sections for inclusive jet production in beauty (charm) events were measured in the range E jet T > 5(4.2) GeV, −1.6 < ηjet < 2.2 for DIS events with 5 < Q2 < 1000 GeV2 and 0.02 < y < 0.7, where the jets are defined as in Section 6. The single-differential cross sections for jet production in beauty and charm events were measured as a function of E jet T , η jet, Q2 and x. The results of the measured cross sections are given in Tables 2–5 and shown in Figs. 5–8. The measurements are compared to the Hvqdis NLO QCD 9 predictions obtained using ZEUS-S and ABKM as proton PDFs, and to the Rapgap predictions scaled by a factor of 1.49 for beauty and 1.40 for charm. The scale factors correspond to the ratio of the measured integrated visible cross section to the Rapgap prediction. The shapes of all measured beauty cross sections are reasonably well described by Hvqdis and the Rapgap MC. Rapgap provides a worse description of the shape of the charm cross sections than Hvqdis.5 For charm, the data are typically 20–30 % above the Hvqdis NLO prediction, but in reasonable agreement within uncertainties. Differences between the NLO predictions using the different proton PDFs are mostly very small. Double-differential cross sections as a function of x for different ranges of Q2 for inclusive jet production in beauty and charm events are listed in Tables 6 and 7, respectively. 9 Extraction of F qq̄ 2 and σqq̄ r The heavy-quark contribution to the proton structure function F2, F qq̄ 2 with q = b, c, can be defined in terms of the inclusive double-differential cross section as a function of x and Q2, d2σqq̄ dx dQ2 = 2πα2em xQ4 { [1 + (1 − y2)]F qq̄2 (x, Q2) − y2F qq̄ L (x, Q 2) } , where F qq̄ L is the heavy-quark contribution to the structure function FL. To extract F qq̄ 2 from the visible jet production cross sections in heavy-quark events, meas- ured in bins of x and Q2, an extrapolation from the measured range in E jet T and η jet to the full kinematic phase space was performed. This implicitly takes into account the jet multiplicity. The measured values of F qq̄ 2 at a reference point in the x–Q 2 plane were calculated using F qq̄ 2 (x, Q 2) = d2σjetq /dx dQ 2 d2σ had,NLO q /dx dQ2 F qq̄,NLO 2 (x, Q 2) , (3) where d2σjetq /dx dQ 2 is determined in analogy to Eq. (2), and F qq̄,NLO 2 and d 2σhad,NLOq /dx dQ 2 were calculated at NLO in the FFNS using the Hvqdis program with the factor Chad applied as in Eq. (1). The proton PDFs were obtained from the FFNS variant of the HERAPDF 1.0 NLO QCD fit [34]. This PDF was used in order to be consistent with the HERA combined results [34]. The strong coupling constant αs(MZ) was set to 0.105 as in the PDF fit. Other settings were as described in Section 4 for the ZEUS-S variant. As discussed in Section 6, d2σjetq /dx dQ 2 was multiplied by 1/Cradq , hence F qq̄ 2 is given at QED Born level, consistent with the usual convention. The procedure of Eq. (3) also corrects for the F qq̄ L contribution to the cross section. This assumes that the calculation correctly predicts the ratio F qq̄ L /F qq̄ 2 . 5 For the acceptance corrections, the Monte Carlo was reweighted as discussed in Section 3. 10 The extrapolation factors for beauty due to cuts on E jet T and η jet typically range from 1.3 to 1.0, decreasing with increasing Q2. The factor is up to 1.7 at high values of x. For charm, the extrapolation factors are typically about 4 in the region 5 < Q2 < 20 GeV2 and about 2 in the region 20 < Q2 < 60 GeV2. The uncertainty on the extrapolation from the measured range to the full kinematic phase space was estimated by varying the paramet- ers of the calculation for the extrapolation factors and adding the resulting uncertainties in quadrature. For charm, the same variations were performed as for the HERA com- bined results [34]: the charm mass was varied by ±0.15 GeV; the strong coupling constant αs(MZ) was changed by ±0.002; renormalisation and factorisation scales were multiplied simultaneously by 0.5 or 2. Uncertainties resulting from the proton PDF uncertainty are small [84] and were neglected. For beauty, the same variations of αs and scales were made and the beauty mass was varied by ±0.25 GeV. For each bin, a reference point in x and Q2 was defined (see Table 8) to calculate the structure function. In addition, beauty and charm reduced cross sections were determined. They are defined as σqq̄r = d2σqq̄ dx dQ2 · xQ4 2πα2em[1 + (1 − y2)] = F qq̄ 2 (x, Q 2) − y2 1 + (1 − y2) F qq̄ L (x, Q 2) , and are extracted in analogy to F qq̄ 2 as described above except that no assumption on F qq̄ L is required. The extracted values of F bb̄2 and F cc̄ 2 are given in Tables 8 and 9, respectively, while σ bb̄ r and σcc̄r are shown in Tables 10 and 11. The total uncertainties of the measurements were calculated from the statistical and systematic uncertainties of the measured cross sections (Tables 6, 7, 12–15) and of the extrapolation uncertainty (Tables 16–19), added in quadrature. The structure function F cc̄2 is shown in Fig. 9 as a function of x for different values of Q 2. The measurements are compared to the NLO QCD HERAPDF 1.5 [85] predictions, the most recent official release of the HERAPDF, based on the RT [86] general-mass variable- flavour-number scheme (GMVFNS). The predictions are consistent with the measure- ments. In Fig. 10, the measured σcc̄r values are compared to the HERA combined results [34] as well as to the two recent results from ZEUS [32, 33] which are not yet included in the combination. For the comparison, some of the measured values of this analysis were swum in Q2 and x using Hvqdis. This measurement is competitive, especially at high Q2, where the extrapolation uncertainty is low, and is in agreement with the HERA combined measurements. The structure function F bb̄2 is shown in Fig. 11 as a function of x for different values of Q 2. The measurements are compared to HERAPDF 1.5 GMVFNS predictions. The increase in the uncertainty on the prediction around Q2 = m2b is a feature of the GMVFNS scheme used. The predictions are consistent with the measurements. 11 The F bb̄2 measurement is also shown as a function of Q 2 for fixed x in Fig. 12, and is compared to previous ZEUS and H1 measurements. Again, Hvqdis was used to swim the measured values in Q2 and x to match the previous measurements. In a wide range of Q2, this measurement represents the most precise determination of F bb̄2 at HERA. It is in good agreement with the previous ZEUS analyses and H1 measurements. Several NLO and NNLO QCD predictions based on the fixed- or variable-flavour-number schemes [85–92] are also compared to the measurements. Predictions from different theoretical approaches agree well with each other. All predictions provide a reasonable description of the data. 10 Measurement of the running beauty-quark mass The reduced beauty cross sections, σbb̄r , (Fig. 13 and Table 10) together with inclusive DIS data were used to determine the beauty-quark mass, in a simultaneous fit of the mass and the parton densities. The measurement procedure follows closely the method presented in a recent H1-ZEUS publication [34], where the running charm-quark mass in the MS scheme was extracted using a simultaneous QCD fit of the combined HERA I inclusive DIS data [93] and the HERA combined charm DIS data [34]. This approach was also used and extended by a similar independent analysis [94], and was preceded by a similar analysis of a partial charm data set [95]. The fit for the running beauty-quark mass was performed within the HERAFitter [96] framework choosing the ABM implementation of the fixed-flavour-number scheme at next- to-leading order [4,5,91,97,98]. The OPENQCDRAD [99] option in HERAFitter was used in the MS running-mass mode. The fit was applied to the beauty data listed in Table 10 and to the same inclusive DIS data as in the charm-quark mass fit [34]. A fit to the inclusive data only does not show any significant dependence on mb. In order to avoid technical complications, no charm data were included in the simultaneous fit and only mb was extracted. The PDFs resulting from the simultaneous fit changed only marginally with respect to the nominal PDFs obtained from the fit to the inclusive DIS data only. The χ2 of the QCD fit, including the beauty data, shows a clear dependence on the beauty-quark mass, mb, as can be seen in Fig. 14. The total χ2 for the best fit is 587 for 596 degrees of freedom, and the partial contribution from the beauty data is 11.4 for 17 points. The beauty-quark mass and its uncertainty are determined from a parabolic parameterisation. The best fit yields mb(mb) = 4.07 ± 0.14 (fit)+0.01−0.07 (mod.)+0.05−0.00 (param.) +0.08−0.05 (theo.) GeV 12 for the MS running beauty-quark mass at NLO. The fit uncertainty6 (fit) is determined from ∆χ2 = 1. It contains the experimental uncertainties, the extrapolation uncertainties, the uncertainties of the standard PDF parameterisation, as well as an estimate of the uncertainty on the hadronisation corrections, as detailed below. In addition, the result has uncertainties attributed to the choices of some extra model parameters (mod.), some additional variations of the PDF parameterisation (param.) and uncertainties on the perturbative QCD parameters (theo.). Details of the uncertainty evaluation include: Fit uncertainty: For the beauty data, all uncertainties from Tables 12, 13 (experimental) and 18 (extrapolation), and the statistical uncertainty, as summarised in Table 10, were accounted for in the fit. Following the discussion in Section 4, an uncertainty of 100 % on ∆had = Chad − 1 (Table 6) was introduced as an additional uncorrelated uncertainty. The uncertainties arising from the default PDF parameterisation [34], including the so-called “flexible” gluon parameterisation, are implicitly part of the fit uncertainty. The statistical uncertainties and the uncertainties δ1, δ2, δ core 4 , δ5 and δ12 from Tables 12 and 13 were treated as uncorrelated, while all other uncertainties, including those from luminosity and from Table 18, were treated as point-to-point correlated. The “multiplicative” uncertainty option [96] from HERAFitter was used. In the case of asymmetric uncertainties, the larger was used in both directions. The uncertainties of the inclusive data were used as published. Since the inclusive data were taken during the HERA I phase and the beauty data during the HERA II phase, the two sets of data were treated as uncorrelated. Model uncertainty: The model choices include an assumption on the strangeness frac- tion, fs, the minimum Q 2 used in the data selection, Q2min, and Q 2 0, the starting value for the QCD evolution. These were treated exactly as in the charm-quark mass fit [34]. Table 20 lists the choices and variations and their individual contribu- tions to the model uncertainty attributed to the model choices. Another source of uncertainty is that the b-quark mass was used earlier to extrapolate the measured visible cross sections to the reduced cross sections. The corresponding uncertainty is parameterised in Table 18 and used in the fit, but the correlation of this uncertainty with the mass used in the QCD fit is lost. Since the Hvqdis [60] program used for the extrapolation uses the pole-mass scheme, and no differential calculations are available in the running-mass scheme, no fully consistent treatment of this correlation is possible. However, the equivalent uncertainty when using the pole-mass scheme can be consistently estimated. For this purpose, the fit was re- peated with the pole-mass option of OPENQCDRAD, which was checked to yield results consistent with the Hvqdis predictions for σbb̄r . 6 For the charm-quark mass fit [34] this uncertainty was denoted “exp”. 13 The result, mb(pole) = 4.35 ± 0.14 (fit) GeV, has a fit uncertainty which is the same as the fit uncertainty for the running-mass fit. However, since the pole-mass defin- ition includes an unavoidable additional theoretical uncertainty due to a nonper- turbative contribution, no attempt to extract a pole-mass measurement with full systematic uncertainties was made. To recover the correlation between the extra- polation and the mass fit, the extrapolated cross sections were iteratively modified using the predictions from the mass values obtained in each fit. This removes the uncertainty on mb in the extrapolation and takes the full correlations into account. The resulting mass mb(pole) = 4.28 ± 0.13 (fit) GeV is slightly lower. The difference between the results from the two procedures (δmext = −0.07 GeV) was treated as an additional model uncertainty. PDF parameterisation uncertainty: The parameterisation of the PDFs is chosen as for the charm-quark mass fit [34], including the “flexible” parameterisation of the gluon distribution. An additional uncertainty is estimated by freeing three extra PDF parameters Duv , DD̄ and DŪ in the fit which allow for small shape variations in the uv, Ū and D̄ parton distributions [34]. The effect is given in Table 20. Perturbative scheme and related theory uncertainty: The parameters used for the per- turbative part of the QCD calculations also introduce uncertainties; the effects are listed in Table 20. As in previous analyses [34, 94, 95], the MS running-mass scheme [100–102] was chosen for all calculations of the reduced cross sections and the fit because it shows better perturbative convergence behaviour than the pole-mass scheme. In order to allow the low-Q2 points of the inclusive DIS measurement to be included without the need of additional charm-quark mass corrections, the number of active flavours (NF) was set to three, i.e. the charm contribution was also treated in the fixed-flavour-number scheme. Accordingly, the strong coupling constant was set to αs(MZ) NF=3 = 0.105 ± 0.002, corresponding to αs(MZ)NF=5 = 0.116 ± 0.002. The theoretical prediction of the charm contribution to the inclusive DIS data is obtained using the running charm-quark mass obtained from the fit to the combined HERA charm data [34], i.e. mc(mc) = (1.26 ± 0.06) GeV. It was checked that, as expected, using this mass together with the central PDF from the mb fit, a good description of the combined HERA charm data [34] was obtained. Thus, the charm contribution to the inclusive data should be well described. The renormalisation and factorisation scales were set to µ = µR = µF = √ Q2 + 4m2 with m = 0, mc, mb for the light quark, charm, and beauty contributions, respect- ively, and varied simultaneously by a factor two as in previous analyses [94, 95]. The measured beauty-quark mass is in very good agreement with the world average mb(mb) = (4.18 ± 0.03) GeV [103]. The resulting predictions for the beauty cross sec- tions are shown together with the data in Fig. 13. Figure 13 also shows the change in the 14 predictions resulting from the fit when different mb values are assumed. The largest sensit- ivity to mb arises from the low-Q 2 region, while at high Q2 the impact of the beauty-quark mass is small. 11 Conclusions Inclusive jet production cross sections in events containing beauty or charm quarks have been measured in DIS at HERA, exploiting the long lifetimes and large masses of b and c hadrons. In contrast to previous analyses at ZEUS, the measurement was not restricted to any particular final state. This resulted in substantially increased statistics. Differential cross sections as functions of E jet T , η jet, Q2 and x were determined. Next-to- leading-order QCD predictions calculated using the Hvqdis program using two different sets of proton PDFs are consistent with the measurements. The heavy-quark contributions to the proton structure function F2 as well as beauty and charm reduced cross sections were extracted from the double-differential cross sections as a function of x and Q2. The F bb̄2 , F cc̄ 2 and σ bb̄ r , σ cc̄ r values are in agreement with previous measurements at HERA. The results were also compared to several NLO and NNLO QCD calculations, which provide a good description of the data. The precision of the F cc̄2 measurement is competitive with other analyses. For a wide range of Q 2, the F bb̄2 measurement represents the most precise determination of F bb̄2 . The running beauty-quark mass in the MS scheme was determined from an NLO QCD fit in the fixed-flavour-number scheme to the σbb̄r cross sections from this analysis and to HERA I inclusive DIS data: mb(mb) = 4.07 ± 0.14 (fit)+0.01−0.07 (mod.)+0.05−0.00 (param.) +0.08−0.05 (theo.) GeV This value agrees well with the world average. 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D 86 (2012) 1. 23 http://projects.hepforge.org/herafitter http://dx.doi.org/10.1016/j.physletb.2011.04.026 http://arxiv.org/abs/1011.5790 http://arxiv.org/abs/1107.0469 http://www-zeuthen.desy.de/~alekhin/OPENQCDRAD http://dx.doi.org/10.1007/BF01614703 http://dx.doi.org/10.1016/S0550-3213(99)00784-1 http://arxiv.org/abs/hep-ph/9911434 http://dx.doi.org/10.1016/S0370-2693(00)00507-4 http://arxiv.org/abs/hep-ph/9912391 http://dx.doi.org/10.1103/PhysRevD.86.010001 Source Beauty Charm (%) (%) δ1 Event and DIS selection ±1.4 ±0.8 δ2 Trigger efficiency +2.0 +1.0 δ3 Tracking efficiency ±2.0 ±0.5 δ4 Decay-length smearing ±1.3 ±1.2 δ5 Signal extraction procedure ±0.8 ±0.8 δ6 Jet energy scale ±0.7 ±0.9 δ7 EM energy scale ±0.3 ±0.1 δ8 Charm Q 2 reweighting (δ Q2,c 8 ) ±1.7 ±1.8 Beauty Q2 reweighting (δ Q2,b 8 ) ±2.9 ±0.4 Charm ηjet reweighting (δ ηjet,c 8 ) +0.3 −0.4 +1.5 −1.0 Beauty ηjet reweighting (δ ηjet,b 8 ) +0.7 −0.4 +0.0 −0.1 Charm E jet T reweighting (δ E jet T ,c 8 ) +1.7 −1.3 +2.2 −1.7 Beauty E jet T reweighting (δ E jet T ,b 8 ) +5.4 −4.2 +0.5 −0.6 δ9 Light-flavour asymmetry ±0.4 ±2.0 δ10 Charm fragmentation function −0.9 +1.0 δ11 Beauty fragmentation function −3.1 +0.0 δ12 BR and fragmentation fractions +1.8 −2.1 +3.5 −2.6 δ13 Luminosity measurement ±1.9 ±1.9 Total +8.0 −7.6 +6.0 −5.1 Table 1: Effects of the systematic uncertainties on the integrated beauty- and charm-jet cross sections. 24 E jet T dσ jet b /dE jet T (pb/GeV) C had Crad (GeV) stat. syst. 5 : 8 134 ± 26 +24 −25 0.95 1.01 8 : 11 66.1 ± 5.8 +5.1 −6.8 1.08 0.98 11 : 14 30.1 ± 1.9 +1.4 −2.0 1.05 0.96 14 : 17 11.27 ± 0.90 +0.52 −0.60 1.04 0.95 17 : 20 4.71 ± 0.50 +0.34 −0.32 0.99 0.93 20 : 25 2.04 ± 0.28 +0.28 −0.28 0.93 0.89 25 : 35 0.380 ± 0.094 +0.078 −0.076 0.80 0.89 E jet T dσ jet c /dE jet T (pb/GeV) C had Crad (GeV) stat. syst. 4.2 : 8 3 660 ± 120 +200 −180 1.06 0.98 8 : 11 748 ± 22 +45 −41 1.05 0.97 11 : 14 222 ± 10 +21 −20 1.03 0.96 14 : 17 91.4 ± 6.5 +11 −9.7 0.99 0.93 17 : 20 38.9 ± 4.4 +6.1 −6.0 0.96 0.93 20 : 25 16.4 ± 3.2 +4.0 −3.7 0.95 0.85 25 : 35 2.6 ± 1.1 +0.9 −0.9 0.86 0.88 Table 2: Differential cross sections for inclusive jet production in beauty events (top) and charm events (bottom) as a function of E jet T . The beauty (charm) cross sections are given for 5 < Q2 < 1 000 GeV2, 0.02 < y < 0.7, E jet T > 5(4.2) GeV and −1.6 < ηjet < 2.2. The measurements are given together with their statistical and systematic uncertainties. Hadronisation and QED radiative corrections, Chad and Crad, respectively, are also shown. 25 ηjet dσ jet b /dηjet (pb) Chad Crad stat. syst. −1.6 : −0.8 89 ± 31 +25 −41 0.96 0.98 −0.8 : −0.5 220 ± 30 +15 −23 0.98 0.98 −0.5 : −0.2 210 ± 24 +18 −21 0.93 0.99 −0.2 : 0.1 280 ± 22 +21 −23 0.91 0.99 0.1 : 0.4 260 ± 22 +21 −19 0.94 0.99 0.4 : 0.7 310 ± 23 +30 −29 1.01 0.99 0.7 : 1.0 270 ± 26 +26 −24 1.06 0.99 1.0 : 1.3 290 ± 31 +30 −30 1.07 0.99 1.3 : 1.6 220 ± 41 +24 −23 1.07 0.99 1.6 : 2.2 220 ± 71 +78 −79 1.07 0.98 ηjet dσjetc /dη jet (pb) Chad Crad stat. syst. −1.6 : −1.1 1 900 ± 260 +200 −180 0.89 0.99 −1.1 : −0.8 3 600 ± 220 +240 −220 0.97 0.98 −0.8 : −0.5 4 200 ± 200 +210 −180 1.02 0.98 −0.5 : −0.2 5 200 ± 190 +260 −240 1.05 0.98 −0.2 : 0.1 5 400 ± 200 +380 −360 1.07 0.98 0.1 : 0.4 6 000 ± 210 +410 −380 1.10 0.98 0.4 : 0.7 5 700 ± 220 +340 −320 1.11 0.98 0.7 : 1.0 5 700 ± 240 +320 −300 1.10 0.98 1.0 : 1.3 4 900 ± 270 +320 −300 1.09 0.98 1.3 : 1.6 4 900 ± 360 +330 −300 1.07 0.97 1.6 : 2.2 4 800 ± 630 +640 −640 1.13 0.97 Table 3: Differential cross sections for inclusive jet production in beauty events (top) and charm events (bottom) as a function of ηjet. For details, see the caption of Table 2. 26 Q2 dσ jet b /dQ2 (pb/GeV2) Chad Crad (GeV2) stat. syst. 5 : 10 43.8 ± 4.1 +4.0 −3.2 1.01 0.99 10 : 20 18.0 ± 1.8 +1.7 −1.5 1.01 0.99 20 : 40 7.58 ± 0.82 +0.74 −0.72 0.99 0.99 40 : 70 3.80 ± 0.39 +0.30 −0.31 0.98 0.99 70 : 120 1.26 ± 0.16 +0.14 −0.15 0.98 0.98 120 : 200 0.623 ± 0.066 +0.042 −0.047 0.99 0.99 200 : 400 0.142 ± 0.018 +0.010 −0.010 0.99 0.99 400 : 1 000 0.0194 ± 0.0034 +0.0020 −0.0019 1.01 0.95 Q2 dσjetc /dQ 2 (pb/GeV2) Chad Crad (GeV2) stat. syst. 5 : 10 835 ± 34 +46 −39 1.15 0.98 10 : 20 460 ± 15 +26 −22 1.08 0.99 20 : 40 207 ± 6.4 +10 −9.5 1.01 0.98 40 : 70 68.5 ± 2.7 +3.8 −3.5 1.00 0.97 70 : 120 22.5 ± 1.0 +1.4 −1.2 1.00 0.97 120 : 200 7.28 ± 0.46 +0.48 −0.41 1.01 0.96 200 : 400 1.82 ± 0.14 +0.10 −0.08 1.01 0.95 400 : 1 000 0.219 ± 0.037 +0.032 −0.029 1.02 0.87 Table 4: Differential cross sections for inclusive jet production in beauty events (top) and charm events (bottom) as a function of Q2. For details, see the caption of Table 2. 27 x dσ jet b /dx (pb) Chad Crad stat. syst. 0.00008 : 0.0002 686 000 ± 110 000 +85 000 −78 000 1.09 0.99 0.0002 : 0.0006 614 000 ± 47 000 +52 000 −45 000 1.05 0.99 0.0006 : 0.0016 218 000 ± 15 000 +16 000 −14 000 0.99 0.99 0.0016 : 0.005 49 800 ± 3 500 +3 600 −3 500 0.95 0.99 0.005 : 0.01 11 200 ± 1 300 +950 −920 0.93 1.00 0.01 : 0.1 374 ± 79 +51 −50 0.92 0.95 x dσjetc /dx (pb) C had Crad stat. syst. 0.00008 : 0.0002 10 700 000± 870 000 +760 000 −650 000 1.19 0.96 0.0002 : 0.0006 10 300 000± 390 000 +540 000 −420 000 1.20 0.98 0.0006 : 0.0016 4 990 000± 140 000 +260 000 −240 000 1.09 0.99 0.0016 : 0.005 1 250 000± 32 000 +71 000 −64 000 0.97 0.99 0.005 : 0.01 264 000 ± 12 000 +19 000 −17 000 0.91 1.00 0.01 : 0.1 12 500 ± 900 +1 000 −970 0.88 0.88 Table 5: Differential cross sections for inclusive jet production in beauty events (top) and charm events (bottom) as a function of x. For details, see the caption of Table 2. 28 Q2 x d2σ jet b /dx dQ 2 (pb/GeV2) Chad Crad (GeV2) stat. syst. 5 : 20 0.00008 : 0.0002 690 000 ± 110 000 +90 000 −80 000 1.09 0.99 5 : 20 0.0002 : 0.0003 830 000 ± 120 000 +80 000 −80 000 1.07 0.98 5 : 20 0.0003 : 0.0005 501 000 ± 55 000 +49 000 −41 000 1.04 0.99 5 : 20 0.0005 : 0.003 48 200 ± 5 800 +5 100 −4 700 0.91 0.99 20 : 60 0.0003 : 0.0005 82 000 ± 24 000 +11 000 −11 000 1.07 0.98 20 : 60 0.0005 : 0.0012 134 000 ± 14 000 +10 000 −10 000 1.05 0.99 20 : 60 0.0012 : 0.002 73 400 ± 8 500 +6 900 −6 900 1.00 1.00 20 : 60 0.002 : 0.0035 25 800 ± 4 600 +3 500 −3 400 0.94 1.01 20 : 60 0.0035 : 0.01 3 600 ± 2 000 +1 000 −1 000 0.81 0.99 60 : 120 0.0008 : 0.0018 33 400 ± 4 500 +3 200 −3 100 1.03 0.98 60 : 120 0.0018 : 0.003 22 500 ± 2 900 +2 000 −2 100 1.02 0.99 60 : 120 0.003 : 0.006 7 400 ± 1 300 +800 −900 0.98 0.98 120 : 400 0.0016 : 0.005 6 700 ± 930 +450 −500 1.01 0.99 120 : 400 0.005 : 0.016 3 820 ± 340 +170 −200 0.99 1.02 120 : 400 0.016 : 0.06 269 ± 130 +70 −80 0.92 0.87 400 : 1 000 0.005 : 0.02 401 ± 88 +56 −53 1.01 0.95 400 : 1 000 0.02 : 0.1 70 ± 21 +15 −16 1.00 0.95 Table 6: Double-differential cross sections for inclusive jet production in beauty events as a function of x for different ranges of Q2. The cross sections are given for 5 < Q2 < 1 000 GeV2, 0.02 < y < 0.7, E jet T > 5 GeV and −1.6 < ηjet < 2.2. The measurements are given together with their statistical and systematic uncertainties. Hadronisation and QED radiative corrections, Chad and Crad, respectively, are also shown. 29 Q2 x d2σjetc /dx dQ 2 (pb/GeV2) Chad Crad (GeV2) stat. syst. 5 : 20 0.00008 : 0.0002 10 700 000± 870 000 +740 000 −600 000 1.19 0.96 5 : 20 0.0002 : 0.0003 13 500 000± 950 000 +890 000 −730 000 1.21 0.98 5 : 20 0.0003 : 0.0005 8 220 000± 470 000 +540 000 −470 000 1.23 0.98 5 : 20 0.0005 : 0.003 1 620 000± 56 000 +100 000 −87 000 1.07 1.00 20 : 60 0.0003 : 0.0005 1 570 000± 230 000 +140 000 −120 000 1.13 0.97 20 : 60 0.0005 : 0.0012 2 600 000± 110 000 +140 000 −120 000 1.09 0.97 20 : 60 0.0012 : 0.002 1 390 000± 68 000 +73 000 −69 000 1.05 0.98 20 : 60 0.002 : 0.0035 650 000± 34 000 +48 000 −46 000 1.01 0.99 20 : 60 0.0035 : 0.01 190 000± 13 000 +14 000 −13 000 0.91 0.99 60 : 120 0.0008 : 0.0018 251 000± 33 000 +33 000 −34 000 1.07 0.97 60 : 120 0.0018 : 0.003 283 000± 21 000 +22 000 −21 000 1.03 0.99 60 : 120 0.003 : 0.006 136 000± 8 100 +10 000 −9 700 1.01 0.98 60 : 120 0.006 : 0.04 17 100 ± 1 600 +1 400 −1 200 0.93 0.93 120 : 400 0.0016 : 0.005 110 000± 7 800 +7 400 −5 600 1.05 0.97 120 : 400 0.005 : 0.016 34 500 ± 2 200 +1 900 −1 700 1.01 1.00 120 : 400 0.016 : 0.06 5 300 ± 1 100 +800 −800 0.96 0.80 400 : 1 000 0.005 : 0.02 5 790 ± 900 +900 −850 1.02 0.88 400 : 1 000 0.02 : 0.1 540 ± 280 +160 −160 1.01 0.84 Table 7: Double-differential cross sections for inclusive jet production in charm events as a function of x for different ranges of Q2. The cross sections are given for 5 < Q2 < 1 000 GeV2, 0.02 < y < 0.7, E jet T > 4.2 GeV and −1.6 < ηjet < 2.2. The measurements are given together with their statistical and systematic uncertainties. Hadronisation and QED radiative corrections, Chad and Crad, respectively, are also shown. 30 Q2 x F bb̄2 (GeV2) stat. syst. extr. 6.5 0.00015 0.00431 ± 0.00068 +0.00054 −0.00048 +0.00034 −0.00029 6.5 0.00028 0.00357 ± 0.00052 +0.00036 −0.00033 +0.00029 −0.00025 12 0.00043 0.00632 ± 0.00069 +0.00062 −0.00052 +0.00044 −0.00034 12 0.00065 0.00438 ± 0.00053 +0.00047 −0.00043 +0.00020 −0.00012 25 0.00043 0.0118 ± 0.0035 +0.0016 −0.0016 +0.0009 −0.0007 25 0.00080 0.0105 ± 0.0011 +0.0008 −0.0007 +0.0006 −0.0005 30 0.0016 0.0099 ± 0.0012 +0.0009 −0.0009 +0.0004 −0.0004 30 0.0025 0.0067 ± 0.0012 +0.0009 −0.0009 +0.0002 −0.0003 30 0.0045 0.0041 ± 0.0023 +0.0011 −0.0012 +0.0001 −0.0001 80 0.0016 0.0364 ± 0.0049 +0.0035 −0.0034 +0.0012 −0.0012 80 0.0025 0.0195 ± 0.0025 +0.0017 −0.0018 +0.0005 −0.0005 80 0.0045 0.0110 ± 0.0020 +0.0013 −0.0013 +0.0002 −0.0003 160 0.0035 0.0230 ± 0.0032 +0.0016 −0.0017 +0.0005 −0.0003 160 0.0080 0.0176 ± 0.0016 +0.0008 −0.0009 +0.0004 −0.0003 160 0.020 0.0078 ± 0.0039 +0.0021 −0.0022 +0.0003 −0.0002 600 0.013 0.0154 ± 0.0034 +0.0022 −0.0020 +0.0001 −0.0002 600 0.035 0.0088 ± 0.0026 +0.0019 −0.0020 +0.0003 −0.0001 Table 8: The structure function F bb̄2 as a function of x for seven different values of Q 2. The first error is statistical, the second systematic and the last is the extrapolation uncer- tainty. The horizontal lines correspond to the bins in Q2 in Table 6. 31 Q2 x F cc̄2 (GeV2) stat. syst. extr. 6.5 0.00015 0.202 ± 0.016 +0.014 −0.011 +0.046 −0.042 6.5 0.00028 0.189 ± 0.013 +0.013 −0.010 +0.039 −0.039 12 0.00043 0.231 ± 0.013 +0.015 −0.013 +0.039 −0.044 12 0.00065 0.224 ± 0.008 +0.014 −0.012 +0.028 −0.028 25 0.00043 0.492 ± 0.071 +0.044 −0.036 +0.085 −0.073 25 0.00080 0.418 ± 0.018 +0.022 −0.020 +0.030 −0.034 30 0.0016 0.304 ± 0.015 +0.016 −0.015 +0.014 −0.011 30 0.0025 0.235 ± 0.012 +0.018 −0.017 +0.006 −0.008 30 0.0045 0.195 ± 0.014 +0.015 −0.014 +0.010 −0.000 80 0.0016 0.385 ± 0.051 +0.051 −0.051 +0.018 −0.010 80 0.0025 0.324 ± 0.024 +0.025 −0.024 +0.001 −0.015 80 0.0045 0.244 ± 0.015 +0.018 −0.017 +0.004 −0.004 80 0.0080 0.214 ± 0.020 +0.017 −0.015 +0.000 −0.002 160 0.0035 0.450 ± 0.032 +0.030 −0.023 +0.010 −0.007 160 0.0080 0.195 ± 0.012 +0.011 −0.010 +0.003 −0.003 160 0.020 0.151 ± 0.031 +0.022 −0.022 +0.002 −0.000 600 0.013 0.242 ± 0.038 +0.038 −0.036 +0.006 −0.002 600 0.035 0.071 ± 0.037 +0.020 −0.021 +0.002 −0.001 Table 9: The structure function F cc̄2 as a function of x for seven different values of Q 2. The first error is statistical, the second systematic and the last is the extrapolation uncer- tainty. The horizontal lines correspond to the bins in Q2 in Table 7. 32 Q2 x σbb̄r (GeV2) stat. syst. extr. 6.5 0.00015 0.00429 ± 0.00068 +0.00053 −0.00048 +0.00034 −0.00029 6.5 0.00028 0.00357 ± 0.00051 +0.00036 −0.00033 +0.00029 −0.00025 12 0.00043 0.00631 ± 0.00069 +0.00061 −0.00052 +0.00043 −0.00034 12 0.00065 0.00436 ± 0.00052 +0.00046 −0.00042 +0.00023 −0.00010 25 0.00043 0.0116 ± 0.0035 +0.0015 −0.0015 +0.0009 −0.0006 25 0.00080 0.0104 ± 0.0011 +0.0008 −0.0007 +0.0006 −0.0005 30 0.0016 0.0099 ± 0.0012 +0.0009 −0.0009 +0.0004 −0.0005 30 0.0025 0.0067 ± 0.0012 +0.0009 −0.0009 +0.0002 −0.0002 30 0.0045 0.0041 ± 0.0023 +0.0011 −0.0012 +0.0001 −0.0003 80 0.0016 0.0354 ± 0.0047 +0.0034 −0.0033 +0.0011 −0.0012 80 0.0025 0.0194 ± 0.0025 +0.0017 −0.0018 +0.0005 −0.0005 80 0.0045 0.0109 ± 0.0020 +0.0012 −0.0013 +0.0003 −0.0003 160 0.0035 0.0223 ± 0.0031 +0.0015 −0.0017 +0.0005 −0.0003 160 0.0080 0.0176 ± 0.0016 +0.0008 −0.0009 +0.0004 −0.0004 160 0.020 0.0078 ± 0.0039 +0.0021 −0.0022 +0.0002 −0.0001 600 0.013 0.0149 ± 0.0032 +0.0021 −0.0019 +0.0001 −0.0002 600 0.035 0.0088 ± 0.0026 +0.0019 −0.0020 +0.0003 −0.0001 Table 10: Reduced beauty cross sections, σbb̄r , as a function of x for seven different values of Q2. For more details, see the caption of Table 8. 33 Q2 x σcc̄r (GeV2) stat. syst. extr. 6.5 0.00015 0.201 ± 0.016 +0.014 −0.011 +0.041 −0.042 6.5 0.00028 0.188 ± 0.013 +0.012 −0.010 +0.040 −0.042 12 0.00043 0.230 ± 0.013 +0.015 −0.013 +0.037 −0.047 12 0.00065 0.224 ± 0.008 +0.014 −0.012 +0.028 −0.034 25 0.00043 0.465 ± 0.067 +0.042 −0.034 +0.081 −0.067 25 0.00080 0.413 ± 0.018 +0.022 −0.019 +0.026 −0.035 30 0.0016 0.304 ± 0.015 +0.016 −0.015 +0.014 −0.013 30 0.0025 0.234 ± 0.012 +0.017 −0.017 +0.006 −0.008 30 0.0045 0.194 ± 0.014 +0.015 −0.014 +0.011 −0.000 80 0.0016 0.369 ± 0.049 +0.049 −0.049 +0.018 −0.010 80 0.0025 0.319 ± 0.024 +0.025 −0.024 +0.002 −0.015 80 0.0045 0.243 ± 0.014 +0.018 −0.017 +0.004 −0.005 80 0.0080 0.213 ± 0.020 +0.017 −0.015 +0.000 −0.003 160 0.0035 0.436 ± 0.031 +0.029 −0.022 +0.009 −0.007 160 0.0080 0.194 ± 0.012 +0.011 −0.010 +0.003 −0.005 160 0.020 0.151 ± 0.031 +0.022 −0.022 +0.001 −0.000 600 0.013 0.235 ± 0.037 +0.037 −0.034 +0.006 −0.002 600 0.035 0.070 ± 0.037 +0.020 −0.020 +0.002 −0.001 Table 11: Reduced charm cross section, σcc̄r , as a function of x for seven different values of Q2. For more details, see the caption of Table 9. 34 Q2 x δ Ee 1 δ y 1 δ E−pZ 1 δ2 δ3 δ core 4 δtail 4 δ5 δ6 δ7 ( GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 5 : 20 0.00008: 0.0002 +2.8 −2.8 +5.0 −5.0 +0.3 −0.3 +4.5 +0.1 −0.1 +0.8 −0.8 −3.2 +3.2 −6.3 +6.3 +2.1 −2.1 −1.6 +1.6 5 : 20 0.0002 : 0.0003 +0.6 −0.6 −1.9 +1.9 −0.8 +0.8 +4.4 +1.0 −1.0 −0.1 +0.1 −1.7 +1.7 −3.8 +3.8 +0.7 −0.7 −1.7 +1.7 5 : 20 0.0003 : 0.0005 −2.8 +2.8 +0.6 −0.6 +0.8 −0.8 +4.1 −0.1 +0.1 −1.8 +1.8 +0.9 −0.9 −4.3 +4.3 +1.1 −1.1 −1.4 +1.4 5 : 20 0.0005 : 0.003 −1.6 +1.6 −4.2 +4.2 +0.5 −0.5 +2.8 +2.2 −2.2 −1.2 +1.2 −2.0 +2.0 +4.4 −4.4 +0.7 −0.7 +2.4 −2.4 20 : 60 0.0003 : 0.0005 +0.3 −0.3 −4.9 +4.9 +2.5 −2.5 +0.5 +1.5 −1.5 +1.7 −1.7 −1.8 +1.8 −7.6 +7.6 −0.4 +0.4 −4.1 +4.1 20 : 60 0.0005 : 0.0012 −1.9 +1.9 +0.3 −0.3 −0.2 +0.2 +0.8 +1.7 −1.7 +0.2 −0.2 −0.2 +0.2 +1.8 −1.8 +1.2 −1.2 −3.4 +3.4 20 : 60 0.0012 : 0.002 −3.1 +3.1 −1.2 +1.2 −5.0 +5.0 +0.8 +1.4 −1.4 +0.7 −0.7 −1.1 +1.1 +3.9 −3.9 +0.1 −0.1 +0.7 −0.7 20 : 60 0.002 : 0.0035 −4.8 +4.8 −3.1 +3.1 +3.0 −3.0 +0.1 +1.9 −1.9 −0.7 +0.7 −1.8 +1.8 +4.2 −4.2 +0.6 −0.6 +7.9 −7.9 20 : 60 0.0035 : 0.01 +1.1 −1.1 −17.0 +17.0 −6.6 +6.6 +0.2 +7.0 −7.0 −7.4 +7.4 +1.4 −1.4 +14.5 −14.5 +1.8 −1.8 −1.3 +1.3 60 : 120 0.0008 : 0.0018 +6.2 −6.2 −2.0 +2.0 +2.3 −2.3 +0.0 +1.5 −1.5 +1.0 −1.0 +0.4 −0.4 −0.1 +0.1 −0.2 +0.2 +2.3 −2.3 60 : 120 0.0018 : 0.003 −0.6 +0.6 +1.0 −1.0 +4.8 −4.8 +0.0 +2.6 −2.6 −0.3 +0.3 −0.3 +0.3 −2.4 +2.4 +0.6 −0.6 −4.0 +4.0 60 : 120 0.003 : 0.006 −1.2 +1.2 +3.6 −3.6 −0.6 +0.6 −0.0 +1.8 −1.8 −0.4 +0.4 +1.2 −1.2 +3.0 −3.0 +0.1 −0.1 −8.0 +8.0 120 : 400 0.0016 : 0.005 −0.3 +0.3 +1.6 −1.6 −2.3 +2.3 +0.4 +1.3 −1.3 −1.1 +1.1 −0.1 +0.1 −2.9 +2.9 +0.9 −0.9 +0.5 −0.5 120 : 400 0.005 : 0.016 −0.1 +0.1 +0.5 −0.5 +1.2 −1.2 +0.4 +1.7 −1.7 −2.0 +2.0 −1.9 +1.9 −0.5 +0.5 +0.1 −0.1 −0.5 +0.5 120 : 400 0.016 : 0.06 −5.6 +5.6 −20.0 +20.0 +6.6 −6.6 +0.1 +6.8 −6.8 +4.3 −4.3 −3.4 +3.4 +7.0 −7.0 +0.7 −0.7 −8.0 +8.0 400 : 1 000 0.005 : 0.02 +1.4 −1.4 +4.8 −4.8 +1.3 −1.3 +4.6 +1.5 −1.5 −3.5 +3.5 +1.5 −1.5 −1.5 +1.5 −0.9 +0.9 +6.0 −6.0 400 : 1 000 0.02 : 0.1 −12.6 +12.6 −11.1 +11.1 −3.0 +3.0 +2.6 +1.5 −1.5 −4.6 +4.6 −3.2 +3.2 −7.5 +7.5 +1.6 −1.6 +4.7 −4.7 Table 12: Systematic uncertainties for the double-differential cross sections of inclusive jet production in beauty events. See Section 7 for more details. 3 5 Q2 x δ Q 2 ,c 8 δ Q 2 ,b 8 δ η jet ,c 8 δ η jet ,b 8 δ E jet T ,c 8 δ E jet T ,b 8 δ9 δ10 δ11 δ BR 12 δ frag 12 (GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 5 : 20 0.00008: 0.0002 −0.0 +0.0 +0.2 −0.2 +0.3 −0.2 +0.6 −0.4 −0.8 +1.0 −4.2 +5.6 −2.0 +2.0 −0.7 −2.9 +2.5 −2.0 +0.2 −0.3 5 : 20 0.0002 : 0.0003 −0.1 +0.1 +0.0 −0.0 −0.4 +0.3 +0.3 −0.2 −1.0 +1.3 −4.3 +5.6 +2.9 −2.9 −1.6 −3.5 +3.8 −3.9 +0.2 −0.2 5 : 20 0.0003 : 0.0005 +0.1 −0.1 −0.1 +0.1 −0.1 +0.0 +0.1 −0.1 −1.2 +1.6 −4.5 +5.9 +0.1 −0.1 +0.7 −2.5 +2.2 −2.3 +0.3 −0.3 5 : 20 0.0005 : 0.003 −0.0 +0.0 −0.1 +0.1 −1.1 +0.7 +1.1 −0.7 −1.4 +1.8 −4.7 +6.2 +1.9 −1.9 −1.5 −1.8 +1.4 −1.8 +0.3 −0.3 20 : 60 0.0003 : 0.0005 −0.0 +0.0 +0.5 −0.5 +0.9 −0.6 +1.5 −0.9 −0.5 +0.7 −4.2 +5.5 +2.1 −2.1 +1.4 −4.2 +4.2 −4.4 +0.4 −0.4 20 : 60 0.0005 : 0.0012 −0.0 +0.0 +0.0 −0.0 +0.0 −0.0 +0.5 −0.3 −0.8 +1.0 −3.9 +5.1 +0.6 −0.6 −1.0 −2.2 +2.2 −2.5 +0.1 −0.1 20 : 60 0.0012 : 0.002 +0.2 −0.2 −0.0 +0.0 −0.1 +0.1 +0.2 −0.1 −1.1 +1.4 −3.6 +4.8 −1.3 +1.3 +0.7 −3.1 +2.5 −2.4 +0.4 −0.4 20 : 60 0.002 : 0.0035 +0.2 −0.2 +0.0 −0.0 −0.5 +0.3 +0.8 −0.5 −1.3 +1.6 −3.4 +4.5 +3.7 −3.7 −1.6 −3.0 +4.0 −2.8 +0.6 −0.7 20 : 60 0.0035 : 0.01 +0.7 −0.7 −0.0 +0.0 −1.2 +0.8 +1.8 −1.2 −1.4 +1.9 −3.1 +4.1 −1.1 +1.1 −9.5 −1.7 +9.0 −6.8 +2.1 −1.9 60 : 120 0.0008 : 0.0018 −0.0 +0.0 +0.5 −0.5 +0.1 −0.0 +1.3 −0.9 −0.4 +0.5 −3.6 +4.7 +0.9 −0.9 +1.1 −3.2 +2.7 −2.0 +0.3 −0.2 60 : 120 0.0018 : 0.003 +0.1 −0.1 −0.2 +0.2 +0.2 −0.1 +0.3 −0.2 −0.8 +1.1 −2.6 +3.4 −1.3 +1.3 −0.4 −3.8 +3.1 −2.9 +0.1 −0.1 60 : 120 0.003 : 0.006 +0.2 −0.2 +0.1 −0.1 −0.5 +0.3 +0.6 −0.4 −1.1 +1.4 −2.5 +3.2 +2.4 −2.4 −1.6 −2.8 +4.4 −5.3 +0.3 −0.4 120 : 400 0.0016 : 0.005 +0.2 −0.2 +0.2 −0.2 +0.0 −0.0 +1.0 −0.6 −1.0 +1.2 −2.5 +3.2 −1.6 +1.6 −0.2 −3.2 +3.1 −3.8 +0.3 −0.3 120 : 400 0.005 : 0.016 +0.0 −0.0 +0.4 −0.4 −0.1 +0.1 +1.0 −0.6 −0.5 +0.6 −1.4 +1.9 −0.1 +0.1 −0.8 −2.6 +1.4 −1.9 +0.2 −0.2 120 : 400 0.016 : 0.06 +0.1 −0.1 +2.6 −2.6 −0.7 +0.4 +2.4 −1.5 −0.6 +0.8 −1.5 +1.9 +4.8 −4.8 +3.9 −4.7 +5.0 −8.2 +0.6 −0.6 400 : 1 000 0.005 : 0.02 −0.0 +0.0 +0.2 −0.2 −0.2 +0.1 +0.9 −0.6 −0.3 +0.4 −1.2 +1.5 +8.4 −8.4 −1.7 −2.5 +4.4 −2.7 +0.2 −0.2 400 : 1 000 0.02 : 0.1 +0.0 −0.0 +0.8 −0.8 −0.3 +0.2 +2.0 −1.2 −0.9 +1.2 −0.5 +0.6 +5.7 −5.7 −1.2 −8.7 +4.0 −3.8 +0.4 −0.4 Table 13: Systematic uncertainties for the double-differential cross sections of inclusive jet production in beauty events (continued). 3 6 Q2 x δ Ee 1 δ y 1 δ E−pZ 1 δ2 δ3 δ core 4 δtail 4 δ5 δ6 δ7 ( GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 5 : 20 0.00008: 0.0002 +1.6 −1.6 +1.9 −1.9 −2.2 +2.2 +3.3 +0.0 −0.0 −1.9 +1.9 +0.6 −0.6 +2.0 −2.0 −1.8 +1.8 −0.8 +0.8 5 : 20 0.0002 : 0.0003 +3.3 −3.3 +1.0 −1.0 −0.1 +0.1 +3.3 +0.1 −0.1 −1.5 +1.5 +0.0 −0.0 +2.1 −2.1 −1.0 +1.0 +1.1 −1.1 5 : 20 0.0003 : 0.0005 +0.4 −0.4 −2.1 +2.1 −1.3 +1.3 +3.2 +0.1 −0.1 −0.9 +0.9 −0.5 +0.5 −1.8 +1.8 −0.8 +0.8 +1.6 −1.6 5 : 20 0.0005 : 0.003 +0.9 −0.9 −0.1 +0.1 −1.4 +1.4 +1.5 +0.5 −0.5 −1.2 +1.2 +0.6 −0.6 −2.8 +2.8 −1.3 +1.3 −0.4 +0.4 20 : 60 0.0003 : 0.0005 +2.4 −2.4 +0.1 −0.1 +1.1 −1.1 +0.3 −0.2 +0.2 −2.0 +2.0 +1.5 −1.5 −0.1 +0.1 −1.0 +1.0 −4.3 +4.3 20 : 60 0.0005 : 0.0012 −0.3 +0.3 −0.3 +0.3 −0.9 +0.9 +0.9 +0.8 −0.8 −1.2 +1.2 +0.6 −0.6 +1.9 −1.9 −0.6 +0.6 +0.4 −0.4 20 : 60 0.0012 : 0.002 −0.4 +0.4 −1.7 +1.7 −1.4 +1.4 +0.5 +0.8 −0.8 −1.4 +1.4 −0.2 +0.2 −1.1 +1.1 −0.4 +0.4 −0.2 +0.2 20 : 60 0.002 : 0.0035 −1.1 +1.1 +2.4 −2.4 −0.8 +0.8 +0.2 +1.0 −1.0 −1.4 +1.4 −0.4 +0.4 −4.5 +4.5 −0.9 +0.9 −0.7 +0.7 20 : 60 0.0035 : 0.01 +2.3 −2.3 −0.2 +0.2 +1.8 −1.8 +0.1 +0.7 −0.7 −0.4 +0.4 +0.3 −0.3 −3.0 +3.0 −1.8 +1.8 −0.3 +0.3 60 : 120 0.0008 : 0.0018 −7.5 +7.5 −0.2 +0.2 +5.1 −5.1 +0.0 +1.1 −1.1 −2.0 +2.0 −0.9 +0.9 +0.9 −0.9 −0.9 +0.9 +4.1 −4.1 60 : 120 0.0018 : 0.003 +2.0 −2.0 −0.2 +0.2 −2.2 +2.2 +0.0 +0.3 −0.3 −1.2 +1.2 −0.5 +0.5 +4.7 −4.7 −0.8 +0.8 +2.0 −2.0 60 : 120 0.003 : 0.006 −1.2 +1.2 −0.7 +0.7 +2.6 −2.6 +0.0 −0.2 +0.2 −1.0 +1.0 +1.3 −1.3 −4.6 +4.6 −0.9 +0.9 +1.9 −1.9 60 : 120 0.006 : 0.04 +0.7 −0.7 −3.5 +3.5 −3.2 +3.2 +0.0 +0.7 −0.7 −2.5 +2.5 +1.5 −1.5 +1.6 −1.6 −0.9 +0.9 +0.0 −0.0 120 : 400 0.0016 : 0.005 −0.0 +0.0 +0.4 −0.4 +0.9 −0.9 +0.1 +1.1 −1.1 −0.7 +0.7 +0.1 −0.1 +1.6 −1.6 −0.6 +0.6 −0.3 +0.3 120 : 400 0.005 : 0.016 −0.5 +0.5 +0.0 −0.0 −1.3 +1.3 +0.2 −0.4 +0.4 −0.4 +0.4 +0.9 −0.9 +2.1 −2.1 +0.2 −0.2 +0.1 −0.1 120 : 400 0.016 : 0.06 +7.3 −7.3 −6.8 +6.8 +3.4 −3.4 +0.0 +0.7 −0.7 −2.1 +2.1 +0.6 −0.6 +1.5 −1.5 +0.2 −0.2 −7.6 +7.6 400 : 1 000 0.005 : 0.02 −3.6 +3.6 +7.1 −7.1 +2.2 −2.2 +4.4 +0.8 −0.8 −2.7 +2.7 −0.1 +0.1 −2.3 +2.3 +0.4 −0.4 +8.8 −8.8 400 : 1 000 0.02 : 0.1 −9.3 +9.3 +5.6 −5.6 −15.1 +15.1 +4.3 +6.1 −6.1 +5.0 −5.0 +6.5 −6.5 −4.6 +4.6 −3.5 +3.5 −6.7 +6.7 Table 14: Systematic uncertainties for the double-differential cross sections of inclusive jet production in charm events. See Section 7 for more details. 3 7 Q2 x δ Q 2 ,c 8 δ Q 2 ,b 8 δ η jet ,c 8 δ η jet ,b 8 δ E jet T ,c 8 δ E jet T ,b 8 δ9 δ10 δ11 δ BR 12 δ frag 12 ( GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 5 : 20 0.00008: 0.0002 +0.3 −0.3 −0.0 +0.0 +1.3 −0.8 −0.1 +0.0 −1.4 +1.9 +0.6 −0.8 −0.5 +0.5 +0.7 +0.4 +2.6 −1.9 +0.9 −0.8 5 : 20 0.0002 : 0.0003 +0.0 −0.0 +0.0 −0.0 +1.1 −0.7 −0.1 +0.1 −1.7 +2.2 +0.6 −0.7 −0.7 +0.7 +0.5 −0.2 +1.9 −1.8 +1.1 −1.1 5 : 20 0.0003 : 0.0005 −0.1 +0.1 +0.0 −0.0 +0.7 −0.4 +0.0 −0.0 −1.7 +2.2 +0.7 −0.9 −1.6 +1.6 −1.1 +0.2 +3.1 −3.2 +1.1 −1.1 5 : 20 0.0005 : 0.003 +0.1 −0.1 +0.0 −0.0 +1.6 −1.0 +0.0 −0.0 −1.5 +2.0 +0.4 −0.5 −1.9 +1.9 +1.1 −0.1 +2.9 −2.4 +1.1 −1.0 20 : 60 0.0003 : 0.0005 +0.8 −0.8 +0.0 −0.0 +1.5 −1.0 −0.2 +0.1 −1.7 +2.2 +0.5 −0.7 −2.0 +2.0 +1.0 +2.2 +5.2 −3.1 +1.5 −1.4 20 : 60 0.0005 : 0.0012 −0.2 +0.2 −0.0 +0.0 +1.3 −0.8 −0.0 +0.0 −1.5 +1.9 +0.5 −0.7 −1.7 +1.7 +1.1 −0.3 +2.9 −2.6 +1.1 −1.1 20 : 60 0.0012 : 0.002 +0.0 −0.0 −0.0 +0.0 +0.9 −0.6 +0.0 −0.0 −1.2 +1.6 +0.4 −0.5 −0.9 +0.9 +0.8 −0.4 +3.5 −3.3 +1.0 −1.1 20 : 60 0.002 : 0.0035 +0.3 −0.3 −0.0 +0.0 +1.1 −0.7 +0.0 −0.0 −1.1 +1.5 +0.3 −0.4 −2.3 +2.3 +0.2 −0.1 +3.5 −3.0 +1.1 −1.1 20 : 60 0.0035 : 0.01 +0.7 −0.7 +0.0 −0.0 +2.1 −1.3 −0.0 +0.0 −1.3 +1.6 +0.1 −0.1 −3.4 +3.4 +2.3 −0.1 +3.0 −3.4 +1.2 −1.2 60 : 120 0.0008 : 0.0018 −0.1 +0.1 −0.2 +0.2 +1.7 −1.1 −0.3 +0.2 −1.5 +1.9 +1.2 −1.6 −7.2 +7.2 +0.9 +0.2 +2.6 −3.6 +1.0 −1.0 60 : 120 0.0018 : 0.003 −0.4 +0.4 −0.0 +0.0 +1.3 −0.8 +0.0 −0.0 −1.1 +1.4 +0.4 −0.6 −1.7 +1.7 +3.0 +0.6 +2.3 −3.5 +1.0 −0.9 60 : 120 0.003 : 0.006 −0.1 +0.1 −0.0 +0.0 +1.2 −0.8 +0.0 −0.0 −0.8 +1.1 +0.3 −0.3 −2.9 +2.9 +1.8 +0.0 +2.0 −1.9 +0.9 −1.1 60 : 120 0.006 : 0.04 +0.3 −0.3 +0.0 −0.0 +2.3 −1.5 −0.0 +0.0 −0.7 +0.9 +0.1 −0.1 −3.1 +3.1 +1.6 +0.1 +3.2 −1.9 +1.0 −1.0 120 : 400 0.0016 : 0.005 −0.4 +0.4 −0.1 +0.1 +1.7 −1.1 −0.1 +0.0 −1.6 +2.0 +0.4 −0.5 −0.6 +0.6 +4.7 +0.2 +3.1 −4.0 +0.7 −0.7 120 : 400 0.005 : 0.016 −0.1 +0.1 −0.3 +0.3 +1.6 −1.0 −0.2 +0.1 −1.1 +1.4 +0.4 −0.5 −2.2 +2.2 +2.8 +0.2 +2.4 −3.0 +0.8 −0.9 120 : 400 0.016 : 0.06 +0.5 −0.5 −0.4 +0.4 +1.9 −1.2 −0.4 +0.2 −0.9 +1.2 +0.2 −0.3 −3.2 +3.2 −1.1 +1.3 +4.8 −3.9 +1.5 −1.6 400 : 1 000 0.005 : 0.02 −0.0 +0.0 −0.2 +0.2 +1.9 −1.2 −0.2 +0.1 −2.0 +2.6 +0.3 −0.4 −2.6 +2.6 +6.3 +0.9 +2.5 −6.4 +1.2 −1.3 400 : 1 000 0.02 : 0.1 −0.0 +0.0 −0.4 +0.4 +3.0 −1.9 −0.8 +0.5 +0.8 −1.0 +0.3 −0.4 −12.0 +12.0 +8.8 +4.1 +6.4 −13.0 +0.3 −0.3 Table 15: Systematic uncertainties for the double-differential cross sections of inclusive jet production in charm events (continued). 3 8 Q2 x δ−mb δ + mb δ−µR, µF δ + µR, µF δ−αs δ + αs (GeV2) (%) (%) (%) (%) (%) (%) 6.5 0.00015 +7.4 −5.9 −3.3 +2.6 +0.7 −0.3 6.5 0.00028 +8.1 −6.8 −1.5 +0.5 +0.1 −0.4 12 0.00043 +6.9 −5.2 −1.4 +1.0 +0.3 −0.2 12 0.00065 +4.2 −2.7 −0.8 +1.7 +0.3 −0.0 25 0.00043 +7.2 −5.1 −2.2 +2.3 +0.8 −0.3 25 0.00080 +5.8 −4.6 −0.7 +0.4 +0.2 −0.0 30 0.0016 +4.3 −4.1 +0.3 −1.2 −0.3 −0.4 30 0.0025 +3.1 −3.3 +1.1 −1.7 −0.3 −0.6 30 0.0045 +1.6 −0.8 +2.6 −0.9 −1.0 −0.2 80 0.0016 +3.2 −3.1 −1.5 −0.2 +0.2 −0.1 80 0.0025 +2.6 −2.3 −0.1 −0.7 +0.3 +0.2 80 0.0045 +1.9 −2.2 +0.8 −1.6 −0.5 −0.0 160 0.0035 +2.2 −1.5 −0.2 −0.1 +0.2 −0.3 160 0.0080 +2.1 −1.6 +1.3 −1.1 +0.1 +0.2 160 0.020 +0.8 +0.0 +3.1 −1.9 +0.9 −0.2 600 0.013 +0.8 −1.3 +0.1 −0.4 +0.2 −0.5 600 0.035 +1.1 +0.4 +2.6 −1.2 +0.3 +0.7 Table 16: Extrapolation uncertainties on the structure function F bb̄2 due to the variations of the beauty-quark mass, mb, factorisation and renormalisation scales, µF and µR, and the strong coupling constant, αs. The plus (minus) superscript indicates the upward (down- ward) variation of the corresponding parameter. See Section 9 for more details. 39 Q2 x δ−mc δ + mc δ−µR, µF δ + µR, µF δ−αs δ + αs (GeV2) (%) (%) (%) (%) (%) (%) 6.5 0.00015 +9.9 −6.8 −19.6 +20.2 +4.8 −1.0 6.5 0.00028 +9.2 −9.6 −17.7 +18.0 +4.3 −3.0 12 0.00043 +7.4 −6.9 −17.5 +14.8 +3.2 −3.4 12 0.00065 +6.1 −4.6 −11.4 +10.8 +2.5 −2.8 25 0.00043 +8.1 −5.1 −13.9 +14.9 +3.7 −0.8 25 0.00080 +5.7 −4.6 −6.7 +4.1 +0.7 −0.8 30 0.0016 +4.5 −3.3 −1.3 −0.5 −0.3 +0.3 30 0.0025 +2.4 −3.4 +0.2 −1.0 −0.4 −0.3 30 0.0045 +3.5 +0.2 +3.5 +0.2 +1.6 +1.5 80 0.0016 +3.6 −1.8 −1.7 +2.6 +0.6 +1.0 80 0.0025 +0.4 −3.1 −2.1 −1.8 −1.4 −1.0 80 0.0045 +1.5 −1.4 −0.2 −0.9 −0.2 −0.4 80 0.0080 −0.8 −0.2 −0.4 −0.3 −0.4 −0.3 160 0.0035 +2.1 −1.2 −0.7 +0.6 −0.3 −0.7 160 0.0080 +1.2 −1.4 +0.7 +0.3 −0.1 −0.5 160 0.020 −0.2 +0.1 +0.3 +0.8 −0.0 +1.1 600 0.013 +2.0 −0.5 −0.8 +0.5 +1.0 +0.6 600 0.035 +1.6 +0.3 +1.7 −1.2 +2.2 +1.2 Table 17: Extrapolation uncertainties on the structure function F cc̄2 due to the variations of the charm-quark mass, mc, factorisation and renormalisation scales, µF and µR, and the strong coupling constant, αs. The plus (minus) superscript indicates the upward (down- ward) variation of the corresponding parameter. See Section 9 for more details. 40 Q2 x δ−mb δ + mb δ−µR, µF δ + µR, µF δ−αs δ + αs (GeV2) (%) (%) (%) (%) (%) (%) 6.5 0.00015 +7.3 −6.0 −3.2 +2.6 +0.7 −0.3 6.5 0.00028 +8.1 −6.8 −1.3 +0.6 +0.3 −0.3 12 0.00043 +6.8 −5.2 −1.4 +0.9 +0.2 −0.3 12 0.00065 +4.7 −2.2 −0.4 +2.1 +0.8 +0.4 25 0.00043 +7.1 −4.9 −2.6 +2.4 +0.8 −0.3 25 0.00080 +5.7 −4.8 −0.7 +0.5 +0.2 −0.1 30 0.0016 +4.0 −4.4 +0.3 −1.7 −0.7 −0.6 30 0.0025 +3.2 −3.0 +1.3 −1.4 +0.1 −0.2 30 0.0045 +1.7 −3.2 +0.5 −4.2 −2.4 −2.2 80 0.0016 +3.1 −3.0 −1.3 −0.0 +0.1 −0.1 80 0.0025 +2.5 −2.4 −0.1 −0.8 +0.2 +0.2 80 0.0045 +2.2 −2.0 +1.0 −1.2 +0.0 +0.2 160 0.0035 +2.2 −1.4 −0.2 −0.1 +0.3 −0.3 160 0.0080 +1.9 −1.7 +1.1 −1.2 −0.0 +0.1 160 0.020 +0.5 −0.2 +2.9 −1.8 +0.5 −0.0 600 0.013 +0.7 −1.3 +0.1 −0.4 +0.3 −0.5 600 0.035 +1.0 +0.4 +2.7 −1.4 +0.2 +0.8 Table 18: Extrapolation uncertainties on the reduced beauty cross section, σbb̄r , due to the variations of the beauty-quark mass, mb, factorisation and renormalisation scales, µF and µR, and the strong coupling constant, αs. The plus (minus) superscript indicates the upward (downward) variation of the corresponding parameter. See Section 9 for more details. 41 Q2 x δ−mc δ + mc δ−µR, µF δ + µR, µF δ−αs δ + αs (GeV2) (%) (%) (%) (%) (%) (%) 6.5 0.00015 +8.3 −7.7 −19.1 +18.2 +3.5 −2.3 6.5 0.00028 +9.3 −9.0 −20.3 +18.7 +3.9 −2.4 12 0.00043 +7.0 −7.5 −18.6 +14.2 +2.1 −3.3 12 0.00065 +5.7 −4.8 −14.1 +11.3 +0.9 −2.8 25 0.00043 +7.8 −4.3 −13.9 +15.1 +3.7 −0.4 25 0.00080 +5.0 −4.8 −6.9 +4.0 +0.8 −0.8 30 0.0016 +4.5 −3.9 −1.2 −0.8 −0.7 +0.3 30 0.0025 +2.4 −3.4 +0.5 −1.0 +0.1 +0.2 30 0.0045 +3.0 +0.4 +4.0 +0.6 +1.9 +1.9 80 0.0016 +3.7 −1.8 −2.0 +2.8 +0.6 +1.0 80 0.0025 +0.6 −3.2 −2.1 −1.8 −1.5 −0.9 80 0.0045 +1.5 −1.8 −0.1 −0.9 −0.3 −0.4 80 0.0080 −1.0 −0.2 −0.7 −0.7 −0.4 −0.2 160 0.0035 +2.1 −1.3 −0.6 +0.6 −0.4 −0.7 160 0.0080 +1.3 −2.2 +0.6 −0.3 −0.5 −0.7 160 0.020 −0.2 +0.3 +0.5 −0.2 +0.1 +0.7 600 0.013 +2.3 −0.5 −0.7 +0.5 +1.1 +0.7 600 0.035 +1.6 +0.3 +1.7 −1.2 +1.6 +1.4 Table 19: Extrapolation uncertainties on the reduced charm cross section, σcc̄r , due to the variations of the charm-quark mass, mc, factorisation and renormalisation scales, µF and µR, and the strong coupling constant, αs. The plus (minus) superscript indicates the upward (downward) variation of the corresponding parameter. See Section 9 for more details. 42 Parameter Variation Uncertainty (GeV) Fit uncertainty Total ∆χ2 = 1 +0.14 −0.14 Model uncertainty fs 0.31 +0.07 −0.08 +0.00 −0.00 Q2min 3.5 → 5.0 GeV2 +0.00−0.00 Q20 1.4 → 1.9 GeV2 +0.01−0.01 δmext see text −0.07 Total +0.01 −0.07 PDF parameterisation uncertainty Duv free in fit +0.03 DD̄ free in fit +0.03 DŪ free in fit +0.02 Total +0.05 −0.00 Theory uncertainty mc(mc) (1.26 ± 0.06) GeV +0.02−0.02 αs 0.105 ± 0.002 +0.02−0.02 µ ×2, ×1/2 +0.07 −0.04 Total +0.08 −0.05 Table 20: List of uncertainties for the beauty-quark mass determination. A description of the uncertainties not explicitly mentioned in the text is given elsewhere [34]. 43 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 210 310 410 510 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 210 310 410 510 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 210 310 410 510 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 210 310 410 510 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 10 210 310 410 510 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 10 210 310 410 510 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 310 410 510 610 S -20 -15 -10 -5 0 5 10 15 20 E n tr ie s 310 410 510 610 ZEUS < 1.4 GeVvtx1 < m < 2 GeVvtx1.4 < m < 6 GeVvtx2 < m vtxNo restriction on m -1ZEUS 354 pb Monte Carlo LF Charm Beauty (a) (b) (c) (d) Figure 1: Distributions of the decay-length significance, S, for (a) 1 < mvtx < 1.4 GeV, (b) 1.4 < mvtx < 2 GeV, (c) 2 < mvtx < 6 GeV and (d) no restriction on mvtx. The data are compared to the sum of all MC distributions as well as the individual contributions from the beauty, charm and light-flavour (LF) MC subsamples. All samples were normalised according to the scaling factors obtained from the fit (see text). 44 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 210 310 410 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 210 310 410 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 210 310 410 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 210 310 410 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 210 310 410 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 210 310 410 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 310 410 510 |S| 4 6 8 10 12 14 16 18 20 E n tr ie s 310 410 510 ZEUS < 1.4 GeVvtx1 < m < 2 GeVvtx1.4 < m < 6 GeVvtx2 < m vtxNo restriction on m -1ZEUS 354 pb Monte Carlo LF Charm Beauty (a) (b) (c) (d) Figure 2: Distribution of the subtracted decay-length significance in four ranges of mvtx. For more details, see the caption of Fig. 1. 45 (GeV) jet TE 5 10 15 20 25 30 35 40 E n tr ie s 1 10 210 310 (GeV) jet TE 5 10 15 20 25 30 35 40 E n tr ie s 1 10 210 310 jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 E n tr ie s 0 100 200 300 400 500 jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 E n tr ie s 0 100 200 300 400 500 )2/GeV2(Q 10 log 0.5 1 1.5 2 2.5 3 E n tr ie s 0 50 100 150 )2/GeV2(Q 10 log 0.5 1 1.5 2 2.5 3 E n tr ie s 0 50 100 150 x 10 log -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 E n tr ie s 0 100 200 300 x 10 log -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 E n tr ie s 0 100 200 300 ZEUS < 6 GeV, |S|>8vtx2 < m -1ZEUS 354 pb Monte Carlo LF Charm Beauty (a) (b) (c) (d) Figure 3: Distributions of (a) E jet T , (b) η jet, (c) log10 Q 2 and (d) log10 x of the selected secondary vertices for a beauty-enriched subsample with 2 < mvtx < 6 GeV and |S| > 8. For more details, see the caption of Fig. 1. 46 (GeV) jet TE 5 10 15 20 25 30 35 40 E n tr ie s 1 10 210 310 410 (GeV) jet TE 5 10 15 20 25 30 35 40 E n tr ie s 1 10 210 310 410 jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 E n tr ie s 0 1000 2000 3000 4000 jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 E n tr ie s 0 1000 2000 3000 4000 )2/GeV2(Q 10 log 0.5 1 1.5 2 2.5 3 E n tr ie s 0 1000 2000 3000 )2/GeV2(Q 10 log 0.5 1 1.5 2 2.5 3 E n tr ie s 0 1000 2000 3000 x 10 log -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 E n tr ie s 0 2000 4000 6000 8000 x 10 log -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 E n tr ie s 0 2000 4000 6000 8000 ZEUS < 2 GeV, |S|>4vtx1 < m -1ZEUS 354 pb Monte Carlo LF Charm Beauty (a) (b) (c) (d) Figure 4: Distributions of (a) E jet T , (b) η jet, (c) log10 Q 2 and (d) log10 x of the selected secondary vertices for a charm-enriched subsample with 1 < mvtx < 2 GeV and |S| > 4. For more details, see the caption of Fig. 1. 47 (GeV) jet TE 5 10 15 20 25 30 35 ( p b / G e V ) je t T / d E σ d -110 1 10 210 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.49 ZEUS e jet X→X b e b→ep (GeV) jet TE 5 10 15 20 25 30 35 D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 (GeV) jet TE 5 10 15 20 25 30 35 ( p b / G e V ) je t T / d E σ d -110 1 10 210 310 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.40 ZEUS e jet X→X c e c→ep (GeV) jet TE 5 10 15 20 25 30 35 D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 (a) (b) Figure 5: Differential cross sections for inclusive jet production in (a) beauty events and (b) charm events as a function of E jet T . The cross sections are given for 5 < Q 2 < 1 000 GeV2, 0.02 < y < 0.7, E jet T > 5(4.2) GeV and −1.6 < ηjet < 2.2. The data are shown as points. The inner error bars are the statistical uncertainties, while the outer error bars show the statistical and systematic uncertainties added in quadrature. The solid line shows the Hvqdis prediction with the ZEUS-S PDF, corrected for hadronisation effects, with the uncertainties indicated by the band; the dotted line shows the same prediction using the ABKM PDF; the dashed line shows the prediction from Rapgap scaled to match the measured integrated cross sections. 48 jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 ( p b ) je t η / d σ d 100 200 300 400 500 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.49 ZEUS e jet X→X b e b→ep jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 ( p b ) je t η / d σ d 1000 2000 3000 4000 5000 6000 7000 8000 9000 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.40 ZEUS e jet X→X c e c→ep jetη -1.5 -1 -0.5 0 0.5 1 1.5 2 D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 (a) (b) Figure 6: Differential cross sections for inclusive jet production in (a) beauty events and (b) charm events as a function of ηjet. For more details, see the caption of Fig. 5. 49 )2 (GeV2Q 10 210 310 ) 2 ( p b / G e V 2 / d Q σ d -210 -110 1 10 210 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.49 ZEUS e jet X→X b e b→ep )2 (GeV2Q 10 210 310D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 )2 (GeV2Q 10 210 310 ) 2 ( p b / G e V 2 / d Q σ d -210 -110 1 10 210 310 410 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.40 ZEUS e jet X→X c e c→ep )2 (GeV2Q 10 210 310D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 (a) (b) Figure 7: Differential cross sections for inclusive jet production in (a) beauty events and (b) charm events as a function of Q2. For more details, see the caption of Fig. 5. 50 x -410 -310 -210 -110 / d x ( p b ) σ d 310 410 510 610 710 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.49 ZEUS e jet X→X b e b→ep x -410 -310 -210 -110D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 x -410 -310 -210 -110 / d x ( p b ) σ d 310 410 510 610 710 810 -1ZEUS 354 pb had C×HVQDIS+ZEUS-S had C×HVQDIS+ABKM Rapgap x 1.40 ZEUS e jet X→X c e c→ep x -410 -310 -210 -110D a ta / H V Q D IS 0.5 1 1.5 2 0 0 0 (a) (b) Figure 8: Differential cross sections for inclusive jet production in (a) beauty events and (b) charm events as a function of x. For more details, see the caption of Fig. 5. 51 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 x -410 -3 10 -210 -110 x -410 -310 -210 -110 x -410 -310 -210 -110 c c 2 F 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 -1ZEUS 354 pb HERAPDF 1.5 GMVFNS ZEUS 2 = 6.5 GeV2Q 2 = 12 GeV2Q 2 = 25 GeV2Q 2 = 30 GeV2Q 2 = 80 GeV2Q 2 = 160 GeV2Q 2 = 600 GeV2Q Figure 9: The structure function F cc̄2 (filled symbols) as a function of x for seven differ- ent values of Q2. The inner error bars are the statistical uncertainty while the outer error bars represent the statistical, systematic and extrapolation uncertainties added in quadrat- ure. Also shown are the NLO QCD HERAPDF 1.5 predictions based on the general-mass variable-flavour-number scheme (solid line and shaded area for the uncertainties). 52 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 x -410 -3 10 -210 x -410 -310 -210 x -410 -310 -210 c c r σ 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 ZEUS 2 = 7 GeV2Q 2 = 12 GeV2Q 2 = 18 GeV2Q 2 = 32 GeV2Q 2 = 60 GeV2Q 2 = 120 GeV2Q 2 = 650 GeV2Q -1ZEUS vtx 354 pb -1ZEUS D* 363 pb -1 354 pb+ZEUS D HERA Figure 10: Reduced charm cross section, σcc̄r , as a function of x for fixed values of Q 2. Results from the current analysis (filled circles) are compared to the ZEUS D∗± data [33] (empty triangles), the ZEUS D+ measurement [32] (empty squares) and the combination of previous HERA results [34] (empty circles). The inner error bars in the ZEUS measure- ments show the statistical uncertainties. The inner error bars of the combined HERA data represent the uncorrelated part of the uncertainty. The outer error bars include statistical, systematic and theoretical uncertainties added in quadrature. 53 0 0.01 0.02 0.03 0 0.01 0.02 0.03 0 0.01 0.02 0.03 0 0.02 0.04 0 0.02 0.04 0 0.02 0.04 0 0.02 0.04 x -410 -3 10 -210 -110 x -410 -310 -210 -110 x -410 -310 -210 -110 b b 2 F 0 0.01 0.02 0.03 0 0.02 0.04 0 0.02 0.04 -1ZEUS 354 pb HERAPDF 1.5 GMVFNS ZEUS 2 = 6.5 GeV2Q 2 = 12 GeV2Q 2 = 25 GeV2Q 2 = 30 GeV2Q 2 = 80 GeV2Q 2 = 160 GeV2Q 2 = 600 GeV2Q Figure 11: The structure function F bb̄2 (filled symbols) as a function of x for seven differ- ent values of Q2. The inner error bars are the statistical uncertainty while the outer error bars represent the statistical, systematic and extrapolation uncertainties added in quadrat- ure. Also shown are the NLO QCD HERAPDF 1.5 predictions based on the general-mass variable-flavour-number scheme (solid line and shaded area for the uncertainties). 54 )2 (GeV2Q 10 210 310 + 0 .0 3 i b b 2 F 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 -1ZEUS vtx 354 pb -1ZEUS e 363 pb -1 114 pbµZEUS -1+vtx 126 pbµZEUS -1H1 vtx 246 pb HERAPDF 1.5 ABKM NNLO MSTW08 NLO MSTW08 NNLO CTEQ6.6 NLO JR09 x=0.032 i=0 x=0.013 i=1 x=0.005 i=2 x=0.002 i=3 x=0.0013 i=4 x=0.0005 i=5 x=0.0002 i=6 x=0.00013 i=7 Figure 12: The structure function F bb̄2 (filled circles) as a function of Q 2 for fixed values of x compared to previous results (open squares [31], open triangles [29], open circles [28] and filled squares [10, 12, 15]). The inner error bars are the statistical uncertainty while the outer error bars represent the statistical, systematic and extrapolation uncertainties added in quadrature. The data have been corrected to the same reference x as the pre- vious analysis [29]. The measurements are compared to several NLO and NNLO QCD predictions [85–92]. 55 0 0.005 0.01 0.015 0.02 0 0.005 0.01 0.015 0.02 0 0.005 0.01 0.015 0.02 0 0.02 0.04 0 0.02 0.04 0 0.02 0.04 0 0.01 0.02 0.03 x -410 -3 10 -210 x -410 -310 -210 x -410 -310 -210 b b r σ 0 0.005 0.01 0.015 0.02 0 0.02 0.04 0 0.01 0.02 0.03 -1ZEUS 354 pb =4.07 GeV (best fit) b QCD fit, m =3.93 GeV b QCD fit, m =4.21 GeV b QCD fit, m ZEUS 2 = 6.5 GeV2Q 2 = 12 GeV2Q 2 = 25 GeV2Q 2 = 30 GeV2Q 2 = 80 GeV2Q 2 = 160 GeV2Q 2 = 600 GeV2Q Figure 13: Reduced beauty cross section, σbb̄r , (filled symbols) as a function of x for seven different values of Q2. The inner error bars are the statistical uncertainty while the outer error bars represent the statistical, systematic and extrapolation uncertainties added in quadrature. Also shown are the results of the QCD fit described in Section 10. The central line indicates the best fit, the lower and upper line give the fit for a higher and lower beauty mass, respectively. 56 ) (GeV) b (mbm 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 2 χ 586 588 590 592 594 596 598 600 ZEUS Inclusive DIS + beauty QCD fit Figure 14: The values of χ2 for the PDF fit to the combined HERA DIS data including the beauty measurements, as a function of the running beauty quark mass mb(mb). The FFNS ABM scheme is used, where the beauty quark mass is defined in the MS scheme. The solid line is a second order polynomial parameterisation of the points. 57 1 Introduction 2 Experimental set-up 3 Monte Carlo simulations 4 Theoretical predictions and uncertainties 5 Data selection 6 Extraction of the heavy-flavour cross sections 7 Systematic uncertainties 8 Cross sections 9 Extraction of F2qbarq and rqbarq 10 Measurement of the running beauty-quark mass 11 Conclusions