L H C b -P R O C -2 01 3- 00 2 16 / 01 / 20 13 Nuclear Physics B Proceedings Supplement 00 (2013) 1–6 Nuclear Physics B Proceedings Supplement CP violation in charm and beauty decays at LHCb M. Pepe Altarelli1 CERN, Geneva, Switzerland Abstract LHCb is a dedicated heavy flavour physics precision experiment at the LHC searching for New Physics (NP) beyond the Standard Model (SM) through the study of very rare decays of beauty and charm-flavoured hadrons and precision measurements of CP-violating observables. In this review I will present a selection of recent precision measurements of CP-violating observables in the decays of beauty and charm-flavoured hadrons. These measurements are based on an integrated luminosity of up to 1.0 fb−1 collected by LHCb in 2011. Keywords: LHCb, Flavour physics, CP violation Fourth Workshop on Theory, Phenomenology and Experiments in Flavour Physics 11 - 13 June 2012, Anacapri, Italy 1. Introduction The LHCb detector has been taking data with high efficiency during the last three years of operation at the LHC, producing a wealth of exciting physics re- sults, which have made an impact on the flavour physics landscape and proved the concept of a dedicated heavy flavour spectrometer in the forward region at a hadron collider. The LHC is the world’s most intense source of b hadrons. The bb cross-section in proton-proton colli- sions at √ s = 7 TeV is measured to be ∼300 µb, imply- ing that more than 1011 bb pairs were produced in LHCb in 2011, when an integrated luminosity of 1.0 fb−1 was collected. The cc cross-section is about 20 times larger Email address: monica.pepe.altarelli@cern.ch (M. Pepe Altarelli) 1On behalf of the LHCb collaboration c© CERN on behalf of the LHCb collaboration, license CC-BY- 3.0. than the bb cross-section, giving LHCb great potential in charm physics studies. As in the case of the Tevatron, a complete spectrum of b hadrons is available, including Bs, Bc mesons and b baryons, such as Λb. At the nominal LHC design luminosity of 1034 cm−2 s−1, multiple pp collisions within the same bunch crossing (so-called pile-up) would signif- icantly complicate the b decay-vertex reconstruction and flavour tagging, and increase the combinatorial background. For this reason the detector was designed to operate at a reduced luminosity. The luminosity at LHCb is locally controlled by transverse displace- ment of the beams (so-called “levelling”) to yield L = 4 × 1032cm−2 s−1 (approximately a factor of two above the original LHCb design value) at which the average event pile-up per visible crossing is ∼2. Running at relatively low luminosity has the additional advantage of reducing detector occupancy in the tracking systems and limiting radiation damage effects. The dominant bb-production mechanism at the LHC http://creativecommons.org/licenses/by/3.0/ http://creativecommons.org/licenses/by/3.0/ M.Pepe Altarelli / Nuclear Physics B Proceedings Supplement 00 (2013) 1–6 2 is through gluon-gluon fusion in which the momenta of the incoming partons are strongly asymmetric in the pp centre-of-mass frame. As a consequence, the bb pair is boosted along the direction of the higher momentum gluon, and both b hadrons are produced in the same for- ward (or backward) direction in the pp centre-of-mass frame. The detector is therefore designed as a single- arm forward spectrometer covering the pseudorapidity range 2 < η < 5, which ensures a high geometric ef- ficiency for detecting all the decay particles from one b hadron together with decay products from the accompa- nying b hadron to be used as a flavour tag. The key de- tector features are a versatile trigger scheme efficient for both leptonic and hadronic final states, which is able to cope with a variety of modes with small branching frac- tions; excellent vertex and proper time resolution; pre- cise particle identification, specifically for hadron (π/K) separation; precise invariant mass reconstruction to re- ject background efficiently. A full description of the de- tector characteristics can be found in Ref.[1]. In this review, I report on a few recent precision measurements of CP-violating observables in decays of beauty and charm-flavoured hadrons, while the study of rare decays at LHCb is covered by a separate contribu- tion [2]. 2. Measurement of the Bs mixing phase The CP-violating phase φs between B0s -B 0 s mixing and the b → ccs decay amplitude of the Bs meson is determined with a flavour tagged, angular analysis of the decay B0s → J/ψφ, with J/ψ → µ +µ− and φ → K+ K−. This phase originates from the interfer- ence between the amplitudes for a Bs (Bs) to decay di- rectly into the final state J/ψφ or to first mix into Bs (Bs) and then decay. In the SM, φs is predicted to be ' −2βs, where 2βs = 2arg(−VtsV∗tb/VcsV∗cb) = (3.6±0.2) 10−2 rad [3]. However, NP could significantly modify this prediction if new particles contribute to the B0s -B 0 s box diagram. The CDF and D0 collaborations [4, 5] have reported measurements of the Bs mixing phase based on approx- imately 11,000 B0s → J/ψφ candidates from an inte- grated luminosity of 9.6 fb−1 (i.e. the full CDF Run II dataset) and 6,500 B0s → J/ψφ candidates from 8 fb −1, respectively. Both results are compatible with the SM expectation at approximately one standard deviation in the (φs, ∆Γs) plane. LHCb has presented results based on a sample that contains approximately 21,200 B0s → J/ψφ candidates from an integrated luminosity of 1.0 fb−1 [6]. Besides having a very large and clean signal yield, LHCb also benefits from an excellent proper time resolution to resolve fast Bs oscillations, which is measured to be ∼45 fs, compared to a Bs oscillation period of ∼350 fs. The other key experimental ingredient is flavour tag- ging, which is performed by reconstructing the charge of the b-hadron accompanying the B meson under study. The analysis uses an opposite-side flavour tagger based on four different signatures, namely high pT muons, electrons and kaons, and the net charge of an inclusively reconstructed secondary vertex, with a combined effec- tive tagging power of ∼2.4%. The decay B0s → J/ψφ is a pseudoscalar to vector-vector transition. Total an- gular momentum conservation implies l = 0, 1, 2 and therefore the J/ψφ final state is a mixture of CP-even (l = 0, 2) and CP-odd (l = 1) eigenstates, which can be disentangled on a statistical basis. This is accom- plished by performing an unbinned maximum likeli- hood fit to the candidate invariant mass, decay time, initial Bs flavour and the decay angles in the so-called transversity frame [7]. The fit yields the following re- sult for the three main observables, namely φs, the de- cay width, Γs, and the decay width difference between the light and heavy Bs mass eigenstates, ∆Γs φs = −0.001 ±0.101(stat) ±0.027(syst) rad, Γs = 0.6580 ±0.0054(stat) ±0.0066(syst) ps −1, ∆Γs = 0.116 ±0.018(stat) ±0.006(syst) ps −1. This is the world’s most precise measurement of φs and the first direct observation for a non-zero value for ∆Γs. These results are fully consistent with the SM, indicat- ing that CP violation in the Bs system is small. Actu- ally, there exists a second mirror solution in the plane ∆Γs vs φs, which arises from the fact that the time- dependent differential decay rates are invariant under the transformation (φs, ∆Γs) → (π − φs,−∆Γs) (plus an appropriate transformation of the strong phases). LHCb has recently resolved this ambiguity [8] by studying the dependence of the strong phase difference between the S -wave and P-wave amplitudes on the K+ K− mass from B0s → J/ψK + K− decays in the region around the φ(1020) resonance. The solution with positive ∆Γs is favoured with a significance of 4.7 standard deviations, indicating that in the Bs system the lighter CP mass eigenstate that is almost CP even decays faster than the state that is almost CP odd. The mixing-induced phase φs is also measured in the decay Bs → J/ψπ+π− [9]. The branching fraction for this decay is ∼ 25% of Bs → J/ψφ, with φ → K+ K−. However, this final state has been shown to be almost CP pure with a CP-odd fraction larger than 0.977 at M.Pepe Altarelli / Nuclear Physics B Proceedings Supplement 00 (2013) 1–6 3 0.25 CDF LHCb ATLAS Combined SM 0.20 0.15 0.10 0.05 0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 68% CL contours ( ) HFAG Fall 2012 LHCb 1.0 fb —1 + CDF 9.6 fb —1 + ATLAS 4.9 fb 1 + D 8 fb — —1 D Figure 1: 68% confidence-level contours in the (φs, ∆Γs) plane for the individual experimental measurements, their combined contour (solid line and shaded area), as well as the SM predic- tions (black rectangle). 95% CL, and there is no need for an angular analysis. About 7,400 signal events are selected in 1.0 fb−1 of data, yielding the result φs = −0.019+0.173+0.004−0.174−0.003 rad. The two datasets are combined in a simultaneous fit, lead- ing to the preliminary result φs = −0.002 ± 0.083 ± 0.027 rad [6], in excellent agreement with the SM. The precision for this result is completely dominated by the statistical uncertainty and therefore significant improve- ments are expected with more data. Figure 1 shows 68% confidence-level contours in the (φs, ∆Γs) plane for the individual experimental measure- ments, their combined contour, as well as the SM pre- dictions [10]. The combined result is consistent with these predictions at the 0.14 σ level. 3. Measurement of the weak phase γ from tree-level decays The angle γ is currently the least precisely known pa- rameter of the CKM unitarity triangle. The direct de- termination of γ via fits to the experimental data gives (66±12)◦ [11] or (76±10)◦ [12], depending on whether a frequentist or Bayesian treatment is used. In terms of the elements of the CKM matrix, this weak phase is defined as γ = arg(−VudV∗ub/VcdV∗cb). It is of par- ticular interest as it can produce direct CP violation in tree-level decays involving the interference between b → cus and b → ucs transitions that are expected to be insensitive to NP contributions, thus providing a benchmark against which measurements sensitive to NP through loop processes can be compared. One of the most powerful ways to measure the angle γ is through charged B decays to open charm, B± → Dh±, where D stands for a D0 or a D0 and h indicates either a pion or kaon. Decays in which the hadron h is a kaon carry greater sensitivity to γ. The method is based on two key observations: 1. These decays can produce neutral D mesons of both flavours via colour- favoured or colour-suppressed decays 2. Neutral D and D mesons can decay to a common final state, for ex- ample through Cabibbo-favoured or doubly Cabibbo- suppressed Feynman diagrams (ADS method [13]) or through decays to CP eigenstates such as K+ K− or π+π− (GLW method [14]). In the ADS case, the reversed sup- pression between B and D decays results in very sim- ilar amplitudes leading to a high sensitivity to γ. The relative phase between the two interfering amplitudes for B+ → DK+ and B+ → DK+ is the sum of the strong and weak interaction phases, while in the case of B− → DK− and B− → DK− it is the difference be- tween the strong phase and γ. Therefore both phases can be extracted by measuring the two charge conjugate modes. In addition, there is a dependence on the ratio between the magnitude of the suppressed amplitude and the favoured amplitude rB. LHCb has performed an analysis of the two-body B± → Dh± modes in which the considered D meson fi- nal states are π+π−, K+ K−, the Cabibbo-favoured K±π∓ and the Cabibbo-suppressed π±K∓ [15]. For both GLW and ADS methods the observables of interest are CP asymmetries and partial widths. Exploiting 1.0 fb−1 of data, the first observation of the suppressed ADS mode B± → [π±K∓]D K± was performed. This is illustrated in the top plots of Fig 2. A large asymmetry is visible in the B± → [π±K∓]D K± mode (by comparing the signal yield for B+ and B−) while for the B± → [π±K∓]Dπ± ADS mode there is the hint of an (opposite) asymme- try. By combining all the various modes CP violation in B± → DK± was observed with a 5.8 σ significance. ) 2 c E v e n ts / ( 5 M e V / 5 10 15 ) 2 c E v e n ts / ( 5 M e V / 5 10 15 - K D ] + K-π[→ - B LHCb + K D ] - K + π[→ + B LHCb 5200 5400 5600 0 10 20 30 40 5200 5400 5600 0 10 20 30 40 -π D ] + K-π[→ - B LHCb )2c) (MeV/ ± Dh(m 5200 5400 5600 )2c) (MeV/ ± Dh(m 5200 5400 5600 + π D ] - K + π[→ + B LHCb Figure 2: Invariant mass spectra for B± → [π±K∓]Dh± events; the left plots are B− candidates, B+ are on the right. The dark (red) curve in the top plots represents the B → DK± events, the light (green) curve in the bottom plots is B → Dπ±. M.Pepe Altarelli / Nuclear Physics B Proceedings Supplement 00 (2013) 1–6 4 The three-body final state D → K0S h +h−, with h = (π, K), was also studied [16] through a Dalitz plot anal- ysis. The strategy relies on comparing the distribu- tions of events in the D → K0s h +h− Dalitz plot for B+ → DK+ and B− → DK− decays. Existing mea- surements of the CLEO-c experiment [17] were used to provide input on the D decay strong-phase parameters. Based on approximately 800 B± → DK± decays with D → K0S h +h− selected from 1.0 fb−1 of data, the fol- lowing results were obtained for the weak phase γ and the ratio rB between the suppressed and favoured B de- cay amplitudes, γ = (44+43 −38) ◦, with a second solution at γ → γ + 180◦, and rB = 0.07 ± 0.04. Other flavour specific final states, such as D → Kπππ are exploited in a similar manner to the two- body case [18]. However, for multi-body final states different intermediate resonances can contribute, dilut- ing CP violation effects. Based on 1.0 fb−1 of data, the suppressed ADS modes B± → [π±K∓π+π−]D K± and B± → [π±K∓π+π−]Dπ± were observed for the first time with significances of 5.1 σ and > 10 σ, respectively. A combination of the B± → DK± results from Refs. [15, 16, 18] was performed to derive an unambigu- ous best-fit value in [0, 180]◦ of γ = (71.1+16.6 −15.7) ◦ [19], suggesting very good prospects for the result based on the full data-set. Additional γ-sensitive measurements will also be included in the future. With the data cur- rently available on tape, LHCb should be able to reduce the error quoted above by at least a factor of two. 4. C P violation in charmless B decays Charmless B decays represent an interesting family of channels for which a precise measurement of the charge or time-dependent CP asymmetries can play an impor- tant role in the search for NP. In particular, NP may show up as virtual contributions of new particles in loop diagrams. A comparison of results from decays domi- nated by tree-level diagrams with those that start at loop level can probe the validity of the SM. In particular, it was pointed out by Fleischer [20] that U-spin related decays (obtained by interchanging d and s quarks) of the type Bs,d → h+h′−, with h, h′ = π, K, offer inter- esting strategies for the measurement of the angle γ: in presence of NP in the penguin loops, such a determina- tion could differ appreciably from that derived from B decays governed by pure tree amplitudes discussed in Sect. 3. LHCb has analysed very large samples of Bs,d → h+h′− decays, separating the final state pions and kaons by using the particle identification provided by the RICH detectors. Figure 3 shows the invariant Kπ mass spectra for Bs,d → Kπ events based on an integrated lu- minosity of 0.35 fb−1 [21]. The selection cuts are opti- mised for the best sensitivity to ACP(Bd → Kπ) (plots a and b) and ACP(Bs → Kπ) (plots c and d), where the CP asymmetry in the B decay rate to the final state f = Kπ is defined as ACP = (Γ(B→ f )−Γ(B→ f ) (Γ(B→ f )+Γ(B→ f ) . LHCb reported [21] the most precise measurement for ACP(Bd → Kπ) avail- able to date, with a significance exceeding 6 σ, as well as the first evidence, at the 3.3 σ level, for CP viola- tion in the decay of the Bs mesons. The effect of the CP asymmetry is visible in Fig. 3 by comparing the yields for the Bd → Kπ in (a) and (b) and those for the Bs → Kπ in (c) and (d). The CP asymmetry results need to be corrected for the effect of a possible B production asymmetry, which is studied by reconstructing a sample of Bd → J/ψK∗ decays, given that CP violation in b → ccs transi- tions is expected to be small. Effects related to the instrumental detection efficiencies are evaluated by us- ing data sets with opposite magnet polarities and recon- structing large samples of tagged D∗± → D0(K−π+)π± and D∗± → D0(K−K+)π± decays, as well as untagged D0 → K−π+ decays. These corrections are found to be small. LHCb has also performed measurements of time- dependent CP violation in charmless two-body B de- cays by studying the processes Bd → π+π− and Bs → K+ K− [22]. The analysis is based on a luminosity of 0.69 fb−1. Direct and mixing-induced CP asymmetries are measured in each channel using a tagged, time- 5 5.2 5.4 5.6 5.8 2 E v e n ts / ( 0 .0 2 G e V /c 0 500 1000 1500 2000 2500 3000 ) LHCb (a) ) 2 invariant mass (GeV/c−π + K ) 2 invariant mass (GeV/c+π − K 5 5.2 5.4 5.6 5.8 ) 2 E v e n ts / ( 0 .0 2 G e V /c 0 500 1000 1500 2000 2500 3000 LHCb (b) B →Kπ B →Kπ B →ππ B →KK B→3-body Comb. bkg 0 0 0 0 s s 0 50 100 150 200 250 300 350 400 ) 2 E v e n ts / ( 0 .0 2 G e V /c 5 5.2 5.4 5.6 5.8 ) 2 invariant mass (GeV/c−π + K LHCb (c) 0 50 100 150 200 250 300 350 400 ) 2 E v e n ts / ( 0 .0 2 G e V /c 5 5.2 5.4 5.6 5.8 ) 2 invariant mass (GeV/c+π − K LHCb (d) Figure 3: Invariant Kπ mass spectra for Bs,d → Kπ events; the selection cuts are optimised for the best sensitivity to ACP(Bd → Kπ) (plots a and b) and ACP(Bs → Kπ) (c and d). Plots a and c (b and d) show the K+π− (K−π+) invariant mass distribution. The main components of the fit model are also shown. M.Pepe Altarelli / Nuclear Physics B Proceedings Supplement 00 (2013) 1–6 5 dependent analysis. This analysis is performed for the first time at a hadron collider, and the Bs → K+ K− de- cay is studied for the first time ever. The preliminary results for the Bd → π+π− channel are in agreement with the world average from the B factories. However, more data need to be analysed to be able to extract a measurement of γ from these decays. 5. C P violation in charm The charm sector is an interesting place to probe for the presence of NP because CP violation is expected to be small in the SM. In particular, in singly Cabibbo sup- pressed decays, such as D → π+π− or D → K+ K−, NP could manifest itself through the interference between tree-level and penguin diagrams. LHCb has collected very large samples of charm: one in every ten LHC in- teraction results in the production of a charm hadron, of which 1-2 kHz are written to storage and are available for offline analysis. In 2012, LHCb has collected ap- proximately 5 × 103 tagged D∗± → (D0 → K+ K−)π± and 3×105 untagged D → K−π+ decays per pb−1 of in- tegrated luminosity and it has the world’s largest sample of two and three-body D(s) decays on tape. The difference in time-integrated asymmetries be- tween D → π+π− and D → K+ K− was measured using 0.6 fb−1 of data collected in 2011 [23]. The flavour of the charm meson is determined by requiring a D∗± → (D0 → h+h−) π±s decay, with h = π or K, in which the sign of the slow pion πs tags the initial D0 or D0. By taking the difference of the measured time-integrated asymmetries for π+π− and K+ K−, effects related to the D∗ production asymmetry and to the detection asym- metry of the slow pion and D meson in the final state cancel to first order, so that one can derive the differ- ence of the CP asymmetries, ∆ACP. Second-order ef- fects are minimised by performing the analysis in bins of the relevant kinematic variables. A nice additional advantage of taking this difference is that in the U-spin limit ACP(K K) = −ACP(ππ) for any direct CP viola- tion [25], so that the effect is amplified. The final result is ∆ACP = [−0.82 ± 0.21 (stat) ± 0.11 (syst)]%. (1) This result (subsequently confirmed by CDF [24]) has generated a great deal of theoretical interest, as it is the first evidence for CP violation in the charm sector, with a significance of 3.5 σ. The difference in time-integrated asymmetries can be written to first order as ∆ACP = [a dir CP(K + K−) − adirCP(π +π−)] + ∆〈t〉 τ aindCP , (2) ind CP a -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 d ir C P a ∆ -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 BaBar CP A∆ Belle Prelim. CP A∆ LHCb CP A∆ CDF Prelim. CP A∆ LHCb Γ A BaBar Prelim. Γ A Belle Prelim. Γ A Figure 4: HFAG combination of ∆ACP and AΓ measure- ments [26], where the bands represent ±1σ intervals. The point of no CP violation (0,0) is displayed as a black dot; the ellipses show the two-dimensional 68% CL, 95% CL and 99.7% CL with the best fit value as a cross. where adirCP is the asymmetry arising from direct CP vi- olation in the decay, 〈t〉 the average decay time of the D0 in the reconstructed sample, and aindCP the asymmetry from CP violation in the mixing. In presence of a differ- ent time acceptance for the π+π− and K+ K− final states, a contribution from indirect CP violation remains. Figure 4 shows the HFAG world-average combina- tion [26] in the plane (aindCP, a dir CP). The combined data is consistent with no CP violation at 0.002% CL. LHCb is currently completing the analysis of the full 2011 data sample and pursuing alternative strategies to verify the effect. In particular, an analysis is being fi- nalised in which the flavour of the D0 meson is tagged using the charge of the muon in semileptonic B decays; furthermore CP violation is searched for in charged D decays where there is no possibility of indirect CP vi- olation and a positive signal would indicate unambigu- ously the presence of direct CP violation. 6. Conclusion This contribution has reviewed measurements of CP violation in charm and beauty decays performed by LHCb using up to 1.0 fb−1 of data collected in 2011. In the B0s system LHCb has obtained the world’s most pre- cise measurement of the mixing phase φs and the first direct observation for a non-zero value for ∆Γs. Impor- tant milestones have been reached in the measurement of the weak phase γ both from decays at tree level and from those where new physics could contribute through loops. The large charm production cross-section at the LHC has allowed for a dramatic improvement in sensi- tivity to CP violating effects. 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