PoS(CKM2016)100. Measurement of γ from time-dependent analysis of. Agnieszka Dziurda. CERN

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1 Measurement o γ rom time-dependent analysis o B s D s K ± CERN agnieszka.dziurda@cern.ch We report the measurement o the time-dependent CP violating observables in B s D s K ± decays. The study is perormed using a dataset corresponding to 3. b o pp collisions recorded in the LHCb detector in Run I o the LHC. We measure C =.735 ±. ±.8, S =.58 ±. ±.73, S =.96 ±.97 ±.7, A Γ =.395 ±.77 ±., A Γ =.3 ±.7 ±.7, where the uncertainties are statistical and systematic, respectively. Using these observables, the CKM angle γ is determined to be (7 +7 ) modulo 8 at 68% CL, where the uncertainty contains both statistical and systematic components. PoS(CKM6) 9th International Workshop on the CKM Unitarity Triangle 8 November - 3 December 6 Tata Institute or Fundamental Research (TIFR), Mumbai, India Speaker. on behal o the LHCb collaboration c Copyright owned by the author(s) under the terms o the Creative Commons Attribution-NonCommercial-NoDerivatives. International License (CC BY-NC-ND.).

2 . Introduction In the Standard Model (SM) charge-parity (CP) violation in weak interactions is described by a single, irreducible phase in the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix [, ]. Time-dependent analyses o B s D s K ± decays are sensitive to the least-well measured angle o the CKM matrix, the angle γ equal to arg( V ud Vub /V cdvcb ). CP violation in such decays occurs due to the intererence o mixing and decay amplitudes [3]. A comparison between the value o the CKM angle γ measured rom tree-level decays with the CKM parameters measured in loop-level processes provides a powerul consistency check o the SM. The time-dependent decay rates o the B s (t = ) and B s (t = ) lavour eigenstates to a inal state are: dγ B s (t) dt dγ B s (t) dt e Γst [cosh( Γ st ) + A Γ sinh( Γ st ) +C cos( m s t) S sin( m s t)], e Γst [cosh( Γ st ) + A Γ sinh( Γ st ) C cos( m s t) + S sin( m s t)]. The CP violating observables in B s D s K ± decays are dependent on the ollowing physical parameters: the magnitude o the amplitude ratio r Ds K A(B s D s K + )/A(B s D s K + ), the strong phase dierence δ and the weak phase dierence γ β s. Here, the weak phase dierence is a combination o the CKM angle γ and the mixing phase β s arg( V ts Vtb /V csvcb ) in the B s system. Thereore, the measurement o physical observables can be interpreted in terms o γ or β s by using an independent measurement o the other parameter as input. For the one inal state ( D s K + ), the our decay rates give ive independently measureable CP-violating parameters: C = r DsK, A Γ = r DsK cos(δ (γ β s )) S = r DsK sin(δ (γ β s )) +r DsK, A Γ, S = r DsK sin(δ+(γ β s )). = r DsK cos(δ+(γ β s )), These observables can be used to measure the CKM angle γ, with negligible [] theoretical uncertainty. PoS(CKM6). Event selection The measurement is based on a proton-proton collision data sample corresponding to an integrated luminosity o 3 b collected by the LHCb detector during Run I period. The ull detector description can be ound in [5]. The B s D s K ± decay is reconstructed using three dierent D s inal states: D s K K + π, D s K π + π, and D s π π + π. In addition, D s K K + π is split depending on the position in the Dalitz plane, into: D s φπ, D s K K and the remaining decays. These D s candidates are subsequently combined with a ourth particle, reerred to as the companion, to orm B s D s h ± candidates. The lavour-speciic Cabibbo-avoured decay mode B s D s π + is used as a control channel. It is used in the selection optimisation as well as in studies o the decay-time acceptance and resolution and to constrain the yields o certain physics backgrounds to the B s D s K ± decay. Inclusion o charge conjugate modes is implied except where explicitly stated.

3 The dierent D s inal states are distinguished by using the particle identiication inormation rom LHCb s Ring Imaging Cherenkov (RICH) detector. This selection is necessarily dierent or each D s decay mode and strongly suppresses cross-eed and peaking backgrounds rom other misidentiied decays o b-hadrons to c-hadrons. In addition, the B s and D s candidates are required to be within m(b s ) [5,58] MeV/c and m(d s ) [93,5] MeV/c, respectively. 3. Multivariate it to B s D s K ± and B s D s π + The signal and background component yields in the samples o B s D s K ± and B s D s π + candidates are obtained rom a three-dimensional simultaneous extended maximum likelihood it in the B s mass, the D s mass, and the log-likelihood dierence L(K/π) between the pion and kaon hypotheses or the companion particle. The total PDF or the multivariate it is built rom the product o the PDFs in each o the three it dimensions, since correlations between the itting variables are measured to be small in simulation. The dominant backgrounds are related to random combinations o D s mesons with pions or kaons, partially reconstructed decays o the type B s D s (π,k) + X, and decays o B and Λ b hadrons in which the D or Λ c candidates are misidentiied as D s candidates. Almost all background yields are let ree to loat, however the backgrounds whose yields are below % o the signal yield are ixed rom known branching ractions and relative eiciencies measured using simulated events. The multivariate it results in a signal yield o 969 ± 35 B s D s π + and 5955 ± 9 B s D s K ± decays, shown in Fig.. The multivariate it is checked or biases using large samples o data-like pseudoexperiments, and none are ound. Candidates / ( 5. MeV/c ) 8 6 LHCb Preliminary BeautyMass m(d - s π + ) [MeV/c ] Candidates / (.85 MeV/c ) LHCb Preliminary CharmMass m(k + K π ±, π + π π ±, K ± π π + ) [MeV/c ] Candidates / (. ) LHCb Preliminary BacPIDK -5 5 Companion ln( L(π/K) ) PoS(CKM6) Candidates / ( 5. MeV/c ) LHCb Preliminary BeautyMass m(d K ± ) [MeV/c s ] ± Candidates / (.85 MeV/c ) 7 LHCb Preliminary CharmMass m(k + K π ±, π + π π ±, K ± π π + ) [MeV/c ] Candidates / (.3 ) 35 LHCb Preliminary BacPIDK 3 5 Companion ln( L(K/π) ) Figure : The multivariate it to the (top) B s D s π + and (bottom) B s D s K ± candidates or all D s decay modes combined. From let to right : distributions o candidates in B s invariant mass, D s invariant mass, absolute value o companion PIDK. The blue solid line represents the sum o the it components. The dashed red line represents the signal, while the other shaded areas represent dierent background components.

4 . Inputs to the time-dependent it The B s D s K ± decay rates depend on the initially produced lavour eigenstates B s (t = ) and B s (t = ). The identiication o the initial lavour is perormed using two lavour-tagging algorithms, reerred to as the opposite-side (OS) and same-side (SS) taggers [6, 7]. The tagging algorithms use a neural network trained on simulated events (SS tagger) or data (OS tagger) to compute the probability η to assign an incorrect lavour ("mistag") to the B s candidate. The estimated η is treated as a per-candidate variable in the it. Due to variations in the properties o tagging tracks or dierent channels, the predicted mistag probability η has to be calibrated using lavour speciic, sel-tagging, decays to represent the true mistag rate ω. Both the OS and SS taggers are calibrated using a time-dependent it to the B s D s π + control channel in which m s is ixed to its world-average value [9]. The statistical uncertainty on C, S, and S scales with / ε e, deined as ε e = ε tag ( ω) where ε tag is the eiciency to tag an event. Thereore, the tagging algorithms are tuned or maximum eective tagging power. The obtained tagging power is.98 ±.6 % with a tagging eiciency at the level o ±.3 %. The ast B s B s oscillations require the inite decay-time resolution o the detector to be taken into account. The per-candidate decay-time uncertainty σ t is calibrated using prompt D s mesons combined with a random track to give a sample o "ake B s " candidates with a known lietime o zero. The eective decay-time resolution depends on the per-candidate decay-time uncertainty as σ(σ t ) =.3 s +.8σ t resulting in an average resolution at the level o 56 s. The decay-time o the B s mesons is distorted by several requirements which are applied in the signal selection. Non-negligible correlations between the CP observables and the acceptance o the selection do not allow the latter to loat in the nominal it. The acceptance is ixed based on inormation rom the B s D s π + it and corrected by the acceptance ratio o B s D s K ± and B s D s π + ound in simulation, where the simulation samples are weighted to match the kinematic distributions observed in data. 5. Decay-time it PoS(CKM6) The determination o the CP parameters is perormed using an unbinned maximum likelihood it with statistically subtracted background using the splot technique [8]. Thereore, only the signal decay-time distribution is described. The ollowing parameters are ixed in the decay-time it: Γ s = (.663 ±.) ps, Γ s = (.83 ±.6) ps, A det (Kπ) = ( ± )%, m s = (7.757 ±.) ps, ρ(γ s, Γ s ) =.39, A prod (B s ) = (. ±.7)%, based on HFAG [9] world average o B s oscillation requency and decay widths, and LHCb measurements o the B s production asymmetry [] and the K + π detection asymmetry []. The quoted uncertainties o ixed parameters are used later in the systematic studies. The tagging calibration parameters are constrained to the values obtained rom the control channel. The decay-time PDF is convolved with a single Gaussian representing the per-candidate decay-time resolution, and multiplied by the decay-time acceptance. The CP violating observables are given in Table, and the decay-time it to the B s D s K ± candidates is shown in Fig.. In the measurement the ollowing sources o systematic uncertainties are ound: uncertainties rom the ixed parameters m s, Γ s, and Γ s, uncertainties rom the limited knowledge o the 3

5 Candidates / (. ps) LHCb Preliminary BeautyTime 6 8 t(b D K ± s s ) [ps] ± Figure : Result o the decay-time it to the B s D s K ± candidates. Table : Fitted values o the CP observables to the B s D s K ± decay-time distribution where the irst uncertainty is statistical, the second is systematic. Parameter Value C.735 ±. ±.8 A Γ.395 ±.77 ±..3 ±.7 ±.7 A Γ S.58 ±. ±.73 S.96 ±.97 ±.7 detection asymmetry, the decay time resolution and acceptances and due to ignoring the correlations among observables. In addition, the sensitivity o the closure test perormed to the ully simulated signal events is assigned as a systematic uncertainty. Since the acceptance parameters are determined rom the it to B s D s π + candidates, where Γ s and Γ s are ixed, the systematic uncertainty on the acceptance is strongly anti-correlated with Γ s and Γ s. The correlations between them are taken into account and quoted together. The summary o systematic uncertainties described as a raction o statistical uncertainties are shown in Table. PoS(CKM6) Table : Total systematic uncertainties, relative to the statistical uncertainty. Parameter C A Γ A Γ S S Detection asymmetry m s Tagging and resolution Correlation among observables Closure test Acceptance, Γ s, Γ s Total Interpretation The measurement o the CP-sensitive parameters is interpreted in terms o γ β s and subsequently γ. The value o β s is constrained to the LHCb measurement, φ s = (. ±.39) rad

6 []. This assumes that penguin pollution and BSM contributions are negligible, which is a good approximation at the present statistical sensitivity. The resulting conidence intervals are: γ = (7 +7 ), δ = ( ), r DsK = , (68.3%CL) γ = ( ), δ = ( ), r DsK = , (95.% CL) where the intervals or the angles are expressed modulo 8. The quoted uncertainties are the sum in quadrature o the statistical and systematic components. The results are shown in Fig. 3. -CL LHCb Preliminary 68.3% 95.5% γ [ ] r DsK contours hold 68%, 95% CL LHCb Preliminary γ [ ] [ ] δ DsK 5 35 contours hold 68%, 95% CL LHCb Preliminary γ [ ] Figure 3: Graph showing -CL or γ, together with the central value and the 68.3% CL interval as obtained rom the requentist method [3]. Proile likelihood contours o r DsK vs. γ (middle), and δ vs. γ (right). The contours are the σ (σ) proile likelihood contours, where χ = ( χ = ), corresponding to 39% CL (86% CL) in Gaussian approximation. The markers denote the best-it values. Reerences [] N. Cabibbo, Phys. Rev. Lett. (963) 53. [] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 9 (973) 65. [3] R. Fleischer, Nucl. Phys. B67 (3) 59. [] J. Brod, J. Zupan, JHEP () 5. [5] LHCb collaboration, A. A. Alves Jr. et al., JINST 3 (8) S85. [6] LHCb collaboration, R. Aaij et al., Eur. Phys. J. C7 (), arxiv:.979. [7] LHCb collaboration, R. Aaij et al., JINST (6) P5, arxiv:6.75 [8] M. Pivk and F. R. Le Diberder, Nucl. Instrum. Meth. A555 (5) 356. [9] Heavy Flavor Averaging Group, [] LHCb collaboration, R. Aaij et al., Phys. Lett. B739 () 8, arxiv:8.75. [] LHCb collaboration, R. Aaij et al., JHEP 7 (), arxiv: [] LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. (5) 8, arxiv:.3. [3] LHCb collaboration, R. Aaij et al., JHEP (6) 87, arxiv: PoS(CKM6) 5