The CKM phase γ is the angle of the unitarity triangle which

is least well known. To reach the highest sensitivity to its value, all currently available measurements using hadronic tree decays by LHCb are combined, resulting in γ = (73+9−10)◦. The combination includes results from measurements of timeintegrated CP violation in B± → Dh±

and B0 → DK∗0 decays, with h a pion or kaon, and from a time-dependent measurement of CP violation using B0s → D±

s K∓ decays

Koopman, R.F.

English

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2015-15139-5Colloquia: LaThuile15IL NUOVO CIMENTO 38 C (2015) 139Measurement of the CP-violating phase γ at LHCbR. F. Koopman on behalf of the LHCb CollaborationFOM-Nikhef - Amsterdam, The Netherlandsreceived 2 October 2015Summary. — The CKM phase γ is the angle of the unitarity triangle whichis least well known. To reach the highest sensitivity to its value, all currentlyavailable measurements using hadronic tree decays by LHCb are combined, resultingin γ = (73+9−10)◦. The combination includes results from measurements of time-integrated CP violation in B± → Dh± and B0 → DK∗0 decays, with h a pion orkaon, and from a time-dependent measurement of CP violation using B0s → D±s K∓decays.PACS 12.15.Hh – Determination of Cabibbo-Kobayashi & Maskawa (CKM) matrixelements.PACS 13.25.Hw – Decays of bottom mesons.1. – IntroductionIn the Standard Model (SM), CP violation is introduced via the Yukawa couplingswhich describe the interactions of the quarks to the Higgs field. Only the weak in-teractions violate CP. The flavour changing weak interactions are characterised by theCabibbo-Kobayashi-Maskawa (CKM) matrix [1],VCKM =⎛⎜⎝Vud Vus VubVcd Vcs VcbVtd Vts Vtb⎞⎟⎠ ≈⎛⎜⎝1− 12λ2 λ Aλ3(ρ− iη)−λ 1− 12λ2 Aλ2Aλ3(1− ρ− iη) −Aλ2 1⎞⎟⎠,(1)which is given here in the Wolfenstein parametrisation [2] to O(λ4). The CKM matrixis a unitary matrix that carries four free parameters, three of which are real parametersand one is a complex phase. It is the imaginary term, iη, that allows for CP violationin the SM. The relations between the different elements of the CKM matrix can berepresented as triangles in the complex plane. The unitarity triangle presented in fig. 1shows our current knowledge on the CKM matrix. Testing the unitarity of the theory byover-constraining the sides and angles of this triangle provides a direct test of the SM.c© CERN on behalf of the LHCb CollaborationCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 R. F. KOOPMAN on behalf of the LHCb COLLABORATIONγααdmΔKεKεsmΔ & dmΔubVβsin 2(excl. at CL > 0.95) < 0βsol. w/ cos 2αβγρ-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0η0.00.10.20.30.40.50.60.7excluded area has CL > 0.95Summer 14CKMf i t t e rFig. 1. – Global CKM fit to the unitarity triangle, illustrating our current knowledge on theCKM mechanism [3].The angle γ is the angle of the unitarity triangle which is least well known. The mea-surements presented in these proceedings are all performed using hadronic tree decays,which are not sensitive to new physics, and therefore provide a test of the SM. More-over, they can be used as a benchmark against which measurements sensitive to newphysics [4] can be tested. The angle γ is associated to the CKM element Vub, makingdecays with a b → u transition sensitive to γ. In order to measure CP violation, oneneeds to study the interference between two competing decay amplitudes, typically oneyielding a b → u transition and one yielding a b → c transition. The sensitivity to γis largest for a large interference, which is achieved when both decay amplitudes are ofcomparable size.Different B meson decay channels have been studied resulting in a combined mea-surement of γ = (73+9−10)◦ [5]. The different measurements can be divided into twocategories: a time-dependent measurement which exploits the decay time structure ofB0s decay; and several time-integrated measurements where the event yield of a processand the CP conjugate process are compared.2. – Selection of events containing B decaysDue to their long lifetime and large boost, B mesons typically fly a few mm beforethey decay. The excellent vertex resolution of the LHCb detector allows to accuratelymeasure the separation between the primary vertex and the secondary vertex. TheB meson decays discussed in these proceedings are all of the type “charmed B mesondecays”, where the B meson first decays to a “bachelor” hadron and a charm mesonwith finite lifetime, that then further decays into the final state particles. The typeof the various final state particles is determined by the RICH pion/kaon identification.Multivariate analysis, like boosted decision trees, is a commonly used tool to separatethe signal from the combinatorial background. Mass fits are used to further separatesignal from background, exploiting the outstanding momentum resolution of the LHCbdetector.MEASUREMENT OF THE CP-VIOLATING PHASE γ AT LHCB 3B−D0K−[K+π−/K+K−]K−D0K−ADS/GLWb cVcbsuV ∗usW−uuB− D0K−c d,sV ∗cd,csusVusW+uuD0K+π−/K−rDeiδDb uVubscV ∗csW−uuB−K−D0rBei(δB−γ)c sVcsd,suV ∗ud,usW−uuD0π−/K−K+Fig. 2. – Feynman diagrams describing the B± → Dh± decay with the subsequent decay of the Dmeson to a GLW and ADS type final state. The thickness of the arrows indicate the size of thedecay amplitude. The parameter rB (rD) is the ratio of the suppressed decay amplitude over thefavoured amplitude of the B (D) decay, and δB (δD) the strong phase difference between them.3. – Direct CP violation in B± → Dh± decaysCharged B decays to a neutral D meson and a charged bachelor hadron (pion orkaon) provide a powerful tool for γ determination. The amplitude of B− → D0K− isproportional to Vcb, whereas the amplitude of B− → D0K− is proportional to Vub. Thelatter is colour suppressed, indicated with the thinner arrow in fig. 2, where rB is the ratioof the two B decay amplitudes and δB and γ are the strong and weak phase differencebetween them, respectively. Decays with a bachelor kaon are more sensitive to γ thandecays with a bachelor pion, due to the larger value of rB . We choose a D final statewhich is accessible to both D0 and D0, such that the two amplitudes can interfere. Wemeasure the number of B− → DK− decays and B+ → DK+ decays separately. Fromthese event yields two observables are constructed. A CP asymmetryADK,f =Γ(B− → [D[→ f ]K−)− Γ(B+ → [D[→ f¯ ]K+)Γ(B− → [D[→ f ]K−) + Γ(B+ → [D[→ f¯ ]K+) ,(2)and the charge-averaged ratio of B± → DK± to B± → Dπ± decays,RfK/π =Γ(B− → [D[→ f ]K−) + Γ(B+ → [D[→ f¯ ]K+)Γ(B− → [D[→ f ]π−) + Γ(B+ → [D[→ f¯ ]π+) .(3)These observables can be expressed in terms of the weak phase γ, the ratio of decayamplitudes and the strong phase difference [6].Various D final states satisfy the requirement of accessibility to both the D0 andthe D0meson, presenting interesting opportunities to measure γ at LHCb. The dif-ferent types of D meson decays are dubbed “GLW” [7, 8], “ADS” [9, 10], “GLS” [11]and “GGSZ” [12], after authors who proposed this type of D meson decays for γdetermination.4 R. F. KOOPMAN on behalf of the LHCb COLLABORATION )2cEvents / ( 5 MeV/20406080 )2cEvents / ( 5 MeV/ -KD]-K+K[→-BLHCb +KD]-K+K[→+BLHCb )2cEvents / ( 5 MeV/51015 )2cEvents / ( 5 MeV/ -KD]+K-π[→-BLHCb +KD]-K+π[→+BLHCb5200 5400 56000)2c) (MeV/±Dh(m5200 5400 5600GLW GLWADS ADSFig. 3. – Invariant mass distributions of B∓ → (K+K−)DK∓ and B∓ → (π∓K±)DK∓ decays.3.1. GLW and ADS method . – In the GLW method the D final state is a CP eigenstate.LHCb performed a measurement using the final states K+K− and π+π− [13]. For thesefinal states the D0 and the D0decay amplitudes are equal, as indicated with arrows ofthe same thickness in fig. 2.In the ADS method a final state is used which is not a CP eigenstate. LHCb performeda measurement using the D final states K±π∓ [13] and K±π∓π+π− [14]. For these finalstates one of the D decay amplitudes is doubly Cabibbo-suppressed. In addition to theobservables in eqs. (2), (3), the ratio of Cabibbo-suppressed to Cabibbo-favoured decays,RDK,f± =Γ(B± → D[→ fsup]K±)Γ(B± → D[→ ffav]K±) ,(4)can be extracted and is related to γ.A large asymmetry, and hence a large sensitivity to γ, is observed for B± →(K∓π±)K± decays, where the favoured B− → D0K− decay is followed by the dou-bly Cabibbo-suppressed D0 decay, while the suppressed B− → D0K− decay is followedby the favoured D0decay. However, the event yields are low compared to the GLWmethod, where the D0 decay is singly Cabibbo-suppressed (fig. 3).3.2. GLS method . – Singly Cabibbo-suppressed D decays to final states that are notCP eigenstates provide a valuable information on γ. A large charge asymmetry wasfound in D → K0SKπ decays [15], however, due to the Cabibbo-suppression, the eventyields are low, as shown in fig. 4. An additional observable is defined asRDπfav/sup =Γ(B− → D[→ ffav]π−) + Γ(B+ → D[→ ffav]π+)Γ(B− → D[→ fsup]π−) + Γ(B+ → D[→ fsup]π+) ,(5)and related to γ in ref. [11].This multibody D decay can proceed through the K∗ resonance, and only the phasespace around this resonance is used in the analysis to maximise the sensitivity to γ. TheMEASUREMENT OF THE CP-VIOLATING PHASE γ AT LHCB 5]2c   [MeV/)− KD]−π+K0S[K(m5200 5400 5600 5800)2 cEntries / (15 MeV/0102030 LHCbSum, incl. combinatoricsSignalMis-IDPartially reconstructed− KD]−π+K0S [K→−B (g)(aGLS]2c   [MeV/)+ KD]+π−K0S[K(m5200 5400 5600 5800)2 cEntries / (15 MeV/0102030 LHCbSum, incl. combinatoricsSignalMis-IDPartially reconstructed+ KD]+π−K0S [K→+B (e)b)GLSFig. 4. – Invariant mass distribution of B∓ → (K0SK±π∓)DK∓ decays.strong phase difference δD varies across the Dalitz plot of the D decay due to resonances.The introduction of a coherence factor κ and an average strong phase difference, as firstproposed in ref. [16], allows the decay to be treated inclusively, without considering theDalitz plot positions individually. To avoid a significant modelling uncertainty, the κ andaverage δD measured by CLEO [17] are used.3.3. GGSZ method . – The D final states K0Sπ+π− and K0SK+K− [18] are also acces-sible to both D0 and D0. The asymmetry in the overall yields is expected to be small,however, it can be large in certain areas of the Dalitz plot. This is due to variations inthe resonant behaviour across the Dalitz plot, which results in a variation of the strongphase. The D Dalitz plot (fig. 5) is divided into bins, and the event yields of B− andB+ decays measured in each bin are used to extractx± = rB cos(δB ± γ),(6)y± = rB sin(δB ± γ).This method requires a good understanding of the variation of strong phase in the Dalitzplot, which is measured by CLEO [19].(a) B−GGSZ(b) B+GGSZFig. 5. – D Dalitz plot for B∓ → (K0Sπ+π−)DK∓ decays.6 R. F. KOOPMAN on behalf of the LHCb COLLABORATION510152025303540452Candidates per 10 MeV/c LHCb0B 0*DK0Bs0*DKCombinatorial0B 0Dρ0Bs0* *D K0B 0* *D KLHCb0B 0*DK0Bs0*DKCombinatorial0B 0Dρ0Bs0* *D K0B 0* *D K5000 5200 5400 5600 580501001502002503002Candidates per 10 MeV/c LHCb*0B 0*DK0Bs0*DKCombinatorial0B 0Dρ0Bs0* *D K0B 0* *D K0 0 5200 5400 5600 5800LHCb*0B 0*DK0Bs0*DKCombinatorial0B 0Dρ0Bs0* *D K0B 0* *D Km(DK∗0) m(DK∗0)GLWD → K+K−GLWD → K+K−ADSD → K+π−ADSD → K−π+Fig. 6. – Invariant mass distribution for the DK∗0 and DK∗0final states, for the GLW modeK+K− and the ADS mode Kπ. The signal yield for the ADS mode is low as this decay isCabibbo-suppressed. In addition to the B0 peak, also the B0s peak is fitted.4. – Direct CP violation in B0 → DK∗0 decaysIn addition to charged B meson decays, neutral B mesons decays add to the sensitivityto γ. In particular, LHCb studied the decay B0 → DK∗0, with the neutral D mesondecaying to the GLW modes, K+K− and π+π−, and the ADS modes, K±π∓ [20]. Theobservables as defined in eqs. (2)–(4) are measured, from which the angle γ can beextracted.Interestingly, for neutral B meson decays a large asymmetry is measured for the GLWmodes (fig. 6). This can be understood considering the amplitudes of the interferingdecay paths. The decays B0 → D0K∗0 and B0 → D0K∗0 are both colour suppressedand therefore similar in size, resulting in a large value of rB . For the GLW modes,the value of rD is one. The total decay paths, B0 → DK∗0 following D → h+h−, aretherefore comparable in size, leading to a large interference for the GLW modes.5. – Time-dependent analysis of B0s → D±s K∓ decaysCP violation occurs in the decay B0s → D±s K∓ through the interference betweenmixing and decay [21]. The final states D+s K− and D−s K+ are accessible to both theB0s and the B0s meson. Moreover, the B0s meson can oscillate to a B0s meson and thendecay, or it can decay as B0s meson. The time-dependent decay equations for a initiallyproduced B0s and B0s decaying to the final state f are given byΓf (t)  e−Γst[cosh(ΔΓst2)+ Df sinh(ΔΓst2)+ Cf cos(Δmst)− Sf sin(Δmst)],(7)Γf (t)  e−Γst[cosh(ΔΓst2)+ Df sinh(ΔΓst2)− Cf cos(Δmst) + Sf sin(Δmst)],MEASUREMENT OF THE CP-VIOLATING PHASE γ AT LHCB 7K) (ps)s D→s (Bτ2 4 6 8 10 12 14Candidates / ( 0.1 ps)110210datatotal±K±s D→0sB+π−s D→0sB)+ρ,+π(−)*(s D→0sB X→)0bΛ,0d(BCombinatorialLHCb(a) (b)) [ps]±K±s D→0s (Bτ2 4 6 8 10 12 14-202) [ps]smΔ/π modulo (2τ0 0.1 0.2 0.3) +K − sA(D-0.6-0.4-0.200.20.40.6 LHCbFig. 7. – a) Decay time distribution of B0s → D±s K∓ decays. b) Folded asymmetry using theD−s K+ final state.with Γs the average decay width, ΔΓs the decay width difference and Δms the massdifference between the heavy and light eigenstates. The CP observables Df , Sf and Cfare related to γ. The CP-conjugate process is described by two additional decay equationswhich contain three more CP observables, Df¯ , Sf¯ and Cf¯ . Under the assumption of noCP violation in either decay or mixing, Cf = −Cf¯ .After the selection of signal candidates, a multidimensional mass fit is made to extractthe yields of the signal and the various sources of background. This fit uses the invariantmass of the B and the D meson and a quantity related to the pion-kaon separation asdiscriminating variables. The measured yields are used in a subsequent fit to the decaytime distribution, from which the CP observables are extracted. The folded asymmetryas a function of folded decay time, measured with the D−s K+ final state, are shown infig. 7.6. – CombinationThe different measurements are combined to give the best precision of γ [5]. The“Robust” combination includes only decays with a kaon bachelor particle. These decaysare more sensitive to γ due to the larger value of rKB compared to rπB . In the “Full” combi-nation, also decays with a pion bachelor particle are included which typically have largerbranching fractions but are potentially more affected by the systematic uncertainties.The combinations follow a frequentist approach. The combined likelihood of all exper-imental observables is maximised, assuming Gaussian distributions for most observables.In the combination the effects from D0 −D0 mixing are taken into account, as well aseffects from CP violation in D0 decay. The best sensitivity to γ is reached includingauxiliary input on the hadronic parameters rD, δD and κ for the different D decays, onCP violation in decay of D decay and on charm mixing. The relevant parameters aremeasured using data from CLEO [17, 19, 22, 23] and Belle [24] and by HFAG [25]. Theangle φs is constrained to its measured value [26].8 R. F. KOOPMAN on behalf of the LHCb COLLABORATION]° [γ1-CL00.20.40.60.811.250 60 70 80 90 100 110robustfull68.3%95.5%LHCbPreliminaryFig. 8. – 1–CL curves for the Robust and the Full combinations.The value of γ is found to be γ = (73+9−10)◦ and γ = (79+6−7)◦ for the “Robust” and“Full” combination, respectively, and the confidence interval is illustrated in fig. 8. Notethat in the “Full” combination, two maxima are found within the 68% confidence levelinterval: the sharp maximum quoted here and a secondary maximum which coincideswith the maxima found in the “Robust” combination. The sharp maximum correspondsto an unexpectedly large value of rDπB , which enhances the sensitivity to γ for decayswith a bachelor pion.7. – ConclusionWe reported a measurement of the CKM angle γ = (73+9−10)◦. This measurement isperformed using a combination of different measurements, using the hadronic tree decaysB± → Dh±, B0 → DK∗0 and B0s → D±s K∓ which are not sensitive to new physicscontributions. LHCb also reported a measurement of the CKM angle γ using B → h+h−decays, which are sensitive to new physics contributions, yielding γ = (63.5+7.2−6.7)◦ [4].The two measurements are in agreement within their uncertainty. The measurementsare currently statistically limited. The expected sensitivity, 4◦ and 1◦ for Run II and theupgrade, respectively, will help to further test the SM.REFERENCES[1] Kobayashi M. and Maskawa T., Prog. Theor. Phys., 49 (1973) 652.[2] Wolfenstein L., Phys. Rev. Lett., 51 (1983) 1945.[3] Charles J. et al., LPT-ORSAY-15-04 (2015).[4] Aaij R. et al., Phys. Lett. B, 741 (2015) 1.[5] Improved constraints on γ: CKM2014 update, LHCb-CONF-2014-004 (Sep 2014).[6] Aaij R. et al., Phys. Lett. B, 726 (2013) 151.[7] Gronau M. and Wyler D., Phys. Lett. B, 265 (1991) 172.[8] Gronau M. and London D., Phys. Lett. B, 253 (1991) 483.[9] Atwood D., Dunietz I. and Soni A., Phys. Rev. Lett., 78 (1997) 3257.[10] Atwood D., Dunietz I. and Soni A., Phys. Rev. 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Measurement of the CP-violating phase γ at LHCb

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Measurement of the CP violating phase $γ$ at LHCb

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Measurement of the CP-violating phase γ at LHCb

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