TTime-integrated CP -violation in beauty at LHCb Emilie Bertholet on behalf of the LHCb collaboration
LPNHE, Sorbonne Universit´e, Paris Diderot Sorbonne Paris Cit´e, CNRS/IN2P3,Paris, France
Precision measurements of time-integrated CP violation in beauty decays permit a betterunderstanding of the different mechanisms underlying CP violation. They allow to betterconstrain the Standard Model and probe for new physics. A selection of recent LHCb resultsthat highlight different aspects of CP violation in b -hadron decays are presented here. γ The CKM phase γ can be measured either in tree dominated decays or in processes that con-tain a significant contribution from loop diagrams. The latter are potentially sensitive to NewPhysics (NP) while no significant NP effects are expected in the former. Thus, the tree-levelmeasurements constitute a benchmark for the Standard Model (SM). The comparison of theresults obtained via these two approaches give valuable input to constrain the SM and set limitson NP.This analysis combines several tree-level LHCb measurements of γ in B → Dh decaymodes, where h represents a hadron. The different methods to extract γ exploit the interferencebetween b → c (favoured) and b → u (suppressed) transitions. The ratio of the correspondingamplitudes is related to γ by A b → u A b → c = r DhB e δ DhB ± γ , (1)where r DhB is the ratio of magnitudes, δ DhB the strong phase difference between A b → u and A b → c ,and the +(-) sign is associated with the decay of a meson containing a b ( b ) quark. Differentmethods are employed depending on the decay channel of the D -meson. The theoretical un-certainties on such tree-level determination are very small, thus the uncertainties on γ dependmainly on the experimental precision. As the B → Dh decay modes have low branching ratios,the best precision on γ is obtained by combining results from many decay modes. A list of allthe modes used by LHCb in this combination along with the status of the analyses since thelast combination is given in Table 1.The result is obtained using a frequentist approach, following the strategy of the previouscombination , with auxiliary inputs coming form HFLAV, CLEO and LHCb. The likelihood a r X i v : . [ h e p - e x ] M a y able 1: List of the LHCb measurements used in the combination. B decay D decay Method Dataset † Status since lastcombination B + → DK + D → h + h − GLW Run 1 & 2 Minor update B + → DK + D → h + h − ADS Run 1 As before B + → DK + D → h + π − π + π − GLW/ADS Run 1 As before B + → DK + D → h + h − π GLW/ADS Run 1 As before B + → DK + D → K S h + h − GGSZ Run 1 As before B + → DK + D → K S h + h − GGSZ Run 2 New B + → DK + D → K S K + π − GLS Run 1 As before B + → D ∗ K + D → h + h − GLW Run 1 & 2 Minor update B + → DK ∗ + D → h + h − GLW/ADS Run 1 & 2 Updated results B + → DK ∗ + D → h + π − π + π − GLW/ADS Run 1 & 2 New B + → DK + π + π − D → h + h − GLW/ADS Run 1 As before B → DK ∗ D → K + π − ADS Run 1 As before B → DK + π − D → h + h − GLW-Dalitz Run 1 As before B → DK ∗ D → K S π + π − GGSZ Run 1 As before B s → D ∓ s K ± D + s → h + h − π + TD Run 1 Updated results B → D ∓ π ± D + → K + π − π + TD Run 1 New † Run 1 corresponds to an integrated luminosity of 3 fb − taken at centre-of-mass energies of 7 and 8 TeV.Run 2 refers to the data collected in 2015 and 2016, which corresponds to an integrated luminosity of 2 fb − taken at a centre-of-mass energy of 13 TeV. function is built from the product of probability density functions of 98 experimental observables,and 40 parameters are left free in the fit. The hadronic parameters r DhB and δ DhB , defined inEq. (1), are also extracted along with γ . Table 2 also gives a summary of the central values andconfidence levels for the parameters of interest.The combination results in γ = (74 . +5 . − . ) ◦ , including both statistical and systematic uncer-tainties. This result supersedes the previous LHCb combination and consists in the most precisedetermination of γ from a single experiment to date. Table 2: Confidence intervals and central values for the parameters of interest.
Quantity Value 68.3% CL 95.5% CL γ [ ◦ ] 74 . . , .
0] [61 . , . r DKB . . , . . , . δ DKB [ ◦ ] 131 . . , .
3] [118 . , . r D ∗ K + B .
191 [0 . , . . , . δ D ∗ K + B [ ◦ ] 331 . . , .
8] [309 , r DK ∗ + B .
092 [0 . , . . , . δ DK ∗ + B [ ◦ ] 40 [20 , , r DK ∗ B .
221 [0 . , . . , . δ DK ∗ B [ ◦ ] 187 [167 , , r DKππB .
081 [0 . , . . , . δ DKππB [ ◦ ] 351 . . , .
8] [180 , r D ∓ s K ± B .
301 [0 . , . . , . δ D ∓ s K ± B [ ◦ ] 355 [339 , , δ D ∓ π ± B [ ◦ ] 17 [0 ,
46] [0 , Amplitude analysis of B ± → π ± K + K − Previous LHCb analysis of B → hh (cid:48) h (cid:48)(cid:48) decay modes reported localised CP asymmetries in someregions of the Dalitz plane (DP). In particular, significant positive (negative) CP asymmetry wasseen in the K + K − ( π + π − ) invariant mass region below 1.5 GeV/ c . These asymmetries, notclearly related to any resonant component, could be due to long-distance ππ ↔ KK hadronicrescattering. Better understanding of these effects require Dalitz plot analyses.A DP amplitude analysis of B ± → π ± K + K − decays is performed for the first time , using3 fb − of data collected by the LHCb experiment at centre-of-mass energies of 7 TeV and 8 TeV.This analysis uses the isobar model, which gives a description of the decay amplitude as afunction of the DP coordinates ( m π ± K ∓ , m K ± K ∓ ) within a quasi two-body approach: A ( m π ± K ∓ , m K ± K ∓ ) = nRes (cid:88) j =1 c j F j ( m π ± K ∓ , m K ± K ∓ ) , (2)where the index j runs over the nRes components included in the model, F j are functions thatdescribe the momentum-dependent part of the strong dynamics and the coefficients c j are theso-called isobar parameters. These are complex numbers that describe the weak interaction andthe momentum-independent part of the strong interaction. The information on CP violation isencoded into these coefficients so that the CP asymmetry for each contribution can be obtainedby A CP,i = | ¯ c i | − | c i | | ¯ c i | + | c i | , (3)where the index i designates one of the isobar components. Other relevant observables are thefit fractions, which are the ratio of the integral of one partial amplitude squared, | A i | , over theintegral of the total amplitude squared. They relate to the relative rate of an isobar component.The flavour-averaged fit fractions are given by F F i = (cid:82)(cid:82) (cid:0) | c i F i ( m π ± K ∓ , m K ± K ∓ ) | + | ¯ c i ¯ F i ( m π ± K ∓ , m K ± K ∓ ) | (cid:1) d m π ± K ∓ d m K ± K ∓ (cid:82)(cid:82) (cid:0) | A | + | ¯ A | (cid:1) d m π ± K ∓ d m K ± K ∓ . (4)After a careful selection of the candidates, a fit to the invariant ( πKK ) mass is performedto obtain the B ± signal yields. The amplitude model is then built in two steps. At first, allthe known resonances that may contribute to the final state are included. The model is thenfurther refined by adding or removing components following a systematic procedure in order tofind the configuration that best describes the data. Seven contributions to the total amplitudeare retained in the final result. Among them, a rescattering component is found to give agood description of the data in the invariant mass window 1 . < m KK < . , which is a phenomenologicaldescription of the partonic interaction that produces the final state. Five resonances are alsoincluded: K ∗ (892) , K ∗ (1430), ρ (1450), f (1270) and φ (1020).The dominant contribution is found to originate from the non-resonant component, with afit fraction of 32.3%. A significant contribution, 16.4%, from the rescattering component is alsoobserved, along with a very small, non significant, contribution from the φ (1020), 0.3%. Therescattering amplitude comes with a very large negative CP asymmetry, − . CP asymmetries observed previously can be explained through ππ ↔ KK rescattering. Study of B → ρ (770) K ∗ (892) The study B → ρ (770) K ∗ (892) , through a full amplitude analysis of the 4-body ( π + π − )( K + π − )final state, is performed for the first time. The analysis uses 3 fb − of data collected by theLHCb experiment at centre-of-mass energies of 7 TeV and 8 TeV. Three leading-order diagramscontribute to the final state: the tree-level contribution is doubly Cabbibo suppressed so thatthe dominant contributions comes from gluonic and electoweak (EW) penguins, which havesimilar sizes. Additionally, the sign of the EW-penguin contribution depends on the helicityeigenstate, which can have an impact on the value of the polarisation fraction. Furthermore, anenhanced direct CP -violating effect is expected due to the interference with B → ωK ∗ (892) decay mode . Finally, the study of B → V V modes can help to understand the so-called polar-isation puzzle: using na¨ıve arguments from the quark helicity conservation and the V-A natureof the weak interaction one expects very large polarisation fractions for B decays into lightvector mesons. This turns out to hold for tree dominated decays but not for penguin dominateddecays. Recent calculations in perturbative QCD and QCD factorisation can accommodatefor low longitudinal polarisation fractions in penguin-dominated decays by taking into accounta strong-interaction effect.The best candidates are retained by applying trigger requirements and a selection basedon topological variables. Cross-feed and combinatorial backgrounds are further reduced byusing particle identification and multivariate analysis. The ( π + π − ) and ( K + π − ) candidatesare selected within invariant mass windows around the masses of the ρ and the K ∗ resonances:300 MeV /c < m ππ < /c and 750 MeV /c < m ππ < /c . A fit to the4-body invariant mass spectrum is then performed (see Fig.1), and the sPlot technique is usedto obtain background-subtracted samples. These background-subtracted samples are then usedto perform a full amplitude analysis. ] c [MeV/ ) - p + K - p + p ( m -
10 110 ) c Y i e l d / ( M e V / sample B ) - p + K )( - p + p ( fi B ) - p + K )( - p + p ( fi s B Combinatorial bkg
LHCb ] c [MeV/ ) + p - K + p - p ( m -
10 110 ) c Y i e l d / ( M e V / sample B ) + p - K )( + p - p ( fi B ) + p - K )( + p - p ( fi s B Combinatorial bkg
LHCb (a) (b)
Figure 1 – Fit to the invariant-mass distributions of the selected (a) B and (b) B candidates. The final state can be described by using combinations of S-waves (spin 0) and P-waves(spin 1). The contributions to the total amplitude included in the fit are listed in Table 3;they correspond to resonances that are expected in the ( ππ ) and ( Kπ ) channels consideringthe invariant mass regions selected. The amplitude is then built by combining the differentcontributions together; the final state can thus be vector-vector (VV), vector-scalar (VS), scalar-vector (SV) or scalar-scalar (SS). In the case of the VV final state, three amplitudes with differentpolarisations contribute to the decay rate: longitudinal A L , parallel A || or transverse A ⊥ . Atotal of fourteen amplitudes is accounted for and modelled using the isobar model. An angularanalysis is needed to study the 4-body final state so that the decay-rate is five-dimensional (two able 3: List of the different contributions to the total amplitude. ( ππ ) ( Kπ )Scalar f (500), f (980), f (1300) K ∗ (1430) +NRVector ω , ρ (770) K ∗ (892) invariant masses and three helicity angles)d Γd cos θ ππ d cos θ K π d φ dm ππ dm K π ∝ Φ ( m ππ , m Kπ ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:88) i A i R i ( m ππ , m Kπ ) g i ( θ ππ , θ Kiπ , φ ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (5)where Φ ( m ππ , m Kπ ) is the four-body phase-space density, R i and g i correspond to the massand the angular distributions, respectively, and A i are the decay amplitudes for each component i . Polarisation fractions are computed for the the VV final state f λ = | A λV V | | A LV V | + | A || V V | + | A ⊥ V V | , (6)where λ represent one of the polarisation configurations. The CP -averaged fraction, ˜ f λ = ( f λ +¯ f λ ) /
2, and CP asymmetries, A λCP = ( ¯ f λ − f λ ) / ( f λ + ¯ f λ ), can be obtained from the polarisationfractions of a mode and its conjugate. CP -averages and asymmetries are measured for eachamplitude included in this analysis. Detailed results can be found in Ref. .A small longitudinal polarisation fraction and a rather large CP asymmetry are measuredfor the B → ρ (770) K ∗ (892) mode˜ f LρK ∗ = 0 . ± . ± . , A LρK ∗ = − . ± . ± . . (7)These results hint for a relevant contribution from the EW-penguin diagram. The significanceof the CP asymmetry is about five standard deviations, which consists in the first significantobservation of CP asymmetry in angular distributions of B → V V decays. Comparison of theseresults to the most recent theoretical predictions pQCD and QCDf show a good agreement.The longitudinal polarisation fraction and the CP asymmetry for B → ωK ∗ (892) result in˜ f LωK ∗ = 0 . ± . ± . , A LωK ∗ = − . ± . ± . . (8)Triple Product Asymmetries (TPA) are also measured and are found to be below 5%, whichis in agreement with theoretical predictions . CP asymmetries in charmless four-body Λ b and Ξ b decays Despite theoretical predictions of about 20% CP violation for some charmless Λ b decays , CP violation was not observed in the baryon sector so far. The abundant production of b -hadronsat the LHC and the characteristics of the LHCb detector make this experiment particularlysuitable to study the decays of these particles.Six decay modes of Λ b , Ξ b → phh (cid:48) h (cid:48)(cid:48) are studied in this analysis, with 3fb − of data collectedby the LHCb experiment at centre-of-mass energies of 7 TeV and 8 TeV . These decays proceedthrough b → u and b → s, d transitions. Experimental effects, such as detection and productionasymmetries are cancelled out by computing the difference, ∆ A CP , between the raw values of the CP asymmetries of the considered modes and the CP asymmetries obtained in control modes,where no measurable CP violation is expected. Further corrections are then applied to accountor kinematical differences between signal and control modes and charge-dependent selectionefficiencies.The results obtained for A CP integrated over the whole phase space are: ∆ A CP (Λ b → pπ − π + π − ) = (+1 . ± . ± . , ∆ A CP (Λ b → pK − π + π − ) = (+3 . ± . ± . , ∆ A CP (Λ b → pK − K + π − ) = ( − . ± . ± . , ∆ A CP (Λ b → pK − K + K − ) = (+0 . ± . ± . , ∆ A CP (Ξ b → pK − π + π − ) = ( − ± ± , ∆ A CP (Ξ b → pK − π + K − ) = ( − . ± . ± . . In addition to the these inclusive results, measurements are also performed in specific regionsof the phase space, for example at low two-body invariant mass or in quasi two- or three-bodydecay regions. A total of eighteen CP asymmetries are measured and no significant CP violationis observed in any of the measurements.A previous LHCb analysis , performed with the same dataset, reported an evidence for CP violation in a specific region of the phase space of Λ b → pπ − π + π − decay, using TPA whilethe present result shows no CP violation for this mode. A comparison of the two results andmethods can shed a light on the nature of this effect. The LHCb collaboration has a very broad program of analyses searches for CP asymmetriesand the four analyses presented here only represent a small part of this program. During thepresentation, measurements of the CP asymmetry and branching fractions of B + → J/ψρ + obtained with run 1 data were also presented : B ( B + → J/ψρ + ) = (cid:0) . +0 . − . ± . (cid:1) × − and A CP ( B + → J/ψρ + ) = − . +0 . − . ± . − taken at a centre-of-mass energy of 13 TeV, areongoing. The additional data sample will increase the sensitivity to the CP observables and giveaccess to more decay channels. References
1. LHCb collaboration, Aaij, R. and others, LHCb-CONF-2018-002.2. LHCb collaboration, Aaij, R. and others, JHEP 05 (2019) 0263. LHCb collaboration, Aaij, R. and others, LHCb-PAPER-2018-051 (in preparation)4. LHCb collaboration, Aaij, R. and others, arXiv:1903.06792 [hep-ex]5. LHCb collaboration, Aaij, R. and others, arXiv:1812.07041 [hep-ex]6. LHCb collaboration, Aaij, R. and others, LHCb-CONF-2017-004.7. Gronau, M. and Zupan, J.,
Phys. Rev. D , 074017 (2005).8. Zou, Zhi-Tian and Ali, Ahmed and Lu, Cai-Dian and Liu, Phys. Rev. D , 054033(2015).9. Beneke, Martin and Rohrer, Johannes and Yang, Deshan, Nucl. Phys. B774 , 64-101(2007).10. Pivk, Muriel and Le Diberder, Francois R., Nucl. Instrum. Meth.
A555 , 356-369 (2005).11. Datta, Alakabha and London, David, Int. J. Mod. Phys.
A19 , 2505-2544 (2004).12. Alvarenga Nogueira, J. H. and Bediaga, I. and Cavalcante, A. B. R. and Frederico, T. andLoureno, O.,
Phys. Rev. D , 054010 (2015).13. Pelaez, J. R. and Yndurain, F. J., Phys. Rev. D , 074016 (2005).14. LHCb collaboration, Aaij, R. and others, Phys. Rev. D , 112004 (2014).15. Hsiao, Y. K. and Geng, C. Q., Phys. Rev. D , 116007 (2015).16. LHCb collaboration, Aaij, Roel et al. , Nature Physics13