International audienceWe discuss the decay of B_c mesons into two light (pseudoscalar and vector) mesons. All these decay channels come from a single type of diagram, namely tree annihilation which allows us to derive simple relations among these processes. The size of annihilation contributions is an important issue in B physics, and we provide two different estimates in the case of non-leptonic charmless B_c decays, either a comparison with annihilation decays of heavy-light mesons or a perturbative model inspired by QCD factorisation. We finally discuss a possible search for these channels at LHCb

Descotes-Genon, S.

He, J.

Kou, E.

Robbe, P.

HAL-IN2P3

Nonleptonic charmless B c decays and their search atLHCbS. Descotes-Genon, E. Kou, P. Robbe, J. HeTo cite this version:S. Descotes-Genon, E. Kou, P. Robbe, J. He. Nonleptonic charmless B c decays and theirsearch at LHCb. the 2009 Europhysics Conference on High Energy Physics (EPS HEP 2009),Jul 2009, Krakow, Poland. Proceedings of Science, pp.210, 2009. <in2p3-00429733>HAL Id: in2p3-00429733http://hal.in2p3.fr/in2p3-00429733Submitted on 1 Feb 2010HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.PoS(EPS-HEP 2009)210Non-leptonic charmless Bc decays(and their search at LHCb)S. Descotes-Genon∗Laboratoire de Physique Théorique, CNRS/Univ. Paris-Sud 11 (UMR 8627),91405 Orsay, FranceE-mail: descotes@th.u-psud.frJ. He, E. Kou and P. RobbeLaboratoire de l’Accélérateur Linéaire, Université Paris-Sud 11, CNRS/IN2P3 (UMR 8607),91405 Orsay, FranceWe discuss the decay of Bc mesons into two light mesons (pi ,K(∗),η(′),ρ ,ω ,φ ). All these decaychannels come from a single type of diagram, namely tree annihilation. This allows us to deriveextremely simple SU(3) relations among these processes. The size of annihilation contributions isan important issue in B physics, and we provide two different estimates in the case of non-leptoniccharmless Bc decays, either a comparison with annihilation decays of heavy-light mesons or aperturbative model inspired by QCD factorisation. We finally discuss a possible search for thesechannels at LHCb.The 2009 Europhysics Conference on High Energy Physics,July 16 - 22 2009Krakow, Poland∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(EPS-HEP 2009)210Non-leptonic charmless Bc decays (and their search at LHCb) S. Descotes-GenonSince the first observation of the Bc meson in 1998 from the CDF collaboration, its mass andwidth have been measured, and bounds on some non-leptonic channels have been set (J/ψ with oneor three pions, D∗+ ¯D0. . . ). The Bc meson shares many features with the better studied quarkonia,with the significant difference that its decays are not mediated through strong interaction but weakinteraction due to its flavour quantum numbers B =−C =±1. The properties of the Bc meson willbe further scrutinized by the LHC experiments; the high luminosity of the LHC machine opens thepossibility to observe many Bc decay channels, in particular at LHCb. We report here on recentinvestigations on the charmless non-leptonic Bc decays [1].The diagram for the non-leptonic charmless Bc decays is shown in fig. 1. The initial b and cquarks annihilate into u and d or s quarks, which form two light mesons by hadronising with a pairof qq (q = u,d,s) emitted from a gluon. There are 32 decay channels of this kind if we consider onlythe lightest pseudoscalar and vector mesons. In the case of two outgoing pseudoscalar mesons (PP),there are 4 modes with strangeness one: K+pi0,K+η ,K+η ′,K0pi+ and 4 modes with strangenesszero: pi+pi0,pi+η ,pi+η ′,K+ ¯K0. The same applies for two vectors (VV) up to the obvious changes:K∗+ρ0,K∗+φ ,K∗+ω ,K∗0ρ+,ρ+ρ0,ρ+φ , ρ+ω ,K∗+ ¯K∗0. In the case of VP decays, one can get 8strange decay modes (∆S = 1 processes): K∗+pi0,K∗+η ,K∗+η ′,K∗0pi+,ρ0K+,φK+,ωK+,ρ+K0and 8 non-strange decay modes (∆S = 0 processes): ρ+pi0,ρ+η ,ρ+η ′,K∗+ ¯K0,ρ0pi+,φpi+,ωpi+,¯K∗0K+. These 32 non-leptonic charmless Bc decays are all pure annihilation and come from asingle-tree annihilation diagram. Understanding these channels can have an important impact onthe discussion of annihilation in other decays, in particular for heavy-light mesons, where similarcontributions come from several operators and interfere with other mechanisms.Compared to the case of Bu,d decays, the SU(3) relations for the Bc decays are extremelysimple and can be derived [1] from the Wigner-Eckart theorem following ref. [2]. Taking intoaccount Clebsch-Gordan coefficients and octet-singlet mixing, we get the V P amplitudes:Mode Amplitude Mode AmplitudeK+∗pi0 12√35SV P + 12√3AVP ωK+ − 12√15 SV P− 12√3AVP +√23 IVPρ0K+ 12√35SV P− 12√3AVP φK+ 1√30SV P + 1√6AVP + 1√3 IV PK∗+η − 13√25SV P +√23 AVP + 13 IVP ρ+K0√310 SV P− 1√6AVPK∗+η ′ 16√5SV P− 16AVP + 2√23 IV P K∗0pi+√310 SV P + 1√6AVPMode Amplitude Mode Amplitudeρ+pi0 1√3AVP ωpi+ 1√15 SVP +√23 IV Pρ0pi+ − 1√3AVP φpi+ −√215SV P + 1√3 IV Pρ+η 23√25SV P + 13 IV P K∗+ ¯K0√310 SV P− 1√6AVPρ+η ′ − 13√5SV P + 2√23 IV P¯K∗0K+√310 SV P + 1√6AVPThe amplitudes are still to be multiplied by GF/√2 and a CKM factor VuDV ∗cb (D = d or s). We getthe relationsA(B+c → K∗0pi+) =√2A(B+c → K∗+pi0) = ˆλA(B+c → ¯K∗0K+) (1)A(B+c → ρ+K0) =√2A(B+c → ρ0K+) = ˆλA(B+c → K∗+ ¯K0) (2)2PoS(EPS-HEP 2009)210Non-leptonic charmless Bc decays (and their search at LHCb) S. Descotes-GenonbcBcud,sqqWxxxxFigure 1: Generic diagram for the non-leptonic charmless Bc decaysDue to the Wigner-Eckhart theorem and the involvement of a single operator, we get all thePV amplitudes in terms of three different reduced matrix elements SV P, AV P and IV P. One cansimplify further the expressions by assuming the validity of the Zweig rule for the ∆S = 0 processesinvolving φ , e.g., setting Br(B+c → φpi+) = 0 to obtain a further relation between IVP and SV P.Similar relations can be derived in the case of PP modes and VV modes, involving different reducedmatrix elements for PP and for the different partial waves (or helicity amplitudes) for VV . TheSU(3) relationships allow one to relate different modes belonging to the same multiplets, but notto fix the overall scale of the reduced matrix elements, and thus that of the branching ratios. Wefollowed two different paths to estimate these matrix elements, by using experimental data on pureannihilation B decays and by relying on a one-gluon picture à la QCD factorisation.There are two pure annihilation processes observed in heavy-light B decays: B0 → K+K− andB0 →D−s K+. Since we are interested in charmless final states, we can try and compare Bc →K+K0and B0 →K+K− processes. After relying on further hypotheses described in ref. [1], we obtain thefollowing branching ratios of interest:[Bd annihil] BR(Bc → φK+)≃ O(10−7−10−8), BR(Bc → ¯K∗0K+)≃ O(10−6)BR(Bc → ¯K0K+)≃ O(10−6), BR(Bc → ¯K∗0K∗+)≃ O(10−6) (3)A second method consists in a model based on one-gluon exchanges, in close relation withthe model proposed in QCD factorisation to estimate annihilation contributions for the decays ofheavy-light mesons. As described in ref. [1], we found that: i) the charmless Bc decays are muchsimpler, since the only operator contributing is O2, and there is only one combination of CKMfactors (V ∗cbVuD where D = d,s depending on the strangeness of the outgoing state), and ii) the long-distance divergences, which prevent us from estimating the annihilation contribution accurately inBu,d decays, do not arise in Bc annihilation (they are tamed by the nonvanishing charm quark mass).The expressions for all the decay channels were recovered from refs. [4] if we identify between theWigner-Eckart reduced matrix elements S, I,A and the O2 reduced coefficients b2. However, theuncertainty coming from endpoint divergences in the case of Bu,d,s decays is absent here, so that theestimation of Bc annihilation in this framework suffers from smaller uncertainties than for heavy-light decays. We obtain finally the following values of branching ratios:[One-gluon] BR(Bc → φK+) = 5×10−9, BR(Bc → ¯K∗0K+) = 9.0×10−8 (4)BR(Bc → ¯K0K+) = 6.3×10−8,BR(Bc → ¯K∗0K∗+) = 9.1×10−8 (5)3PoS(EPS-HEP 2009)210Non-leptonic charmless Bc decays (and their search at LHCb) S. Descotes-GenonOur estimates of the branching ratios in the above two ways are not consistent. This stems fromthe conceptual differences between two methods. The method based on Bd annihilation treats thecharm quark as massless. It takes into account some of the non-perturbative long-distance effectsexpected to occur in Bd and Bc decays, but treats the relation between matrix elements of theoperators O1 and O2 in a very naïve way. It relies also on extremely naive assumptions concerningthe respective size of matrix elements for PP, V P and VV modes. The method based on one-gluonexchange treats the charm quark as heavy. It assumes the dominance from a specific set of diagramscomputed in a perturbative way within a consistent framework. It is well known that both kindsof estimation yield rather different results. This is illustrated by the fact that the estimate of Bd →K+K− in the annihilation models of QCD factorisation (around 10−8 with substantial uncertainties)is one order of magnitude below the current experimental average. There are well-known caseswhere final-state interaction can increase significantly estimates based on factorisation, for instanceB→ Kχc or D+s → ρ0pi+. Therefore, an observation of the non-leptonic charmless Bc decays willcertainly have an important key to clarify such a controversy.We can estimate the expected sensitivity of LHCb for a specific channel. Taking into accountthe trigger and reconstruction efficiencies, as well as Zweig-rule and Cabibbo suppression, we drawthe conclusion that the B+c → K∗0K+ channel might be the best candidate for the detection. Sincethe selection criteria and trigger efficiencies are different for each channel, detailed simulationsare necessary in order to estimate the expected sensitivity for different channels. For example,such a study has been done for Bc → J/ψpi+ [5]. From the expected branching ratio Br(Bc →J/ψpi+)≃ 1 %, it was deduced that over a thousand of events are expected after the one year runof LHCb. By scaling this observation to the processes of interest, we can very roughly estimate thatan assumption of Br(B+c → K∗0K+) = 10−6 yields a few events per year at LHCb. The analysis ofLHCb data will thusset first experimental limits on the non-leptonic charmless Bc decays, and givehints on the annihilation mechanisms at work in these decays.AcknowledgmentsWork supported in part by EU Contracts No. MRTN-CT-2006-035482 (“FLAVIAnet”) qndMIF1-CT-2006-027144 and by the ANR contracts “DIAM” ANR-07-JCJC-0031 and “LFV-CPV-LHC” ANR-NT09-508531.References[1] S. Descotes-Genon, J. He, E. Kou and P. Robbe, arXiv:0907.2256 [hep-ph].[2] D. Zeppenfeld, Z. Phys. C 8, 77 (1981).[3] J. J. de Swart, Rev. Mod. Phys. 35, 916 (1963) [Erratum-ibid. 37, 326 (1965)].[4] M. Beneke and M. Neubert, Nucl. Phys. B 675, 333 (2003) [arXiv:hep-ph/0308039].M. Beneke, J. Rohrer and D. Yang, Nucl. Phys. B 774, 64 (2007) [arXiv:hep-ph/0612290].[5] O. P. Yushchenko, Note LHCb 2003-113.Y. Gao, J. He, Z. Yang. Note LHCb-2008-077 ; CERN-LHCb-2008-077.4

Nonleptonic charmless B_c decays and their search at LHCb

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