We evaluate semileptonic and two--meson nonleptonic decays of the $B_c^-$
meson in the framework of a nonrelativistic quark model. The former are done in
spectator approximation using one--body current operators at the quark level.
Our model reproduces the constraints of heavy quark spin symmetry obtained in
the limit of infinite heavy quark mass. For the two--meson nonleptonic decays
we work in factorization approximation. We compare our results to the ones
obtained in different relativistic approaches.Comment: Talk given at the IVth International Conference on Quarks an Nuclear
  Physics, Madrid, June 5th-10th 200

Hernandez, E.

Nieves, J.

Verde-Velasco, J. M.

English

arXiv

We evaluate semileptonic and two-meson nonleptonic decays of the B-c- meson in the framework of a nonrelativistic quark model. The former are done in spectator approximation using one-body current operators at the quark level. Our model reproduces the constraints of heavy-quark spin symmetry obtained in the limit of infinite heavy-quark mass. For the two-meson nonleptonic decays we work in factorization approximation. We compare our results to the ones obtained in different relativistic approaches

Hernández Gajate, Eliecer

Nieves Pamplona, Juan Miguel

Verde Velasco, José María

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:hep-ph/0610125v1  11 Oct 2006EPJ manuscript No.(will be inserted by the editor)Study of semileptonic and nonleptonic decays of the B−cmesonE. Herna´ndez1, J. Nieves2 and J.M. Verde-Velasco11 Grupo de F´ısica Nuclear, Departamento de F´ısica Fundamental e IUFFyM, Universidad de Salamanca, Spain.2 Departamento de F´ısica Ato´mica, Molecular y Nuclear, Universidad de Granada, Spain.Received: date / Revised version: dateAbstract. We evaluate semileptonic and two–meson nonleptonic decays of the B−c meson in the frameworkof a nonrelativistic quark model. The former are done in spectator approximation using one–body currentoperators at the quark level. Our model reproduces the constraints of heavy quark spin symmetry obtainedin the limit of infinite heavy quark mass. For the two–meson nonleptonic decays we work in factorizationapproximation. We compare our results to the ones obtained in different relativistic approaches.PACS. 12.39.Hg – 12.39.Jh – 13.20.Fc – 13.20.He1 IntroductionIn this work we have studied, in the framework of a non-relativistic quark model, exclusive semileptonic and two–meson nonleptonic decays of the B−c meson driven bya b → c or c¯ → d¯, s¯ transitions at the quark level. Wehave not considered semileptonic processes driven by thequark b → u transition to avoid known problems both attoo high q2 transfers, where one might need to include theexchange of B∗c resonances, and at too low q2 where recoileffects could be important [1].In order to check the sensitivity of our results to theinterquark interaction we have used five different quark–quark potentials taken from refs. [3,4]. All the potentialsused have a confinement term plus coulomb and hyperfineterms coming from one–gluon exchange, and differ fromone another in the power of the confining term or in theuse of different form factors in the coulomb and hyper-fine terms. Their free parameters had been adjusted toreproduce the light and heavy–light meson spectra. Ourcentral results have been obtained with the AL1 potentialof ref. [4], while our errors show the spread of the resultswhen using the other four potentials.A detailed account of the full contents of this work isnow available in ref. [2].2 Semileptonic decaysWe have made our calculations in the spectator approx-imation using one–body current operators. In table 1 weshow our branching ratios for semileptonic B−c decays andcompare them to the results obtained by Ivanov et al. [5,7], within a relativistic quark model calculation, and Ebertet al. [6,8], within the quasipotential approach to the rel-ativistic quark model. The three calculations give similarresults.Table 1. Branching ratios in % for semileptonic B−c → cc¯ andB−c → B decays. In the first part of the table l stands forl = e, µ.This work [5] [6]B−c → ηc l− ν¯l 0.48+0.02 0.81 0.42B−c → ηc τ− ν¯τ 0.17+0.01 0.22B−c → χc0 l− ν¯l 0.11+0.01 0.17B−c → χc0 τ− ν¯τ 0.013+0.001 0.013B−c → J/Ψ l− ν¯l 1.54+0.06 2.07 1.23B−c → J/Ψ τ− ν¯τ 0.41+0.02 0.49B−c → χc1 l− ν¯l 0.066+0.003−0.002 0.092B−c → χc1 τ− ν¯τ 0.0072+0.0002−0.0003 0.0089B−c → hc l− ν¯l 0.17+0.02 0.27B−c → hc τ− ν¯τ 0.015+0.001 0.017B−c → χc2 l− ν¯l 0.13+0.01 0.17B−c → χc2 τ− ν¯τ 0.0093+0.0002−0.0005 0.0082B−c → Ψ(3836) l− ν¯l 0.0043−0.0005 0.0066B−c → Ψ(3836) τ− ν¯τ 0.000083−0.000010 0.000099This work [7] [8]B−c → B0e ν¯e 0.046+0.004−0.007 0.071 0.042B−c → B0µ ν¯µ 0.044+0.005−0.006B−c → B0s e ν¯e 1.06+0.05−0.02 1.10 0.84B−c → B0s µ ν¯µ 1.02+0.04−0.02B−c → B∗0e ν¯e 0.11+0.01−0.01 0.063 0.12B−c → B∗0µ ν¯µ 0.11+0.01−0.02B−c → B∗0s e ν¯e 2.35+0.14−0.10 2.37 1.75B−c → B∗0s µ ν¯µ 2.22+0.12−0.10In table 2 we show the forward-backward asymmetry,with the forward direction being defined by the three–momentum of the final meson, of the charged lepton mea-sured in the leptons center of mass frame. Our results are2 E. Herna´ndez, J. Nieves, J.M. Verde-Velasco: Study of semileptonic and nonleptonic decays of the B−c mesonTable 2. Forward-backward asymmetry AFB of the finalcharged lepton (e, µ or τ ) measured in the leptons center ofmass frame.AFB(e) AFB(µ) AFB(τ )Bc → ηcThis work 0.60+0.0110−6 0.13+0.0110−1 0.35[5] 0.953 10−6 0.36Bc → χc0This work 0.72+0.0210−6 0.15 10−1 0.40[5] 1.31 10−6 0.39Bc → J/ΨThis work −0.19 −0.18−0.01 −0.35+0.0210−1[5] −0.21 −0.48 10−1Bc → χc1This work −0.60−0.01 −0.60−0.01 −0.46[5] 0.19 0.34Bc → hcThis work −0.83−0.0510−2 0.97+0.01−0.0510−2 0.35[5] −3.6 10−2 0.31Bc → χc2This work −0.14 −0.13 0.55+0.0210−1[5] −0.16 0.44 10−1Bc → Ψ(3836)This work −0.59 −0.59 −0.42[5] 0.21 0.41AFB(e) AFB(µ)B−c → B0This work 0.67+0.0210−5 0.82+0.0110−1B−c → B0sThis work 0.89+0.0110−5 0.96+0.0110−1B−c → B∗0This work 0.17−0.01 0.19−0.01B−c → B∗0sThis work 0.14−0.01 0.16+0.01Table 3. α∗ angular asymmetry for the µ+µ− pair in the decayB−c → µ+µ−(J/Ψ) lν¯l.α∗(e) α∗(µ) α∗(τ )Bc → J/ΨThis work −0.29−0.01 −0.29 −0.19[5] −0.34 −0.24in reasonable agreement with the ones of ref. [5] with twoexceptions corresponding to final χc1 and Ψ(3836) wherenot even the sign of the asymmetry is the same.For the decay B−c → J/Ψ lν¯l with the J/Ψ decayinginto a µ+µ− pair one can evaluate another angular asym-metry. Calling xµ the cosine of the polar angle of the µ+µ−pair, measured in the µ+µ− rest frame relative to the mo-mentum of the decaying J/Ψ , we have that the differentialdecay width dΓB−c →µ+µ−(J/Ψ)lν¯l/dxµ ≡ 1+α∗ xµ. Our re-sults for the asymmetry parameter α∗ are given in table 3.They are in reasonable agreement with the ones obtainedby Ivanov et al. [5].McB 12M−Fig. 1. Diagrammatic representation of B−c two–meson non-leptonic decay in the factorization approximation2.1 Heavy quark spin symmetryWhile one can not apply ordinary heavy quark symmetryto hadrons with two heavy quarks, there is a symmetrythat survives for those systems which is heavy quark spinsymmetry (HQSS). This symmetry reflects the fact thatfor infinite heavy quark masses the spins of the two heavyquarks decouple.We have checked that our model reproduces the con-straints imposed by HQSS in the infinite heavy quarkmass limit. Those constraints relate the form factors forBc semileptonic decays into final 0− and 1− mesons nearthe zero recoil point [9].For the actual heavy quark masses we find small devi-ations from the infinite heavy quark mass limit relationsfor the Bc → ηc, J/Ψ case, while corrections are largefor some of the form factors in the Bc → B0, B∗0andBc → B0s, B∗0s cases. See ref. [2] for details.3 Two-meson nonleptonic decaysNeglecting penguin contributions, the effective Hamilto-nians used for these calculations are given by local four–quark operators of the current–current type [6,10]. Wework, as it is usually done, in factorization approximationin which the amplitude only contains contributions as theones depicted in fig. 1. To evaluate the amplitude we needdifferent meson decay constants that we take from experi-ment or lattice data. For the ηc we use our own theoreticalresult obtained with the model described in ref. [11].In table 4 we show results for decays that include a cc¯meson in the final state. For decays with a pi−, ρ−, K−, K∗−meson in the final state we find good agreement with thedata by Ebert et al. [6] while our results are roughly afactor of two smaller than the ones obtained by Ivanov etal. [10]. For decays with a D−, D∗−, D−s , D∗−s meson inthe final state we are in good agreement with the resultsby El-Hady et al. [12], obtained using the Bethe–Salpeterequation, and the ones by Kiselev [13], obtained within thethree point sum rules of QCD and nonrelativistic QCD.In table 5 we show results for decays that include ameson with a b quark. Our branching ratios for decayswith a B0, B∗0meson in the final state are in very goodagreement, being B−c → B∗0pi− the exception, with theE. Herna´ndez, J. Nieves, J.M. Verde-Velasco: Study of semileptonic and nonleptonic decays of the B−c meson 3Table 4. Branching ratios in % for exclusive two–meson non-leptonic decays of the B−c meson that include a cc¯ meson inthe final state.This work [10] [6]B−c → ηc pi− 0.094+0.006 0.19 0.083B−c → ηc ρ− 0.24+0.01 0.45 0.20B−c → ηcK− 0.0075+0.0005 0.015 0.006B−c → ηcK∗− 0.013+0.001 0.025 0.011B−c → J/Ψ pi− 0.076+0.008 0.17 0.060B−c → J/Ψ ρ− 0.24+0.02 0.49 0.16B−c → J/Ψ K− 0.0060+0.0006 0.013 0.005B−c → J/Ψ K∗− 0.014+0.002 0.028 0.010B−c → χc0 pi− 0.026+0.003 0.055B−c → χc0 ρ− 0.067+0.006−0.001 0.13B−c → χc0 K− 0.0020+0.0002 0.0042B−c → χc0 K∗− 0.0037+0.0005 0.0070B−c → χc1 pi− 0.00014+0.00001 0.0068B−c → χc1 ρ− 0.010+0.001−0.001 0.029B−c → χc1 K− 1.1+0.1 10−5 5.1 10−4B−c → χc1 K∗− 0.00073+0.00007−0.00002 0.0018B−c → hc pi− 0.053+0.007 0.11B−c → hc ρ− 0.13+0.01 0.25B−c → hcK− 0.0041+0.0006 0.0083B−c → hcK∗− 0.0071+0.0008 0.013B−c → χc2 pi− 0.022+0.002 0.046B−c → χc2 ρ− 0.065+0.006−0.002 0.12B−c → χc2 K− 0.0017+0.0001 0.0034B−c → χc2 K∗− 0.0038+0.0003−0.0002 0.0065B−c → Ψ(3836) pi− 4.1+0.03−0.02 10−5 0.0017B−c → Ψ(3836) ρ− 0.0020−0.0003 0.0055B−c → Ψ(3836)K− 3.1+0.2−0.2 10−6 0.00012B−c → Ψ(3836)K∗− 0.00014−0.00002 0.00032This work [10] [12] [13]B−c → ηcD− 0.014+0.001 0.019 0.014 0.015B−c → ηcD∗− 0.012+0.001 0.019 0.013 0.010B−c → J/Ψ D− 0.0083+0.0005 0.015 0.009 0.009B−c → J/Ψ D∗− 0.031+0.001 0.045 0.028 0.028B−c → ηcD−s 0.44+0.02 0.44 0.26 0.28B−c → ηcD∗−s 0.24+0.02 0.37 0.24 0.27B−c → J/Ψ D−s 0.24+0.02 0.34 0.15 0.17B−c → J/Ψ D∗−s 0.68+0.03 0.97 0.55 0.67results by Ebert et al. [8], while for the case with a B0s, B∗0smeson in the final state we are in very good agreementwith the results by Ivanov et al. [10]. Finally for the casewith a B−, B∗− meson in the final state we find, with justone exception (B−c → B∗−pi0), very good agreement withthe results by Ebert et al. [8].This research was supported by DGI and FEDER funds, un-der contracts FIS2005-00810, BFM2003-00856 and FPA2004-05616, by Junta de Andaluc´ıa and Junta de Castilla y Leo´nunder contracts FQM0225 and SA104/04, and it is part of theEU integrated infrastructure initiative Hadron Physics Projectunder contract number RII3-CT-2004-506078. J. M. V.-V. ac-knowledges a contract E.P.I.F. with the University of Sala-manca.Table 5. Branching ratios in % for exclusive two–meson non-leptonic decays of the B−c meson that include a B, B mesonin the final state.This work [10] [8]B−c → B0pi− 0.11+0.01−0.01 0.20 0.10B−c → B0ρ− 0.14+0.02−0.02 0.20 0.13B−c → B0K− 0.010+0.001−0.001 0.015 0.009B−c → B0K∗− 0.0039+0.0003−0.0005 0.0048 0.004B−c → B∗0pi− 0.072+0.012−0.012 0.057 0.026B−c → B∗0ρ− 0.58+0.05−0.08 0.30 0.67B−c → B∗0K− 0.0048+0.0007−0.0008 0.0036 0.004B−c → B∗0K∗− 0.030+0.002−0.004 0.013 0.032B−c → B0s pi− 3.51+0.19−0.06 3.9 2.46B−c → B0s ρ− 2.34+0.05−0.06 2.3 1.38B−c → B0sK− 0.29+0.01−0.01 0.29 0.21B−c → B0sK∗− 0.013−0.001 0.011 0.0030B−c → B∗0s pi− 2.34+0.19−0.14 2.1 1.58B−c → B∗0s ρ− 13.4+0.5−0.6 11 10.8B−c → B∗0s K− 0.13+0.01−0.01 0.13 0.11This work [10] [8]B−c → B− pi0 0.0038+0.0005−0.0006 0.007 0.004B−c → B− ρ0 0.0050+0.0004−0.0007 0.0071 0.005B−c → B−K0 0.25+0.03−0.04 0.38 0.24B−c → B−K∗0 0.093+0.006−0.013 0.11 0.09Bc → B∗− pi0 0.0025+0.0004−0.0005 0.0020 0.001Bc → B∗− ρ0 0.020+0.002−0.003 0.011 0.024Bc → B∗−K0 0.12+0.02−0.02 0.088 0.11Bc → B∗−K∗0 0.73+0.06−0.10 0.32 0.84References1. C. Albertus, J.M. Flynn, E. Herna´ndez, J. Nieves, and J.M.Verde-Velasco, Phys. Rev. D 72, (2005) 033002.2. E. Herna´ndez, J. Nieves, and J.M. Verde-Velasco, Phys.Rev. D in print, hep-ph/06071503. R.K. Bhaduri, L.E. Cohler , and Y. Nogami, Nuovo CimentoA 65 (1981) 376.4. B. Silvestre-Brac, Few–Body Systems 20 (1996) 1.5. M.A. Ivanov, J.G. Ko¨rner, and P. Santorelli, Phys. Rev. D71, (2005) 094006. Erratum to be published.6. D. Ebert, R. N. Faustov, and V.O. Galkin, Phys. Rev. D68, (2003) 094020.7. M.A. Ivanov, J.G. Ko¨rner, and P. Santorelli, Phys. Rev. D63, (2001) 074010.8. D. Ebert, R. N. Faustov, and V.O. Galkin, Eur. J. Phys. C32, (2003) 29.9. E. Jenkins, M. Luke, A.V. Manohar, and M.J. Savage, Nucl.Phys. B 390, (1993) 463.10. M.A. Ivanov, J.G. Ko¨rner, and P. Santorelli, Phys. Rev. D73, (2006) 054024.11. C. albertus, E. Herna´ndez, J. Nieves, and J.M. Verde-Velasco, Phys. Rev. D 71, (2005) 113006.12. A. Abd El-Hady, J.M. Munoz, and J.P. Vary, Phys. Rev.D 62, (2000) 014019.13. V.V. Kiselev, hep-ph/0211021.

Study of semileptonic and nonleptonic decays of the B-c(-) meson

We evaluate semileptonic and two-meson nonleptonic decays of the B
c
- meson in the framework of a nonrelativistic quark model. The former are done in spectator approximation using one-body current operators at the quark level. Our model reproduces the constraints of heavy-quark spin symmetry obtained in the limit of infinite heavy-quark mass. For the two-meson nonleptonic decays we work in factorization approximation. We compare our results to the ones obtained in different relativistic approaches

E. Hernández

J. Nieves

J. M. Verde-Velasco

EDP Sciences OAI-PMH repository (1.2.0)

Study of semileptonic and nonleptonic decays of the B

Study of semileptonic and nonleptonic decays of the $B_c^-$ meson

Study of semileptonic and nonleptonic decays of the $B_c^-$ meson

Abstract

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Study of semileptonic and nonleptonic decays of the Bc−B_c^-Bc−​ meson

Abstract

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Study of semileptonic and nonleptonic decays of the $B_c^-$ meson