Relativistic corrections to the axial vector and vector currents in the \(\overline{b}c\) meson system at order \(\alpha_s\). (English) Zbl 1214.81304
Summary: We compute the short distance coefficients for the NRQCD factorization formulas of the meson-to-vacuum matrix elements for the axial vector and vector parts of the charged weak current in the \(S\)-wave spin-singlet and -triplet \(\overline{b}c\) mesons, respectively. The computation is carried out to order \(\alpha_s\) including relativistic corrections of all orders in \(q^{2n}\), where \(q\) is the relative momentum of the \(\bar{b}\) and \(c\) in the meson rest frame. The relativistic corrections at order \(\alpha s\) are new. The results reveal that the relativistic corrections to the leptonic decay rate of the \(B_c\) meson at order \(\alpha_s\) or less converge rapidly, which shows a strong contrast to the uncomfortably large corrections of order \(\alpha_s^{2}|q|^{0}\). The short distance coefficients listed in this paper can be employed to compute the resummation of relativistic corrections to the phenomenological measurables that involve \(B_c\) and \(B_c^*\) production and decay.
MSC:
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 81V35 | Nuclear physics |
References:
| [1] | CDF collaboration, F. Abe et al., Observation of the Bcmeson in \(p\bar{p}\) collisions at \(\sqrt{s} = 1.8\;TeV \), Phys. Rev. Lett.81 (1998) 2432 [hep-ex/9805034] [SPIRES]. · doi:10.1103/PhysRevLett.81.2432 |
| [2] | G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev.D 51 (1995) 1125 [Erratum ibid.D 55 (1997) 5853] [hep-ph/9407339] [SPIRES]. |
| [3] | N. Isgur, D. Scora, B. Grinstein and M.B. Wise, Semileptonic B and D decays in the quark model, Phys. Rev.D 39 (1989) 799 [SPIRES]. |
| [4] | M. Lusignoli and M. Masetti, Bcdecays, Z. Phys.C 51 (1991) 549 [SPIRES]. |
| [5] | C.-H. Chang and Y.-Q. Chen, The decays of Bcmeson, Phys. Rev.D 49 (1994) 3399 [SPIRES]. |
| [6] | D. Scora and N. Isgur, Semileptonic meson decays in the quark model: An update, Phys. Rev.D 52 (1995) 2783 [hep-ph/9503486] [SPIRES]. |
| [7] | M. Beneke and G. Buchalla, The Bcmeson lifetime, Phys. Rev.D 53 (1996) 4991 [hep-ph/9601249] [SPIRES]. |
| [8] | V.V. Kiselev, A.E. Kovalsky and A.K. Likhoded, Bcdecays and lifetime in QCD sum rules, Nucl. Phys.B 585 (2000) 353 [hep-ph/0002127] [SPIRES]. · doi:10.1016/S0550-3213(00)00386-2 |
| [9] | Particle Data Group collaboration, K. Nakamura et al., Review of Particle Physics, J. Phys.G 37 (2010) 075021 [SPIRES]. |
| [10] | Quarkonium Working Group collaboration, N. Brambilla et al., Heavy quarkonium physics, hep-ph/0412158 [SPIRES]. |
| [11] | E. Eichten and F. Feinberg, Spin dependent forces in quantum chromodynamics, Phys. Rev.D 23 (1981) 2724 [SPIRES]. |
| [12] | S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev.D 32 (1985) 189 [SPIRES]. |
| [13] | W. Kwong and J.L. Rosner, Masses of new particles containing b quarks, Phys. Rev.D 44 (1991) 212 [SPIRES]. |
| [14] | E.J. Eichten and C. Quigg, Mesons with beauty and charm: Spectroscopy, Phys. Rev.D 49 (1994) 5845 [hep-ph/9402210] [SPIRES]. |
| [15] | S.S. Gershtein, V.V. Kiselev, A.K. Likhoded, and A.V. Tkabladze Bcspectroscopy, Phys. Rev.D 51 (1995) 3613 [hep-ph/9406339] [SPIRES]. |
| [16] | C.-H. Chang and Y.-Q. Chen, The Bcand \({\bar{B}_c}\) mesons accessible to experiments by Z0bosons decay, Phys. Lett.B 284 (1992) 127 [SPIRES]. |
| [17] | C.-H. Chang and Y.-Q. Chen, The production of Bcor \({\bar{B}_c}\) meson associated with two heavy-quark jets in Z0boson decay, Phys. Rev.D 46 (1992) 3845 [Erratum ibid.D 50 (1994) 6013] [SPIRES]. |
| [18] | C.-H. Chang, C.-F. Qiao, J.-X. Wang and X.-G. Wu, Hadronic production of Bc (Bc*) meson induced by the heavy quarks inside the collision hadrons, Phys. Rev.D 72 (2005) 114009 [hep-ph/0509040] [SPIRES]. |
| [19] | C.-H. Chang and Y.-Q. Chen, Hadronic production of the Bcmeson at TeV energies, Phys. Rev.D 48 (1993) 4086 [SPIRES]. |
| [20] | K. Cheung, Bcmeson production at hadron colliders by heavy quark fragmentation, Phys. Rev. Lett.71 (1993) 3413 [hep-ph/9307222] [SPIRES]. · doi:10.1103/PhysRevLett.71.3413 |
| [21] | E. Braaten, K. Cheung and T.C. Yuan, QCD fragmentation functions for Bcand Bc*production, Phys. Rev.D 48 (1993) 5049 [hep-ph/9305206] [SPIRES]. |
| [22] | G.T. Bodwin, X. Garcia i Tormo and J. Lee, Factorization Theorems for Exclusive Heavy-Quarkonium Production, Phys. Rev. Lett.101 (2008) 102002 [arXiv:0805.3876] [SPIRES]. · doi:10.1103/PhysRevLett.101.102002 |
| [23] | G.T. Bodwin, X. Garcia i Tormo and J. Lee, Factorization of low-energy gluons in exclusive processes, Phys. Rev.D 81 (2010) 114005 [arXiv:0903.0569] [SPIRES]. |
| [24] | G.T. Bodwin, X. Garcia i Tormo and J. Lee, Factorization in exclusive quarkonium production, Phys. Rev.D 81 (2010) 114014 [arXiv:1003.0061] [SPIRES]. |
| [25] | E. Braaten and S. Fleming, QCD radiative corrections to the leptonic decay rate of the Bcmeson, Phys. Rev.D 52 (1995) 181 [hep-ph/9501296] [SPIRES]. |
| [26] | D.S. Hwang and S. Kim, QCD radiative correction to the decay of Bcand Bc*, Phys. Rev.D 60 (1999) 034022 [SPIRES]. |
| [27] | A.I. Onishchenko and O.L. Veretin, Two-loop QCD corrections to the leptonic constant of the Bc-meson, Eur. Phys. J.C 50 (2007) 801 [hep-ph/0302132] [SPIRES]. · doi:10.1140/epjc/s10052-007-0255-1 |
| [28] | M. Beneke, A. Signer and V.A. Smirnov, Two-loop Corrections to the Leptonic Decays of Quarkonium, Phys. Rev. Lett.80 (1998) 2535 [hep-ph/9712302] [SPIRES]. · doi:10.1103/PhysRevLett.80.2535 |
| [29] | A. Czarnecki and K. Melnikov, Two-loop QCD corrections to the Heavy Quark Pair Production Cross Section in e+e−Annihilation near Threshold, Phys. Rev. Lett.80 (1998) 2531 [hep-ph/9712222] [SPIRES]. · doi:10.1103/PhysRevLett.80.2531 |
| [30] | M.E. Luke and M.J. Savage, Power counting in dimensionally regularized nonrelativistic QCD, Phys. Rev.D 57 (1998) 413 [hep-ph/9707313] [SPIRES]. |
| [31] | H.W. Griesshammer, Threshold expansion and dimensionally regularised NRQCD, Phys. Rev.D 58 (1998) 094027 [hep-ph/9712467] [SPIRES]. |
| [32] | G.T. Bodwin, H.S. Chung, J. Lee and C. Yu, Order-αscorrections to the quarkonium electromagnetic current at all orders in the heavy-quark velocity, Phys. Rev.D 79 (2009) 014007 [arXiv:0807.2634] [SPIRES]. |
| [33] | M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys.B 522 (1998) 321 [hep-ph/9711391] [SPIRES]. · doi:10.1016/S0550-3213(98)00138-2 |
| [34] | E.B. Gregory et al., Prediction of the Bc*Mass in Full Lattice QCD, Phys. Rev. Lett.104 (2010) 022001 [arXiv:0909.4462] [SPIRES]. · doi:10.1103/PhysRevLett.104.022001 |
| [35] | E. Braaten and Y.-Q. Chen, Helicity decomposition for inclusive J/ψ production, Phys. Rev.D 54 (1996) 3216 [hep-ph/9604237] [SPIRES]. |
| [36] | E. Braaten and Y.-Q. Chen, Dimensional regularization in quarkonium calculations, Phys. Rev.D 55 (1997) 2693 [hep-ph/9610401] [SPIRES]. |
| [37] | W.-l. Sang, L.-f. Yang and Y.-q. Chen, Relativistic corrections to heavy quark fragmentation to S-wave heavy mesons, Phys. Rev.D 80 (2009) 014013 [SPIRES]. |
| [38] | S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett.B 303 (1993) 113 [hep-ph/9302240] [SPIRES]. |
| [39] | A. Petrelli, M. Cacciari, M. Greco, F. Maltoni and M.L. Mangano, NLO production and decay of quarkonium, Nucl. Phys.B 514 (1998) 245 [hep-ph/9707223] [SPIRES]. · doi:10.1016/S0550-3213(97)00801-8 |
| [40] | G.T. Bodwin, D. Kang and J. Lee, Potential-model calculation of an order-v2nonrelativistic QCD matrix element, Phys. Rev.D 74 (2006) 014014 [hep-ph/0603186] [SPIRES]. |
| [41] | G.T. Bodwin, H.S. Chung, D. Kang, J. Lee and C. Yu, Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium, Phys. Rev.D 77 (2008) 094017 [arXiv:0710.0994] [SPIRES]. |
| [42] | M. Gremm and A. Kapustin, Annihilation of S-wave quarkonia and the measurement of αs, Phys. Lett.B 407 (1997) 323 [hep-ph/9701353] [SPIRES]. |
| [43] | H.S. Chung, J. Lee and C. Yu, NRQCD matrix elements for S-wave bottomonia and Γ[ηb (nS) → γγ] with relativistic corrections, arXiv:1011.1554 [SPIRES]. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
