×

\( \mathcal{O}\left( {{\alpha_s}{v^2}} \right) \) correction to pseudoscalar quarkonium decay to two photons. (English) Zbl 1298.81393

Summary: We investigate the \( \mathcal{O}\left( {{\alpha_s}{v^2}} \right) \) correction to the process of pseudoscalar quarkonium decay to two photons in nonrelativistic QCD (NRQCD) factorization framework. The short-distance coefficient associated with the relative-order \(v^{2}\) NRQCD matrix element is determined to next-to-leading order in \(\alpha_{s}\) through the perturbative matching procedure. Some technical subtleties encountered in calculating the \( \mathcal{O}\left( {{\alpha_s}} \right) \) QCD amplitude are thoroughly{ }addressed.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81U99 Quantum scattering theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory

Software:

FeynCalc; LoopTools

References:

[1] T. Appelquist and H.D. Politzer, Orthocharmonium and e+e−Annihilation, Phys. Rev. Lett.34 (1975) 43 [SPIRES]. · doi:10.1103/PhysRevLett.34.43
[2] A. De Rujula and S.L. Glashow, Is Bound Charm Found?, Phys. Rev. Lett.34 (1975) 46 [SPIRES]. · doi:10.1103/PhysRevLett.34.46
[3] R. Barbieri, R. Gatto and R. Kogerler, Calculation of the Annihilation Rate of P Wave Quark - anti-Quark Bound States, Phys. Lett.B 60 (1976) 183 [SPIRES].
[4] V.A. Novikov et al., Charmonium and Gluons: Basic Experimental Facts and Theoretical Introduction, Phys. Rept.41 (1978) 1 [SPIRES]. · doi:10.1016/0370-1573(78)90120-5
[5] 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 [hep-ph/9407339] [SPIRES].
[6] D. Ebert, R.N. Faustov and V.O. Galkin, Two photon decay rates of heavy quarkonia in the relativistic quark model, Mod. Phys. Lett.A 18 (2003) 601 [hep-ph/0302044] [SPIRES].
[7] J.P. Lansberg and T.N. Pham, Two-photon width of ηcand ηc′from heavy-quark spin symmetry, Phys. Rev.D 74 (2006) 034001 [hep-ph/0603113] [SPIRES].
[8] M.Z. Yang, Radiative and leptonic decays of the pseudoscalar charmonium state ηc, Phys. Rev.D 79 (2009) 074026 [arXiv:0902.1295] [SPIRES].
[9] G.T. Bodwin and A. Petrelli, Order v4corrections to S-wave quarkonium decay, Phys. Rev.D 66 (2002) 094011 [hep-ph/0205210] [SPIRES].
[10] N. Brambilla, E. Mereghetti and A. Vairo, Electromagnetic quarkonium decays at order v7, JHEP08 (2006) 039 [hep-ph/0604190] [SPIRES]. · doi:10.1088/1126-6708/2006/08/039
[11] I. Harris and L.M. Brown, Radiative Corrections to Pair Annihilation, Phys. Rev.105 (1957) 1656 [SPIRES]. · Zbl 0079.42803 · doi:10.1103/PhysRev.105.1656
[12] R. Barbieri, E. d’Emilio, G. Curci and E. Remiddi, Strong Radiative Corrections to Annihilations of Quarkonia in QCD, Nucl. Phys.B 154 (1979) 535 [SPIRES]. · doi:10.1016/0550-3213(79)90047-6
[13] K. Hagiwara, C.B. Kim and T. Yoshino, Hadronic decay rate of ground state paraquarkonia in quantum chromodynamics, Nucl. Phys.B 177 (1981) 461 [SPIRES]. · doi:10.1016/0550-3213(81)90181-4
[14] A. Czarnecki and K. Melnikov, Charmonium decays: J/ψ → e+e−and ηc → γγ, Phys. Lett.B 519 (2001) 212 [hep-ph/0109054] [SPIRES].
[15] W.-Y. Keung and I.J. Muzinich, Beyond the static limit for quarkonium decays, Phys. Rev.D 27 (1983) 1518 [SPIRES].
[16] Z.-G. He, Y. Fan and K.-T. Chao, Relativistic corrections to J/ψ exclusive and inclusive double charm production at B factories, Phys. Rev.D 75 (2007) 074011 [hep-ph/0702239] [SPIRES].
[17] 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].
[18] H.S. Chung, J. Lee and C. Yu, NRQCD matrix elements for S-wave bottomonia and Γ[ηb(nS) → γγ] with relativistic corrections, Phys. Lett.B 697 (2011) 48 [arXiv:1011.1554] [SPIRES].
[19] Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett.B 667 (2008) 1 [SPIRES].
[20] Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys.G 37 (2010) 075021 [SPIRES].
[21] M.E. Luke and M.J. Savage, Power counting in dimensionally regularized NRQCD, Phys. Rev.D 57 (1998) 413 [hep-ph/9707313] [SPIRES].
[22] 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
[23] 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].
[24] J. Lee, W. Sang and S. Kim, Relativistic corrections to the axial vector and vector currents in the \(\bar{b}c\) meson system at order αs, JHEP01 (2011) 113 [arXiv:1011.2274] [SPIRES]. · Zbl 1214.81304 · doi:10.1007/JHEP01(2011)113
[25] M.S. Chanowitz, M. Furman and I. Hinchliffe, The Axial Current in Dimensional Regularization, Nucl. Phys.B 159 (1979) 225 [SPIRES]. · doi:10.1016/0550-3213(79)90333-X
[26] J.G. Korner, D. Kreimer and K. Schilcher, A Practicable γ5scheme in dimensional regularization, Z. Phys.C 54 (1992) 503 [SPIRES].
[27] G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys.B 44 (1972) 189 [SPIRES]. · doi:10.1016/0550-3213(72)90279-9
[28] P. Breitenlohner and D. Maison, Dimensional Renormalization and the Action Principle, Commun. Math. Phys.52 (1977) 11 [SPIRES]. · doi:10.1007/BF01609069
[29] 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
[30] E. Braaten and Y.-Q. Chen, Helicity Decomposition for Inclusive J/ψ Production, Phys. Rev.D 54 (1996) 3216 [hep-ph/9604237] [SPIRES].
[31] E. Braaten and Y.-Q. Chen, Dimensional regularization in quarkonium calculations, Phys. Rev.D 55 (1997) 2693 [hep-ph/9610401] [SPIRES].
[32] T.H. West, FeynmanParameter and Trace: Programs for expressing Feynman amplitudes as integrals over Feynman parameters, Comput. Phys. Commun.77 (1993) 286 [SPIRES]. · doi:10.1016/0010-4655(93)90011-Z
[33] R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun.64 (1991) 345 [SPIRES]. · doi:10.1016/0010-4655(91)90130-D
[34] G.T. Bodwin, J. Lee and C. Yu, Resummation of Relativistic Corrections to e+e− → J/ψ + ηc, Phys. Rev.D 77 (2008) 094018 [arXiv:0710.0995] [SPIRES].
[35] R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP02 (2008) 002 [arXiv:0712.1851] [SPIRES]. · doi:10.1088/1126-6708/2008/02/002
[36] T. Hahn and M. Pérez-Victoria, Automatized one-loop calculations in four and D dimensions, Comput. Phys. Commun.118 (1999) 153 [hep-ph/9807565] [SPIRES]. · doi:10.1016/S0010-4655(98)00173-8
[37] H.K. Guo, Y.Q. Ma and K.T. Chao, O(αsv2) Corrections to Hadronic and Electromagnetic Decays of1S0Heavy Quarkonium, arXiv:1104.3138 [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.