Abstract
Recently we have proved factorization of infrared divergences in NRQCD S-wave heavy quarkonium production at high energy colliders at all orders in coupling constant. One of the problem which still exists in the higher order pQCD calculation of color singlet P-wave heavy quarkonium production/anihillation is the appearance of noncanceling infrared divergences due to real soft gluons exchange, although no such infrared divergences are present in the color singlet S-wave heavy quarkonium. In this paper we find that since the non-perturbative matrix element of the color singlet P-wave heavy quarkonium production contains derivative operators, the gauge links are necessary to make it gauge invariant and be consistent with the factorization of such non-canceling infrared divergences at all orders in coupling constant.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G.C. Nayak, Proof of NRQCD factorization at all orders in the coupling constant in heavy quarkonium production, Eur. Phys. J. C 76 (2016) 448 [arXiv:1506.02593] [INSPIRE].
E598 collaboration, J.J. Aubert et al., Experimental Observation of a Heavy Particle J , Phys. Rev. Lett. 33 (1974) 1404 [INSPIRE].
SLAC-SP-017 collaboration, J.E. Augustin et al., Discovery of a Narrow Resonance in e + e − Annihilation, Phys. Rev. Lett. 33 (1974) 1406 [Adv. Exp. Phys. 5 (1976) 141] [INSPIRE].
T. Appelquist and H.D. Politzer, Orthocharmonium and e + e − Annihilation, Phys. Rev. Lett. 34 (1975) 43 [INSPIRE].
T. Appelquist and H.D. Politzer, Heavy Quarks and Longlived Hadrons, Phys. Rev. D 12 (1975) 1404 [INSPIRE].
D.J. Gross and F. Wilczek, Ultraviolet Behavior of Nonabelian Gauge Theories, Phys. Rev. Lett. 30 (1973) 1343 [INSPIRE].
H.D. Politzer, Reliable Perturbative Results for Strong Interactions?, Phys. Rev. Lett. 30 (1973) 1346 [INSPIRE].
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] [INSPIRE].
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 [INSPIRE].
R. Barbieri, R. Gatto and E. Remiddi, Singular Binding Dependence in the Hadronic Widths of 1++ and 1+- Heavy Quark anti-Quark Bound States, Phys. Lett. 61B (1976) 465 [INSPIRE].
R. Barbieri, M. Caffo and E. Remiddi, Gluon Jets From Quarkonia, Nucl. Phys. B 162 (1980) 220 [INSPIRE].
R. Barbieri, M. Caffo, R. Gatto and E. Remiddi, Strong QCD Corrections to p Wave Quarkonium Decays, Phys. Lett. 95B (1980) 93 [INSPIRE].
R. Barbieri, M. Caffo, R. Gatto and E. Remiddi, QCD corrections to P-wave quarkonium decays, Nucl. Phys. B 192 (1981) 61 [INSPIRE].
W. Kwong, P.B. Mackenzie, R. Rosenfeld and J.L. Rosner, Quarkonium Annihilation Rates, Phys. Rev. D 37 (1988) 3210 [INSPIRE].
I. Harris and L.M. Brown, Radiative Corrections to Pair Annihilation, Phys. Rev. 105 (1957) 1656 [INSPIRE].
P.B. Mackenzie and G.P. Lepage, QCD Corrections to the Gluonic Width of the Upsilon Meson, Phys. Rev. Lett. 47 (1981) 1244 [INSPIRE].
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] [INSPIRE].
G.C. Nayak, J.-W. Qiu and G.F. Sterman, Fragmentation, factorization and infrared poles in heavy quarkonium production, Phys. Lett. B 613 (2005) 45 [hep-ph/0501235] [INSPIRE].
G.C. Nayak, J.-W. Qiu and G.F. Sterman, Fragmentation, NRQCD and NNLO factorization analysis in heavy quarkonium production, Phys. Rev. D 72 (2005) 114012 [hep-ph/0509021] [INSPIRE].
G.C. Nayak, J.-W. Qiu and G.F. Sterman, NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production, Phys. Rev. D 74 (2006) 074007 [hep-ph/0608066] [INSPIRE].
G.A. Schuler, Quarkonium production and decays, hep-ph/9403387 [INSPIRE].
E. Braaten and Y.-Q. Chen, Calculation of P wave charmonium decay rates using dimensional regularization, Phys. Rev. D 55 (1997) 7152 [hep-ph/9701242] [INSPIRE].
T. Matsui and H. Satz, J/ψ Suppression by quark-gluon Plasma Formation, Phys. Lett. B 178 (1986) 416 [INSPIRE].
G. Grammer, Jr. and D.R. Yennie, Improved treatment for the infrared divergence problem in quantum electrodynamics, Phys. Rev. D 8 (1973) 4332 [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Factorization for Short Distance Hadron-Hadron Scattering, Nucl. Phys. B 261 (1985) 104 [INSPIRE].
G.C. Nayak, General Form of the Color Potential Produced by Color Charges of the Quark, JHEP 03 (2013) 001 [arXiv:1201.2666] [INSPIRE].
G.C. Nayak, General Form of Color Charge of the Quark, Eur. Phys. J. C 73 (2013) 2442 [arXiv:1201.2672] [INSPIRE].
G.C. Nayak and P. van Nieuwenhuizen, Soft-gluon production due to a gluon loop in a constant chromo-electric background field, Phys. Rev. D 71 (2005) 125001 [hep-ph/0504070] [INSPIRE].
G.C. Nayak, Non-perturbative quark-antiquark production from a constant chromo-electric field via the Schwinger mechanism, Phys. Rev. D 72 (2005) 125010 [hep-ph/0510052] [INSPIRE].
F. Cooper and G.C. Nayak, Non-perturbative gluon pair production from a constant chromo-electric field via the Schwinger mechanism in arbitrary gauge, Phys. Rev. D 73 (2006) 065005 [hep-ph/0511053] [INSPIRE].
G.C. Nayak, Light-Like Wilson Line in QCD Without Path Ordering, Phys. Part. Nucl. Lett. 13 (2016) 417 [arXiv:1506.07146] [INSPIRE].
G.C. Nayak, Jet Quenching and Gluon to Hadron Fragmentation Function in Non-Equilibrium QCD at RHIC and LHC, Phys. Part. Nucl. Lett. 14 (2017) 18 [arXiv:1509.01148] [INSPIRE].
R. Tucci, Factorization of Soft and Collinear Divergences in QCD in Feynman Gauge via Background Field Gauge, Phys. Rev. D 32 (1985) 945 [Erratum ibid. D 34 (1986) 1235] [INSPIRE].
L.F. Abbott, The Background Field Method Beyond One Loop, Nucl. Phys. B 185 (1981) 189 [INSPIRE].
G. ’t Hooft, An algorithm for the poles at dimension four in the dimensional regularization procedure, Nucl. Phys. B 62 (1973) 444 [INSPIRE].
H. Kluberg-Stern and J.B. Zuber, Renormalization of Nonabelian Gauge Theories in a Background Field Gauge. 1. Green Functions, Phys. Rev. D 12 (1975) 482 [INSPIRE].
T. Muta, World Scientific Lecture nNtes in Physics. Vol. 5: Foundations of Quantum Chromodynamics, World Scientific, New York U.S.A. (1987).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1704.07449
G.C. Nayak was affiliated with C.N. Yang Institute for Theoretical Physics in 2004-2007. (Gouranga C. Nayak)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Nayak, G.C. Correct definition of color singlet P-wave non-perturbative matrix element of heavy quarkonium production. J. High Energ. Phys. 2017, 90 (2017). https://doi.org/10.1007/JHEP09(2017)090
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2017)090