Abstract
We present the first calculation at next-to-leading order (NLO) in α s of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of z, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction terms in 4 − 2ϵ dimensions. We also extract the divergences in the virtual NLO corrections analytically, and detail the cancellation of all divergences after renormalization. The NLO corrections have a dramatic effect on the shape of the fragmentation function, and they significantly increase the fragmentation probability.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.C. Collins and D.E. Soper, Parton distribution and decay functions, Nucl. Phys. B 194 (1982) 445 [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.T. Bodwin et al., Quarkonium at the frontiers of high energy physics: a Snowmass white paper, arXiv:1307.7425 [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].
M. Butenschoen and B.A. Kniehl, J/ψ polarization at Tevatron and LHC: nonrelativistic-QCD factorization at the crossroads, Phys. Rev. Lett. 108 (2012) 172002 [arXiv:1201.1872] [INSPIRE].
K.-T. Chao, Y.-Q. Ma, H.-S. Shao, K. Wang and Y.-J. Zhang, J/ψ polarization at hadron colliders in nonrelativistic QCD, Phys. Rev. Lett. 108 (2012) 242004 [arXiv:1201.2675] [INSPIRE].
B. Gong, L.-P. Wan, J.-X. Wang and H.-F. Zhang, Polarization for prompt J/ψ and ψ(2s) production at the Tevatron and LHC, Phys. Rev. Lett. 110 (2013) 042002 [arXiv:1205.6682] [INSPIRE].
C.-H. Chang, Y.-Q. Chen and R.J. Oakes, Comparative study of the hadronic production of B(c) mesons, Phys. Rev. D 54 (1996) 4344 [hep-ph/9602411] [INSPIRE].
Z.B. Kang, J.W. Qiu and G. Sterman, Factorization and quarkonium production, Nucl. Phys. Proc. Suppl. 214 (2011) 39.
Z.-B. Kang, J.-W. Qiu and G. Sterman, Heavy quarkonium production and polarization, Phys. Rev. Lett. 108 (2012) 102002 [arXiv:1109.1520] [INSPIRE].
S. Fleming, A.K. Leibovich, T. Mehen and I.Z. Rothstein, The systematics of quarkonium production at the LHC and double parton fragmentation, Phys. Rev. D 86 (2012) 094012 [arXiv:1207.2578] [INSPIRE].
S. Fleming, A.K. Leibovich, T. Mehen and I.Z. Rothstein, Anomalous dimensions of the double parton fragmentation functions, Phys. Rev. D 87 (2013) 074022 [arXiv:1301.3822] [INSPIRE].
Y.-Q. Ma, J.-W. Qiu and H. Zhang, Heavy quarkonium fragmentation functions from a heavy quark pair. I. S wave, Phys. Rev. D 89 (2014) 094029 [arXiv:1311.7078] [INSPIRE].
Y.-Q. Ma, J.-W. Qiu and H. Zhang, Heavy quarkonium fragmentation functions from a heavy quark pair. II. P wave, Phys. Rev. D 89 (2014) 094030 [arXiv:1401.0524] [INSPIRE].
E. Braaten and T.C. Yuan, Gluon fragmentation into heavy quarkonium, Phys. Rev. Lett. 71 (1993) 1673 [hep-ph/9303205] [INSPIRE].
E. Braaten and T.C. Yuan, Gluon fragmentation into spin triplet S wave quarkonium, Phys. Rev. D 52 (1995) 6627 [hep-ph/9507398] [INSPIRE].
E. Braaten, K.-m. Cheung and T.C. Yuan, Z0 decay into charmonium via charm quark fragmentation, Phys. Rev. D 48 (1993) 4230 [hep-ph/9302307] [INSPIRE].
E. Braaten and J. Lee, Next-to-leading order calculation of the color octet 3S(1) gluon fragmentation function for heavy quarkonium, Nucl. Phys. B 586 (2000) 427 [hep-ph/0004228] [INSPIRE].
S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 [arXiv:0712.1851] [INSPIRE].
G.J. van Oldenborgh, FF: a package to evaluate one loop Feynman diagrams, Comput. Phys. Commun. 66 (1991) 1 [INSPIRE].
G.P. Lepage, VEGAS: an adaptive multidimensional integration program, CLNS-80/447 (1980).
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: 1412.3834
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
Artoisenet, P., Braaten, E. Gluon fragmentation into quarkonium at next-to-leading order. J. High Energ. Phys. 2015, 121 (2015). https://doi.org/10.1007/JHEP04(2015)121
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)121