Higher-order relativistic corrections to gluon fragmentation into spin-triplet S-wave quarkonium

• Published in: The journal of high energy physics Vol. 2012; no. 11; p. 20
• Main Authors: Bodwin, Geoffrey T., Kim, U-Rae, Lee, Jungil
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 06.11.2012; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Color; Elementary Particles; Fragmentation; Gluons; High energy physics; Matching; Phenomenology; Physics; Physics and Astronomy; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; S waves; String Theory; NLO Computations; Hadronic Colliders
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2012)020

A bstract We compute the relative-order- v 4 contribution to gluon fragmentation into quarkonium in the color-singlet channel, using the nonrelativistic QCD (NRQCD) factorization approach. The QCD fragmentation process contains infrared divergences that produce single and double poles in ∈ in 4 − 2 ∈ dimensions. We devise subtractions that isolate the pole contributions, which ultimately are absorbed into long-distance NRQCD matrix elements in the NRQCD matching procedure. The matching procedure involves two-loop renormalizations of the NRQCD operators. The subtractions are integrated over the phase space analytically in 4 − 2 ∈ dimensions, and the remainder is integrated over the phase-space numerically. We find that the order- v 4 contribution is enhanced relative to the order- v 0 contribution. However, the order- v 4 contribution is not important numerically at the current level of precision of quarkonium-hadroproduction phenomenology. We also estimate the contribution to hadroproduction from gluon fragmentation into quarkonium in the color-octet channel and find that it is significant in comparison to the complete next-to-leading-order-in-α s contribution in that channel.