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

Abstract

We compute the relative-order-nu(4) contribution to gluon fragmentation into quarkonium in the S-3(1) color-singlet channel, using the nonrelativistic QCD (NRQCD) factorization approach. The QCD fragmentation process contains infrared divergences that produce single and double poles in epsilon in 4 - 2 epsilon 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 epsilon dimensions, and the remainder is integrated over the phase-space numerically. We find that the order-nu(4) contribution is enhanced relative to the order-nu(0) contribution. However, the order-nu(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 P-3(J) color-octet channel and find that it is significant in comparison to the complete next-to-leading-order-in-as contribution in that channel.