Fragmentation function of gluon into spin-singlet $P$-wave quarkonium

Abstract

Following the operator definition of the fragmentation function developed by Collins and Soper, we compute the gluon-to-$h_c$ fragmentation function at the lowest order in the velocity expansion in NRQCD factorization approach. Utilizing some modern technique developed in the area of multi-loop calculation, we are able to analytically deduce the infrared-finite color-singlet short-distance coefficient associated with the fragmentation function. The fragmentation probability for gluon into $h_c$ is estimated to be order $10^{-6}$.

arXiv comment10 pages, 2 figures

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• Gluon fragmentation into $B_c^{(\ast )}$ in NRQCD factorization
• Fragmentation functions for a quark into a spin-singlet quarkonium: Different flavor case
• Next-to-leading-order QCD corrections to heavy quark fragmentation into ${}^1{S}_0^{(1,8)}$ quarkonia
• An analysis of the fragmentation function of gluon at next-to-leading order approximation
• Relativistic effect of $J/\psi$ hadroproduction in large $p_T$ region