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 $10^{-6}$.
Highlights
Like parton distribution functions (PDFs), fragmentation functions (FFs) constitute one of the fundamental probes to uncover the nonperturbative partonic structure related to a hadron
Where dσdenotes the partonic cross section and the fragmentation function Di→HðzÞ characterizes the probability for the parton i to materialize into a complicated multihadron state that contains the hadron H carrying the fractional light-cone momentum z with respect to the parent parton
In contrast to the fragmentation functions for light hadrons, the functions for a parton to fragmentate into a heavy quarkonium, a nonrelativistic bound state composed of a heavy quark and heavy antiquark, need not be viewed as genuinely nonperturbative objects
Summary
Conducted to confront with copious large-P⊥ J=ψ, χcJ, and ψ0 data accumulated at LHC experiments [5,6]. The goal of this work is to compute the FF of gluon into the spin-singlet P-wave quarkonium, exemplified by the hc;b states. It is conceivable that they will be established at LHC experiments in the future, owing to the enormous partonic luminosity there For this purpose, it is desirable if one can make accurate predictions for the fragmentation functions for the hc;b states. [28] seem not to employ a gauge-invariant regulator to regularize the encountered IR singularity in the course of their calculation Their final results are expressed in terms of a twofold integral with a rather complicated integrand. A gauge-invariant operator definition for the fragmentation functions was formulated by Collins and Soper in 1981.
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