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

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 nonrelativistic QCD factorization approach. Utilizing some modem technique developed in the area of multiloop 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 of the order of 10(-6).