Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; Chinese Acad Sci, Grad Sch, Beijing 100049, Peoples R China
We analyze the uncertainties induced by different definitions of the momentum fraction z in the application of gluon to heavy quarkonium color-singlet fragmentation functions. We numerically calculate the initial g -> J/psi fragmentation functions at leading order (LO) by using the noncovariant definitions of z with finite gluon momentum and find that these fragmentation functions have strong dependence on the gluon momentum (k) over right arrow. As vertical bar(k) over right arrow vertical bar ->infinity, these fragmentation functions approach the fragmentation function in the light cone definition. Our numerical results show that large uncertainties remain while the noncovariant definitions of z are employed in the application of the fragmentation functions. We present for the first time the polarized gluon to J/psi color-singlet fragmentation functions at the leading nontrivial order in alpha(s) and relativistic expansion.