Abstract
We analyze the uncertainties induced by different definitions of the momentum fraction z in the application of gluon to heavy quarkonium fragmentation function. We numerically calculate the initial g -> J/psi fragmentation functions by using the non-covariant definitions of z with finite gluon momentum and find that these fragmentation functions have strong dependence on the gluon momentum k. As vertical bar k vertical bar -> infinity, these fragmentation functions approach to the fragmentation function in the light-cone definition. We find that when vertical bar k vertical bar is small (for instance in the typical energy scale (about 4-20GeV) of the gluon production at the hadron colliders, such as Tevatron and LHC), large uncertainty remains while the in-covariant definitions of z are employed in the application of the fragmentation functions.
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