The role of spin in fragmentation production image and image

In this work we calculate the process-independent fragmentation functions for a heavy quark Q to fragment into vector image and pseudoscalar image heavy quarkonium to leading order perturbative QCD. We investigate the role of the spin orientation of the initial and final heavy quarks on the fragmentation functions. In the special case, we calculate fragmentation functions by using average over spin of initial state heavy quark and sum over spin of final states. The universal fragmentation probabilities for the image and image are about image and image, respectively. Moreover, the spin dependent observables such as image and image ratios are estimated.