Direct Fragmentation of Quarkonia Including Fermi Motion Using Light-cone Wave Function

We investigate the effect of Fermi motion on the direct fragmentation of the $J/\psi$ and $\Upsilon$ states employing a light-cone wave function. Consistent with such a wave function we set up the kinematics of a heavy quark fragmenting into a quarkonia such that the Fermi motion of the constituents split into longitudinal as well as transverse direction and thus calculate the fragmentation functions for these states. In the framework of our investigation, we estimate that the fragmentation probabilities of $J/\psi$ and $\Upsilon$ may increase at least up to 14 percent when including this degree of freedom.