Relativistic and binding energy corrections to heavy quark fragmentation functions

Abstract

We calculate the fragmentation function for a charm quark to decay inclusively into $S$-wave charmonium states, including relativistic and binding energy corrections in powers of the quark relative velocity $v$. We also use these fragmentation functions to estimate their contribution to the production rate of ${\ensuremath{\eta}}_{c}$ and $J/\ensuremath{\psi}$ in ${Z}^{0}$ decay. These corrections contribute about $38$% to the integrated $c\ensuremath{\rightarrow}J/\ensuremath{\psi}+X$ fragmentation. For ${\ensuremath{\eta}}_{c},$ these corrections are found to be small.