Quark Fragmentation into ^3P_J Quarkonium

Abstract

We calculate the functions of parton fragmentation into ${}^3{P}_J$ quarkonium at order ${\alpha }_s^2$, where the parton can be a heavy or light quark. The obtained functions explicitly satisfy the Altarelli-Parisi equation and they are divergent, behaving as $z^{-1}$ near $z=0$. However, if one choses the renormalization scale as twice of the heavy quark mass, the fragmentation functions are regular over the whole range of $z$.

Comments: 12 pages+2 Figs, postscript file format, uuencoded and compressed