We calculate the functions of parton fragmentation into ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{\mathit{J}}$ quarkonium at order ${\mathrm{\alpha }}_{\mathit{s}}^2$, 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 ${\mathit{z}}^{\mathrm{-}1}$ near z=0. However, if one chooses the renormalization scale as twice the heavy quark mass, the fragmentation functions are regular over the whole range of z. © 1996 The American Physical Society.

• Received 19 April 1995

DOI:https://doi.org/10.1103/PhysRevD.53.1185