Perturbative Prediction for Parton Fragmentation into Heavy Hadron

By expanding functions of parton fragmentation into a heavy hadron in the inverse of the heavy quark mass $m_Q$ we attempt to factorize them into perturbative- and nonperturbative parts. In our approach the nonperturbative parts can be defined as matrix elements in heavy quark effective theory, the shape of the functions is predicted by perturbative QCD. In this work we neglect effect at order of $m_Q^{-2}$ and calculate the perturbative parts at one-loop level for heavy quark- and gluon fragmentation. We compare our results from leading log approximation with experimental results from $e^+e^-$ colliders and find a deviation below or at 10% level. Adding effect of higher order in $\alpha_s$ it can be expected to reduce the deviation. The size of matrix elements appearing at the order we consider for several types of heavy hadrons is determined.