Compatibility of various approaches to heavy-quark fragmentation

Abstract

We find that the definition of the heavy-quark fragmentation function given by Jaffe and Randall differs by a factor of the longitudinal-momentum fraction z from the standard Collins-Soper definition. Once this factor is taken into account, the explicit calculation of Braaten et al. is found to be in agreement with the general analysis of Jaffe and Randall. We also examine the model of Peterson et al. for heavy-quark fragmentation and find that the quoted values of the width and of the value of $z$ at the maximum are in error. The corrected values are in agreement with the analysis of Jaffe and Randall.