Power-suppressed effects in heavy quark fragmentation functions

This talk summarizes the results of a phenomenological analysis of heavy quark fragmentation data published by the CLEO and BELLE collaborations at \sqrt{s} = 10.6 GeV and by the LEP collaborations at \sqrt{s} = 91.2 GeV. Several theoretical ingredients are employed: next-to-leading order initial conditions, evolution and coefficient functions; soft-gluon resummation to next-to-leading-log accuracy; a next-to-leading order matching condition for the crossing of the bottom threshold in the evolution. Important initial-state electromagnetic radiation effects in the CLEO and BELLE data are also accounted for. We find that with reasonably simple choices of a non-perturbative correction to the fixed-order initial condition for the evolution, the data from CLEO and BELLE can be fitted with remarkable accuracy. The fitted fragmentation function, when evolved to LEP energies, does not however represent fairly the D* fragmentation spectrum measured by ALEPH. Large non-perturbative corrections to the coefficient functions of the meson spectrum are needed in order to reconcile CLEO/BELLE and ALEPH results.