Non-Perturbative Corrections to Heavy Quark Fragmentation in $e^+e^-$ Annihilation

We estimate the non-perturbative power-suppressed corrections to heavy flavour fragmentation and correlation functions in e^+e^- annihilation, using a model based on the analysis of one-loop Feynman graphs containing a massive gluon. This approach corresponds to the study of infrared renormalons in the large-n_f limit of QCD, or to the assumption of an infrared-finite effective coupling at low scales. We find that the leading corrections to the heavy quark fragmentation function are of order $\lambda/M$, where $\lambda$ is a typical hadronic scale ($\lambda\sim 0.4$ GeV) and M is the heavy quark mass. The inclusion of higher corrections corresponds to convolution with a universal function of M(1-x) concentrated at values of its argument of order $\lambda$, in agreement with intuitive expectations. On the other hand, corrections to heavy quark correlations are very small, of the order of $(\lambda/Q)^p$, where Q is the centre-of-mass energy and $p \ge 2$.