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-nf 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 λM, where λ is a typical hadronic scale (λ ∼ 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 λ, in agreement with intuitive expectations. On the other hand, corrections to heavy quark correlations are very small, of the order of (λQ)p, where Q is the centre-of-mass energy and p ≥ 2.