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D^* production from e^+e^- to ep collisions in NLO QCD

Fragmentation functions for D mesons, based on the convolution of a perturbative part, related to the heavy quark perturbative showering, and a non-perturbative model for its hadronization into the meson, are used to describe D^* production in e^+e^- and ep collisions. The non-perturbative part is determined by fitting the e^+e^- data taken by ARGUS and OPAL at 10.6 and 91.2 GeV respectively. When fitting with a non perturbative Peterson fragmentation function and using next-to-leading evolution for the perturbative part, we find an epsilon parameter sensibly different from the one commonly used, which is instead found with a leading order fit. The use of this new value is shown to increase considerably the cross section for D^* production at HERA, suggesting a possible reconciliation between the next-to-leading order theoretical predictions and the experimental data.