QCD sum rule determination of the charm - quark mass

QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the MS scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form p(s) = 1 − (s0/s) , where s0 is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range s ≃ 20 − 25 GeV. This feature leads to a substantial reduction in the sensitivity of the results to changes in s0, as well as to a much reduced impact of the experimental uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the MS scheme at a scale of 3 GeV is mc(3 GeV) = 987 ± 9 MeV, where the error includes all sources of uncertainties added in quadrature.