More Insight into Heavy Quark Masses from QCD

Using the non-relativistic version of Borel sum rules, combined to the very accurate experimental information on the Charmonium and Upsilon spectra, we rigorously investigate the Euclidean mass of the Charm and Bottom quark. Our analysis is performed with an improved expansion of the heavy current correlator in the infinite heavy quark mass limit. The optimal results, which take into account the most recent world average values of the strong coupling constant, as well as a conservative range of the gluon condensate, are: m_c^Eucl=1.20+-0.034 GeV and m_b^Eucl=4.18+-0.037 GeV. Their conversions to the corresponding pole mass and running mass give respectively: M_c=1.49+-0.08 GeV, M_b=4.65+-0.06 GeV and m_c(m_c)=1.21+-0.08 GeV, m_b(m_b)=4.20+-0.06 GeV in good agreement with the most recent direct estimates.