A fresh look into the heavy quark-mass values

Using the recent {\it world average} \alpha_s(M^2_Z)= 0.118 \pm 0.006, we give the {\it first direct extraction} from the \Psi and \Upsilon data of the values of the {\it running heavy quark masses} within QCD spectral sum rules to two-loops in the \overline {MS}-scheme: \mr_b(M^{PT2}_b) = (4.23~^{+0.03}_{-0.04} \pm 0.02) GeV and \mr_c(M^{PT2}_c) = (1.23~^{+ 0.02}_{-0.04} \pm 0.03) GeV, (the errors are respectively due to \alf and to the gluon condensate), and the corresponding value of the {\it short-distance perturbative pole masses to two-loops}: M^{PT2}_b=(4.62 \pm 0.02) GeV, M^{PT2}_c= (1.41\pm 0.03) GeV, which we compare with the updated values of the {\it non-relativistic pole masses} re-extracted {\it directly} from the two-loop non-relativistic sum rules: M^{NR}_b= (4.69~^{-0.01}_{+0.02} \pm 0.02) GeV and M^{NR}_c=(1.44\pm 0.02\pm 0.03) GeV. It is also informative to compare the {\it three-loop} values of the short-distance pole masses: M^{PT3}_b=(4.87\pm 0.05 \pm 0.02) GeV and M^{PT3}_c= (1.62\pm 0.07 \pm 0.03) GeV, with the {\it dressed mass} M^{nr}_b = (4.94 \pm 0.10 \pm 0.03) GeV, entering into the {\it non-relativistic Balmer formula} including higher order \alf corrections. The small mass-differences M^{NR}_b-M^{PT2}_b \simeq M^{nr}_b-M^{PT3}_b \simeq 70 MeV and M_c^{NR}-M_c^{PT2} \simeq (30 \pm 20) MeV {\it can measure the size} of the non-perturbative effect induced by {\it renormalon} type-singularities. An analogous analysis is pursued for the heavy-light mesons, where a simultaneous {\it re-fit} of the B and B^* masses from relativistic sum rules leads to: M_b^{PT2}= (4.63 \pm 0.08) GeV,