Abstract :
Using the recent world average αs(Mz2)= 0.118±0.006, we give the first direct extraction from the Ψ and γ data of the values of the running heavy quark masses within QCD spectral sum rules to two-loops in the MS-scheme: mb(MbPT2) = (4.23 −0.04+0.03 ± 0.02) GeV and mc (McPT2) = (1.23 −0.04+0.02 ± 0.03) GeV, (the errors are respectively due to αs to the gluon condensate), and the corresponding value of the short-distance perturbative pole masses to two-loops:MbPT2 = 4.62 ±0.02) GeV, McPT2 = (1.42±0.03) GeV, which we compare with the updated values of the non-relativistic pole masses re-extracted directly from the two-loop non-relativistic sum rules: MbNR = (4.69−0.01+0.02±0.02) GeV and McNR = = (1.45−0.03+0.04±0.03) GeV. It is also informative to compare the three-loop values of the short-distance pole masses: MbPT3 = (4.87±0.05±0.02) GeV and McPT3 = (1.64−0.07+0.10±0.03) GeV, with the dressed mass Mbnr = (4.94±0.10±0.03) GeV, entering into the non-relativistic Balmer formula including higher order αs corrections. The small mass-differences MbNRMbPT2≅MbnrMbPT3≅70 MeV and McNR−McPT2≅(30±30) MeV can measure the size of the non-perturbative effect induced by renormalon type- singularities. Finally, the b and c quark-pole mass difference is found to be: δMbcMbMc = (3.22±0.03) Gev. An analogous analysis is pursued for the heavy-light mesons, where a simultaneous re-fit of the B and B∗ masses from relativistic sum rules leads to: MbPT2 = (4.63±0.08) GeV, while the average of the results from full-QCD and HQET sum rules in the large mass limit gives the meson-quark mass difference to two-loops: δMb∞Λ(MBMbNR)∞≅(0.58±0.05) GeV. A comparison of these new and accurate results with the existing ones in the literature is done. As a consequence, the updated values of the pseudoscalar decay constants to two-loops are: ƒD=(1.35±0.04±0.06) ƒπ and ƒB=(1.49±0.06±0.05)ƒπ, which lead to 7z.hfl;BBB=(1.49±0.14)ƒπ.
