Résumé
Explicit studies [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison, addendum (to appear in Int. J. Mod. Phys. A).] of the correlations between the c , b -quark running masses m‾c,b , the gluon condensate 〈αsG2〉 and the QCD coupling αs in the MS‾ -scheme from a global fit of charmonium and bottomium spectra are reviewed. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the μ -subtraction stability point where higher orders PT and D≤6−8 -dimensions non-perturbative condensates corrections are included. Our results clarify the (apparent) discrepancies between different estimates of 〈αsG2〉 from J/ψ sum rule but also shows the sensitivity of the sum rules on the choice of the μ -subtraction scale which does not permit a high-precision estimate of m‾c,b from the alone vector channel. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO lead to: m‾c(m‾c)|average=1264(6)MeV and m‾b(m‾b)|average=4190(8)MeV . The values of the gluon condensate 〈αsG2〉 from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new sum rule average : 〈αsG2〉|average=(6.35±0.35)×10−2GeV4 . The (pseudo)scalar mass-splittings Mχ0c(0b)−Mηc(b) allow to predict the QCD coupling αs at two different scales: αs(2.85)=0.262(9) for the charm and αs(9.50)=0.180(8) for the bottom. The strongest one from Mχ0c−Mηc leads to: αs(Mτ)=0.318(15)⇝αs(MZ)=0.1183(19)(3) in good agreement with the world average: αs(MZ)=0.1181(11) [For a review, see e.g: S. Bethke, Nucl. Part. Phys. Proc. 282–284 (2017) 149; PDG, C. Patrignani et al. (Particle Data Group), Chin. Phys. C40, 100001 (2016) and 2017 update.].