Résumé
Correlations between the QCD coupling αs, the gluon condensate 〈αsG2〉 and the c, b-quark running masses m̄c,b in the MS¯-scheme are explicitly studied (for the first time) from the (axial-)vector and (pseudo)scalar charmonium and bottomium ratios of Laplace sum rules (LSR) evaluated at the μ-subtraction stability point where perturbative (PT) @N2LO, N3LO and 〈αsG2〉 @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of 〈αsG2〉 from J/ψ sum rule and also show the sensitivity of the sum rules on the choice of the μ-subtraction scale which does not permit a high-precision estimate of m̄c,b. We obtain from the (axial-)vector [respectively (pseudo)scalar] channels: 〈αsG2〉 = (7.4 ± 2.2) [respectively (6.34 ± 0.39)] × 10−2 GeV4, m̄c(m̄c) = 1264(22) [respectively 1266(16)] MeV and m̄b(m̄b) = 4192(15) MeV. Combined with our recent determinations from vector channel, one obtains the average: m̄c(m̄c)|average = 1264(10) MeV and m̄b(m̄b)|average = 4184(9) MeV. Adding the two above values of the gluon condensate to different previous estimates in Table 1, one obtains the 2018 sum rule average: 〈αsG2〉| average = (6.35 ± 0.35) × 10−2 GeV4. The mass-splittings Mχ0c(0b) − Mηc(b) give @N2LO: αs(MZ) = 0.1182(15)(3) in good agreement with the world average.