QCD parameter correlations from heavy quarkonia

Correlations between the QCD coupling [Formula: see text], the gluon condensate [Formula: see text] and the [Formula: see text], [Formula: see text]-quark running masses [Formula: see text] in the [Formula: see text]-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 [Formula: see text]-subtraction stability point where perturbative (PT) @N2LO, N3LO and [Formula: see text] @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of [Formula: see text] from [Formula: see text] sum rule and also show the sensitivity of the sum rules on the choice of the [Formula: see text]-subtraction scale which does not permit a high-precision estimate of [Formula: see text]. We obtain from the (axial-)vector [respectively (pseudo)scalar] channels: [Formula: see text] [respectively [Formula: see text] GeV 4 , [Formula: see text] [respectively 1266(16)] MeV and [Formula: see text] MeV. Combined with our recent determinations from vector channel, one obtains the average: [Formula: see text] MeV and [Formula: see text] MeV. Adding the two above values of the gluon condensate to different previous estimates in Table 1, one obtains the 2018 sum rule average: [Formula: see text] GeV 4 . The mass-splittings [Formula: see text] give @N2LO: [Formula: see text] in good agreement with the world average.