QCD parameter correlations from heavy quarkonia

Abstract

Correlations between the QCD coupling αs, the gluon condensate (αsG2) and the c, b-quark running masses mc,b in the MS̄-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/ 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 mc,b. We obtain from the (axial-)vector [respectively (pseudo)scalar] channels: (αsG2) = (7.4 ± 2.2) [respectively (6.34 ± 0.39)] × 10-2 GeV4, mc(mc) = 1264(22) [respectively 1266(16)] MeV and mb(mb) = 4192(15) MeV. Combined with our recent determinations from vector channel, one obtains the average: mc(mc)|average = 1264(10) MeV and mb(mb)|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 M0c(0b)-Mc(b) give @N2LO: αs(MZ) = 0.1182(15)(3) in good agreement with the world average.