QCD Parameters Correlations from Heavy Quarkonia

TL;DR

This paper investigates correlations between QCD parameters using sum rules from heavy quarkonia, providing refined estimates for the gluon condensate and quark masses, and analyzing the impact of scale choices on precision.

Contribution

It offers the first explicit study of QCD parameter correlations from heavy quarkonia sum rules, including higher-order corrections and a comprehensive analysis of scale sensitivities.

Findings

Refined estimates of <α_s G^2> and quark masses m_c, m_b.

Clarification of discrepancies in gluon condensate estimates.

Determination of α_s(M_Z) consistent with world averages.

Abstract

Correlations between the QCD coupling \alpha_s, the gluon condensate < \alpha_s G^2 >, and the c,b-quark running masses m_c,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 \mu-subtraction stability point where PT @N2LO, N3LO and < \alpha_s G^2> @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of < \alpha_s G^2> from J/\psi sum rule but also shows the sensitivity of the sum rules on the choice of the \mu-subtraction scale which does not permit a high-precision estimate of m_c,b. We obtain from the (axial-)vector [resp. (pseudo)scalar] channels <\alpha_s G^2>=(8.5+- 3.0)> [resp. (6.34+-.39)] 10^-2 GeV^4, m_c(m_c)= 1256(30) [resp. 1266(16)] MeV and m_b(m_b)=4192(15) MeV. Combined with our recent determinations from vector channel, one obtains the average: m_c(m_c)= 1263(14) MeV and m_b(m_b) 4184(11) MeV. Adding our value of the gluon condensate with different previous estimates, we obtain the new sum rule average: <\alpha_s G^2>=(6.35+- 0.35) 10^-2 GeV^4. The mass-splittings M_\chi_0c(0b)-M_\eta_c(b) give @N2LO: \alpha_s(M_Z)=0.1183(19)(3) in good agreement with the world average (see more detailed discussions in the section: addendum). .