QCD Parameters Correlations from Heavy Quarkonia

Abstract

Correlations between the QCD coupling α_s, the gluon condensate < α_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 μ-subtraction stability point where PT @N2LO, N3LO and < α_s G^2> @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of < α_s G^2> from J/ψsum 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. We obtain from the (axial-)vector [resp. (pseudo)scalar] channels <α_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: <α_s G^2>=(6.35+- 0.35) 10^-2 GeV^4. The mass-splittings M_χ_0c(0b)-M_η_c(b) give @N2LO: α_s(M_Z)=0.1183(19)(3) in good agreement with the world average (see more detailed discussions in the section: addendum). .

22 pages, 1 Table, 16 Figures. Extended version of talks presented at QCD 17 (Montpellier-FR) and HEPMAD 16/17 (Antananarivo-MG). New Addendum where more detailed discussions on the extraction of alpha_s from the M_χ_0c(0b)-M_η_c(b) mass-splittings are given

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