QCD parameters and $f_{B_c}$ from heavy quark sum rules

TL;DR

This paper uses heavy quark sum rules to determine QCD parameters like quark masses, the gluon condensate, and the B_c decay constant, achieving results consistent with world averages and clarifying previous discrepancies.

Contribution

It provides updated and precise determinations of QCD parameters using optimized sum rules and analyzes the sensitivity to the subtraction scale, improving upon prior estimates.

Findings

Determined _s(M_Z)=0.1183(19)(3) in agreement with world average.

Estimated quark masses: m_c(m_c)=1266(6) MeV, m_b(m_b)=4196(8) MeV.

Calculated B_c decay constant: f_{B_c}=371(17) MeV.

Abstract

We report results of our recent works [1,2] where we where the correlations between the c,b-quark running masses{m}_{c,b}, the gluon condensate<\alpha_s G^2> and the QCD coupling \alpha_s in the MS-scheme from an analysis of the charmonium and bottomium spectra and the B_c-meson mass. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the \mu-subtraction stability point where higher orders PT and D< 6-8-dimensions non-perturbative condensates corrections are included. We obtain [1] \alpha_s(2.85)=0.262(9) and \alpha_s(9.50)=0.180(8) from the (pseudo)scalar M_{\chi_{0c(0b)}}-M_{\eta_{c(b)}} mass-splittings at \mu=2.85(9.50) GeV. The most precise result from the charm channel leads to \alpha_s(M_\tau)=0.318(15) and \alpha_s(M_Z)=0.1183(19)(3) in excellent agreement with the world average: \alpha_s(M_Z)=0.1181(11)[3,4]. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO [1] combined with the one from M_{B_c} [2] lead to the new tentative QCD spectral sum rules (QSSR) average : m_c(m_c)|_average= 1266(6) MeV and m_b(m_b)|_average=4196(8) MeV. The values of the gluon condensate <\alpha_s G^2> from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new QSSR average [1]: <\alpha_s G^2>_average=(6.35\pm 0.35)x 10^{-2} GeV^4. 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. As a biproduct, we deduce the B_c-decay constants f_{B_c}=371(17) MeV and f_{B_c}(2S)< 139(6) MeV.