QCD sum rule determination of the charm-quark mass

TL;DR

This paper uses optimized QCD sum rules with specific kernels to accurately determine the charm-quark mass in the ar scheme, reducing uncertainties from experimental data and resonance contributions.

Contribution

It introduces a novel integration kernel that enhances resonance contributions and minimizes sensitivity to data uncertainties in charm-quark mass determination.

Findings

Charm-quark mass ar(3 GeV) = 987 b1 9 MeV

Reduced sensitivity to the choice of s_0 and experimental uncertainties

Effective use of mixed inverse moment kernels in QCD sum rules

Abstract

QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the $\bar{MS}$ scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form $p(s) = 1 - (s_0/s)^2$, where $s_0$ is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range $s \simeq 20 - 25 GeV^2$. This feature leads to a substantial reduction in the sensitivity of the results to changes in $s_0$, as well as to a much reduced impact of the experimental uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the $\bar{MS}$ scheme at a scale of 3 GeV is $\bar{m}_c (3 GeV) = 987 \pm 9 MeV$, where the error includes all sources of uncertainties added in quadrature.