Up- and down-quark masses from QCD sum rules

TL;DR

This paper determines the up- and down-quark masses using an optimized QCD Finite Energy Sum Rule, reducing systematic uncertainties and providing precise mass values at 2 GeV.

Contribution

It introduces an optimized FESR approach with reduced systematic uncertainties for quark mass determination in QCD.

Findings

Up-quark mass: (2.6 ± 0.4) MeV at 2 GeV

Down-quark mass: (5.3 ± 0.4) MeV at 2 GeV

Average light-quark mass: (3.9 ± 0.3) MeV at 2 GeV

Abstract

The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: $\bar{m}_u (2\, \mbox{GeV}) = (2.6 \, \pm \, 0.4) \, {\mbox{MeV}}$, $\bar{m}_d (2\, \mbox{GeV}) = (5.3 \, \pm \, 0.4) \, {\mbox{MeV}}$, and the sum $\bar{m}_{ud} \equiv (\bar{m}_u \, + \, \bar{m}_d)/2$, is $\bar{m}_{ud}({ 2 \,\mbox{GeV}}) =( 3.9 \, \pm \, 0.3 \,) {\mbox{MeV}}$.