Up- and down-quark masses from finite-energy QCD sum rules to five loops

Abstract

The up- and down-quark masses are determined from an optimized QCD finite-energy sum rule involving the correlator of axial-vector divergences, to five-loop order in perturbative QCD, and including leading nonperturbative QCD and higher order quark-mass corrections. This finite-energy sum rule is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3--4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of contour improved perturbation theory, which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window ${s}_{0}=1.0--4.0\text{ }\text{ }{\mathrm{GeV}}^{2}$, where ${s}_{0}$ is the radius of the integration contour in the complex energy (squared) plane. The results are ${m}_{u}(Q=2\text{ }\text{ }\mathrm{GeV})=2.9\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{MeV}$, ${m}_{d}(Q=2\text{ }\text{ }\mathrm{GeV})=5.3\ifmmode\pm\else\textpm\fi{}0.4\text{ }\text{ }\mathrm{MeV}$, and $({m}_{u}+{m}_{d})/2=4.1\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{MeV}$ (at a scale $Q=2\text{ }\text{ }\mathrm{GeV}$).