Determination of the up/down-quark mass within QCD sum rules in the scalar channel

Abstract

In this work, we determine up/down-quark mass m q=u/d in the isoscalar scalar channel from both the Shifman-Vainshtein-Zakharov (SVZ) and the Monte-Carlo-based QCD sum rules. The relevant spectral function, including the contributions from the f 0 (500), f 0 (980) and f 0 (1370) resonances, is determined from a sophisticated U (3) chiral study. Via the traditional SVZ QCD sum rules, we give the prediction to the average light-quark mass m q (2 GeV) = 1 2 (m u (2 GeV) + m d (2 GeV)) = (3.44±0.06±0.31) MeV. Meanwhile, by considering the uncertainties of the input QCD parameters and the spectral functions of the isoscalar scalar channel, we obtain m q (2 GeV) = (3.51 ± 0.14 ± 0.33) MeV from the Monte-Carlo-based QCD sum rules. Both results are perfectly consistent with each other, and nicely agree with the Particle Data Group value within the uncertainties.