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 $$m_{q=u/d}$$ 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 ( 500 ) , $$f_0(980)$$ f 0 ( 980 ) and $$f_0(1370)$$ 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 $$m_q(2 ~\text {GeV})=\frac{1}{2}(m_u(2 ~\text {GeV}) + m_d(2 ~\text {GeV}))=(3.46^{+0.16}_{-0.22} \pm 0.33) ~\text {MeV}$$ m q ( 2 GeV ) = 1 2 ( m u ( 2 GeV ) + m d ( 2 GeV ) ) = ( 3 . 46 - 0.22 + 0.16 ± 0.33 ) MeV . Meanwhile, by considering the uncertainties of the input QCD parameters and the spectral functions of the isoscalar scalar channel, we obtain $$m_q (2~\text {GeV}) = (3.44 \pm 0.14 \pm 0.32) ~\text {MeV}$$ m q ( 2 GeV ) = ( 3.44 ± 0.14 ± 0.32 ) 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.