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

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 $$m_q(2 ~\text {GeV})=\frac{1}{2}(m_u(2 ~\text {GeV}) + m_d(2 ~\text {GeV}))=(3.46^{+0.16}_{-0.22} \pm 0.33) ~\text {MeV}$$. Meanwhile, by considering the uncertainties of the input QCD parameters and the spectral functions of the isoscalar scalar channel, we obtain $$m_q (2~\text {GeV}) = (3.44 \pm 0.14 \pm 0.32) ~\text {MeV}$$ 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