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.