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 $m_q(2\text{GeV})=\frac{1}{2}(m_u(2\text{GeV})+m_d(2\text{GeV}))=(3.46_{-0.22}^{+0.16}\pm 0.33)\text{MeV}$. 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.

Comments: 25 pages,7 figures,2 tables