In this paper, we reanalyze the $I=0$ scalar channel with the improved Monte-Carlo-based QCD sum rules, which combines the rigorous Hölder-inequality-determined sum rule window and a parametrization with two-Breit-Wigner-type resonances for the phenomenological spectral density that satisfies the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances $\sigma$ and $f_0(980)$, we obtain a prediction for light quark mass $m_q(2\mathrm{GeV})=\frac{1}{2}(m_u(2\mathrm{GeV})+m_d(2\mathrm{GeV}))={4.7}_{-0.7}^{+0.8}\mathrm{MeV}$, which is consistent with the Particle Data Group value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of $\sigma$ and $f_0(980)$ at 2 GeV, which are approximately 0.64–0.83 and 0.40–0.48 GeV, respectively.

• Received 4 May 2017

DOI:https://doi.org/10.1103/PhysRevD.96.014034