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arXiv · 1705.00397

Constraint on the light quark mass $m_q$ from QCD Sum Rules in the $I=0$ scalar channel

Jia-Min Yuan·Zhu-Feng Zhang·T. G. Steele·Hong-Ying Jin·Zhuo-Ran Huang
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Abstract

In this paper, we reanalyze the $I=0$ scalar channel with the improved Monte-Carlo based QCD sum rules, which combines the rigorous H\"older-inequality-determined sum rule window and a two Breit-Wigner type resonances parametrization for the phenomenological spectral density that satisfies the 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 $m_q(2\,\textrm{GeV})$ = $\frac{1}{2}(m_u(2\,\textrm{GeV})$ + $m_d(2\,\textrm{GeV}))$ = $4.7^{+0.8}_{-0.7}\,\textrm{MeV}$, which is consistent with the PDG (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 $0.64-0.83$ GeV and $0.40-0.48$ GeV respectively.

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Jia-Min Yuan, Zhu-Feng Zhang, T. G. Steele, Hong-Ying Jin, Zhuo-Ran Huang. 2017-05-01. Constraint on the light quark mass $m_q$ from QCD Sum Rules in the $I=0$ scalar channel. https://doi.org/10.1103/physrevd.96.014034

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