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

Fang-Hui Yin; Wen-Ya Tian; Liang Tang; Zhi-Hui Guo

doi:10.1140/epjc/s10052-021-09599-3

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 818
https://doi.org/10.1140/epjc/s10052-021-09599-3

Regular Article - Theoretical Physics

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

Fang-Hui Yin¹, Wen-Ya Tian¹, Liang Tang¹^c and Zhi-Hui Guo²^d

¹ College of Physics and Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, 050024, Shijiazhuang, China
² School of Physics, Southeast University, 211189, Nanjing, China

^c tangl@hebtu.edu.cn
^d zhguo@seu.edu.cn

Received: 11 May 2021
Accepted: 28 August 2021
Published online: 15 September 2021

Abstract

In this work, we determine up/down-quark mass $m_{q = u / d}$ $m_{q=u/d}$ 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 $f_{0} (500)$ $$f_0(500)$$ , $f_{0} (980)$ $$f_0(980)$$ and $f_{0} (1370)$ $$f_0(1370)$$ 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 $m_{q} (2 GeV) = \frac{1}{2} (m_{u} (2 GeV) + m_{d} (2 GeV)) = (3 . 46_{- 0.22}^{+ 0.16} \pm 0.33) MeV$ $m_q(2 ~\text {GeV})=\frac{1}{2}(m_u(2 ~\text {GeV}) + m_d(2 ~\text {GeV}))=(3.46^{+0.16}_{-0.22} \pm 0.33) ~\text {MeV}$ . Meanwhile, by considering the uncertainties of the input QCD parameters and the spectral functions of the isoscalar scalar channel, we obtain $m_{q} (2 GeV) = (3.44 \pm 0.14 \pm 0.32) MeV$ $m_q (2~\text {GeV}) = (3.44 \pm 0.14 \pm 0.32) ~\text {MeV}$ 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.

© The Author(s) 2021

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