Renormalization group improved determination of light quark masses from Borel-Laplace sum rules

TL;DR

This paper uses an improved renormalization group method with Borel-Laplace sum rules to precisely determine light quark masses, reducing theoretical uncertainties and enhancing convergence of the calculations.

Contribution

It introduces a renormalization group summed perturbation theory (RGSPT) approach that significantly reduces scale dependence and improves convergence in light quark mass determinations.

Findings

Determined $m_s(2 GeV)=104.34_{-4.21}^{+4.23} MeV$

Determined $m_d(2 GeV)=4.21_{-0.45}^{+0.48} MeV$

Determined $m_u(2 GeV)=2.00_{-0.40}^{+0.33} MeV$

Abstract

We determine masses of light quarks ($m_u$,$m_d$,$m_s$) using Borel-Laplace sum rules and renormalization group summed perturbation theory (RGSPT) from the divergence of the axial vector current. The RGSPT significantly reduces the scale dependence of the finite order perturbative series for the renormalization group (RG) invariant quantities such as spectral function, the second derivative of the polarization function of the pseudoscalar current correlator, and its Borel transformation. In addition, the convergence of the spectral function is significantly improved by summing all running logarithms and kinematical $\pi^2$-terms. Using RGSPT, we find $m_s(2 GeV)=104.34_{-4.21}^{+4.23}\hs\MeV$, and $m_d(2 GeV)=4.21_{-0.45}^{+0.48}\hs\MeV$ leading to $m_u(2 GeV)=2.00_{-0.40}^{+0.33}\hs\MeV$.