Renormalization Group Improvement and QCD Sum Rules

TL;DR

This paper refines the determination of light and heavy quark masses and the strong coupling constant using QCD sum rules with renormalization group improvements, providing updated precise values based on experimental data.

Contribution

It introduces a renormalization group improved approach to QCD sum rules for more accurate extraction of quark masses and the strong coupling constant.

Findings

Precise values for u, d, s quark masses at 2 GeV.

Determination of strong coupling constant $\alpha_s(M_Z)$ as 0.1171.

Heavy quark masses for charm and bottom quarks.

Abstract

We summarize the results obtained for the quark masses (u,d,s,c, and b) in Refs.~\cite{AlamKhan:2023ili,AlamKhan:2023kgs} and strong coupling ($\alpha_s$) using renormalization group (RG) improvement of the theoretical expressions and experimental inputs that enter in the QCD sum rules. We obtain $m_{u}(2 GeV)=2.00_{-0.40}^{+0.33}$ MeV, $m_{d}(2 GeV)=4.21_{-0.45}^{+0.48}$ MeV, and $m_{s}(2 GeV)=104.34_{-4.24}^{+4.32}$ MeV using Borel Laplace sum rules for the divergence of the axial vector currents. The relativistic sum rules for the moments of the heavy quark currents lead to the determination of $\alpha_s(M_Z)=0.1171(7)$, $\overline{m}_{c}=1281.1(3.8)$ MeV and $\overline{m}_{b}=4174.3(9.5)$ MeV.