Renormalization group improved determination of $\alpha_s$, $m_c$, and $m_b$ from the low energy moments of heavy quark current correlators

TL;DR

This paper uses renormalization group improved perturbation theory with heavy quark sum rules to precisely determine the strong coupling constant and heavy quark masses, reducing theoretical uncertainties.

Contribution

It introduces a stable method using RGSPT for extracting $ ext{alpha}_s$, $m_c$, and $m_b$ from low energy moments with reduced uncertainties.

Findings

$ ext{alpha}_s^{(n_f=5)}(M_Z)=0.1171(7)$

$ar{m}_c=1281.1(3.8)$ MeV

$ar{m}_b=4174.3(9.5)$ MeV

Abstract

We determine $\alpha_s$, $m_c$, and $m_b$ using the relativistic quarkonium sum rule and the renormalization group summed perturbation theory (RGSPT). Theoretical uncertainties, especially originating from the variation of the renormalization scale, are considerably reduced for the higher moments. Our determinations using RGSPT are also found to be stable with respect to the use of $\overline{\text{MS}}$ quark mass for the condensate terms. We obtain $\alpha_s^{\left(n_f=5\right)}(M_Z)=0.1171(7)$, $\overline{m}_c=1281.1(3.8)\hspace{.4mm}\mathrm{MeV}$, and $\overline{m}_b=4174.3(9.5)\hspace{.4mm}\mathrm{MeV}$.