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

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 \(\overline{m}_b=4174.3(9.5)\hspace{.4mm}\mathrm{MeV}\).