# Strong coupling constant and heavy quark masses in 2+1 flavor QCD

## TL;DR

This paper accurately determines the strong coupling constant and heavy quark masses in 2+1 flavor QCD using lattice calculations with multiple lattice spacings, providing precise values for fundamental parameters in particle physics.

## Contribution

The study introduces a novel analysis using up to eleven lattice spacings for continuum extrapolation, improving precision in determining QCD parameters.

## Key findings

- Determined $ar{MS}$ strong coupling constant at four low-energy scales.
- Calculated charm quark mass as 1.265 GeV.
- Calculated bottom quark mass as 4.188 GeV.

## Abstract

We present a determination of the strong coupling constant and heavy quark masses in (2+1)-flavor QCD using lattice calculations of the moments of the pseudo-scalar quarkonium correlators at several values of the heavy valence quark mass with Highly Improved Staggered Quark (HISQ) action. We determine the strong coupling constant in the $\overline{MS}$ scheme at four low-energy scales corresponding to $m_c$, $1.5m_c$, $2m_c$, and $3m_c$, with $m_c$ being the charm quark mass. The novel feature of our analysis that up to eleven lattice spacings are used in the continuum extrapolations, with the smallest lattice spacing being $0.025$ fm. We obtain $\Lambda_{\overline{MS}}^{n_f=3}=298 \pm 16$ MeV, which is equivalent to $\alpha_s(\mu=M_Z,n_f=5)=0.1159(12)$. For the charm and bottom quark masses in the $\overline{MS}$ scheme, we obtain: $m_c(\mu=m_c,n_f=4)=1.265(10)$ GeV and $m_b(\mu=m_b,n_f=5)=4.188(37)$ GeV.