Short-distance charmonium correlator on the lattice with M\"obius domain-wall fermion and a determination of charm quark mass

TL;DR

This study uses lattice QCD with M"obius domain-wall fermions to compute charmonium correlators, enabling precise extraction of the charm quark mass and strong coupling constant by matching lattice data with perturbative QCD.

Contribution

The paper introduces a lattice QCD calculation of charmonium correlators with M"obius domain-wall fermions and determines charm quark mass and coupling constants with continuum extrapolation.

Findings

Charm quark mass at 3 GeV: 1.003(10) GeV

Strong coupling constant at 3 GeV: 0.253(13)

Correlators agree with experimental data in the vector channel

Abstract

We calculate charmonium correlators on the lattice with 2+1-flavors of sea quarks and charm valence quark both described by the M\"obius domain-wall fermion. Temporal moments of the correlators are calculated and matched to perturbative QCD formulae to extract the charm quark mass $m_c(\mu)$ and strong coupling constant $\alpha_s(\mu)$. Lattice data at three lattice spacings, 0.044, 0.055, and 0.080~fm, are extrapolated to the continuum limit. The correlators in the vector channel are confirmed to be consistent with the experimental data for $e^+e^-\to c\bar{c}$, while the pseudo-scalar channel is used to extract $m_c(\mu)$ and $\alpha_s(\mu)$. We obtain $m_\mathrm{c}(3 \mathrm{\ GeV})$ = 1.003(10)~GeV and $\alpha_s^{\bar{\mathrm{MS}}(4)}(3\mathrm{\ GeV})$ = 0.253(13). Dominant source of the error is the truncation of perturbative expansion at $\alpha_s^3$.