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Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass

We calculate charmonium correlators on the lattice with 2+1-flavors of sea quarks and charm valence quark both described by the Möbius domain-wall fermion. Temporal moments of the correlators are calculated and matched to perturbative QCD formulae to extract the charm quark mass $m_c(μ)$ and strong coupling constant $α_s(μ)$. 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 $m_c(μ)$ and $α_s(μ)$. We obtain $m_\mathrm{c}(3 \mathrm{\ GeV})$ = 1.003(10)~GeV and $α_s^{\bar{\mathrm{MS}}(4)}(3\mathrm{\ GeV})$ = 0.253(13). Dominant source of the error is the truncation of perturbative expansion at $α_s^3$.