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

Abstract

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 $m_c(\mu )$ 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 ${\alpha }_s^{\overline{\mathrm{MS}}(4)}(3\mathrm{GeV})$ = 0.253(13). Dominant source of the error is the truncation of perturbative expansion at ${\alpha }_s^3$.

Comments: 32 pages, 10 figures, 10 tables