Charmonium, $D_s$ and $D_s^*$ from overlap fermion on DWF configurations

TL;DR

This paper introduces a new method to determine fundamental QCD parameters and computes the charmonium and charm-strange meson spectrum using overlap fermions on domain-wall configurations, achieving precise results for quark masses and decay constants.

Contribution

It presents a novel approach combining continuum, chiral, and quark mass extrapolations to accurately determine quark masses, the scale parameter, and meson properties from lattice QCD data.

Findings

Determined charm and strange quark masses with high precision.

Predicted hyperfine splitting of charmonium to be 112 MeV.

Calculated decay constant f_{D_s} as 254 MeV.

Abstract

We take a new approach to determine the scale parameter $r_0$, the physical masses of strange and charm quarks through a global fit which incorporates continuum extrapolation, chiral extrapolation and quark mass interpolation to the lattice data. The charmonium and charm-strange meson spectrum are calculated with overlap valence quarks on $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaboration. We use the masses of $D_s$, $D_s^*$ and $J/\psi$ as inputs and obtain $m_c^{\overline{\rm MS}}(2\,{\rm GeV})=1.110(24)\,{\rm GeV}$, $m_s^{\overline{\rm MS}}(2\,{\rm GeV})=0.104(9)\,{\rm GeV}$ and $r_0=0.458(11)\,{\rm fm}$. Subsequently, the hyperfine-splitting of charmonium and $f_{D_s}$ are predicted to be $112(5)\,{\rm MeV}$ and $254(5)\,{\rm MeV}$, respectively.