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

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.