Potential description of charmonium and charmed-strange mesons from lattice QCD

We present spin-independent and spin-spin interquark potentials for the charmonium and charmed-strange mesons, which are calculated in 2+1 flavor lattice QCD simulations using the PACS-CS gauge configurations generated at the lightest pion mass ($M_\pi \approx 156(7)$~MeV) with a lattice cutoff of $a^{-1}\approx 2.2$ GeV and a spatial volume of $(3~{\rm fm})^3$. For the charm quark, we use a relativistic heavy quark (RHQ) action with fine tuned RHQ parameters, which closely reproduce both the experimental spin-averaged mass and hyper-fine splitting of the $1S$ charmonium. The interquark potential and the quark kinetic mass, both of which are key ingredients within the potential description of heavy-heavy and heavy-light mesons, are determined from the equal-time Bethe-Salpeter (BS) amplitude. The charmonium potentials are obtained from the BS wave function of $1S$ charmonia ($\eta_c$ and $J/\psi$ mesons), while the charmed-strange potential are calculated from the $D_s$ and $D_s^{\ast}$ heavy-light mesons. We then use resulting potentials and quark masses as purely theoretical inputs so as to solve the nonrelativistic Schr\"odinger equation for calculating accessible energy levels of charmonium and charmed-strange mesons without unknown parameters. The resultant spectra below the $D\bar{D}$ and $DK$ thresholds excellently agree with well-established experimental data.