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We present spin-independent and spin-spin interquark potentials forcharmonium states, that are calculated using a relativistic heavy quark actionfor charm quarks on the PACS-CS gauge configurations generated with the Iwasakigauge action and 2+1 flavors of Wilson clover quark. The interquark potentialwith finite quark masses is defined through the equal-time Bethe-Salpeteramplitude. The light and strange quark masses are close to the physical pointwhere the pion mass corresponds to $M_\pi \approx 156(7)$ MeV, and charm quarkmass is tuned to reproduce the experimental values of $\eta_c$ and $J/\psi$states. Our simulations are performed with a lattice cutoff of $a^{-1}\approx2.2$ GeV and a spatial volume of $(3 {\rm fm})^3$. We solve the nonrelativisticSchr\"odinger equation with resulting charmonium potentials as theoreticalinputs. The resultant charmonium spectrum below the open charm threshold showsa fairly good agreement with experimental data of well-established charmoniumstates.

Potential description of the charmonium from lattice QCD