Charmonium potential from full lattice QCD

Abstract

We present both spin-independent and spin-dependent parts of a central interquark potential for charmonium states, which is calculated in $2+1$ flavor dynamical lattice QCD using the PACS-CS gauge configurations with a lattice cutoff of ${a}^{\ensuremath{-}1}\ensuremath{\approx}2.2\text{ }\text{ }\mathrm{GeV}$. Our simulations are performed with a relativistic heavy-quark action for the charm quark at the lightest pion mass, ${M}_{\ensuremath{\pi}}=156(7)\text{ }\text{ }\mathrm{MeV}$, in a spatial volume of $(3\text{ }\text{ }\mathrm{fm}{)}^{3}$. We observe that the spin-independent charmonium potential obtained from lattice QCD with almost physical quark masses is quite similar to the Cornell potential used in nonrelativistic potential models. The spin-spin potential, which is calculated in full lattice QCD for the first time, properly exhibits a finite-range repulsive interaction. Its $r$-dependence is different from the Fermi-Breit type potential, which is widely adopted in quark potential models.