Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice

We present the determination of the interquark potential together with quark kinetic mass m(Q) from the equal-time Q (Q) over bar Bethe-Salpeter amplitude in lattice QCD. Our approach allows us to calculate spin-dependent Q (Q) over bar potentials, e.g., the spin-spin potential, as well. To investigate several systematic uncertainties on such Q (Q) over bar potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, a approximate to 0.093, 0.068, and 0.047 fm, and two different physical volumes, L approximate to 2.2 and 3.0 fm. For heavy quarks, we employ the relativistic heavy quark action, which can control large discretization errors introduced by large quark mass m(Q). The spin-independent central Q (Q) over bar potential for the charmonium system yields the Coulomb plus linear behavior with good scaling and small volume dependence. We explore the quark mass dependence over the wide mass range from the charm to beyond the bottom region and then demonstrate that the spin-independent central Q (Q) over bar potential in the m(Q) -> infinity limit is fairly consistent with the static Q (Q) over bar potential obtained from Wilson loops. The spin-spin potential at finite quark mass provides a repulsive interaction with a finite range, which becomes narrower as the quark mass increases. We also discuss the applicability of the 1/m(Q) expansion approach for the spin-spin potential.