Interquark Potential with Finite Quark Mass from Lattice QCD

We present an investigation of the interquark potential determined from the q (q) over bar Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The q (q) over bar potential at finite quark mass m(q) can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schrodinger equation. The definition of the potential itself requires information about a kinetic mass of the quark. We then propose a self-consistent determination of the quark kinetic mass on the same footing. To verify the proposed method, we perform quenched lattice QCD simulations with a relativistic heavy-quark action at a lattice cutoff of 1/a approximate to 2.1 GeV in a range 1.0 <= m(q) <= 3.6 GeV. Our numerical results show that the q (q) over bar potential in the m(q) -> infinity limit is fairly consistent with the conventional one obtained from Wilson loops. The quark-mass dependence of the q (q) over bar potential and the spin-spin potential are also examined.