Interquark potential with finite quark mass from lattice QCD

TL;DR

This study develops a method to determine the interquark potential at finite quark mass from lattice QCD, verifying it through simulations and comparing with traditional approaches, revealing mass dependence and spin effects.

Contribution

A self-consistent method to extract the qq̄ potential at finite quark mass from lattice QCD using the Bethe-Salpeter amplitude is proposed and validated.

Findings

The qq̄ potential at infinite quark mass matches Wilson loop results.

The quark mass dependence of the potential is characterized.

Spin-spin potential shows notable mass dependence.

Abstract

We present an investigation of the interquark potential determined from the qq^bar Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The qq^bar potential at finite quark mass m_q can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schr\"odinger 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 ~ 2.1 GeV in a range of the quark kinetic mass, 1.0 {\ge} m_q {\ge} 3.6 GeV. Our numerical results show that the qq^bar potential in the infinitely heavy quark limit (m_q -> {\infty}) is fairly consistent with the conventional one obtained from Wilson loops. The quark mass dependence of the qq^bar potential and the spin-spin potential are also examined.