Quark-anti-quark potentials from Nambu-Bethe-Salpeter amplitudes on lattice

TL;DR

This study derives quark-antiquark potentials from lattice QCD simulations using Nambu-Bethe-Salpeter wave functions, revealing linear plus Coulomb behavior and their dependence on quark mass and channel.

Contribution

It introduces a method to extract anti-q-q potentials from lattice QCD NBS wave functions, extending previous approaches to finite quark masses and different channels.

Findings

Potentials exhibit linear plus Coulomb form.

Dependence of potentials on quark mass and channel.

Consistent results across multiple quark masses.

Abstract

Quark--anti-quark (anti-q-q) potentials with finite quark masses are studied from the anti-q-q Nambu-Bethe-Salpeter (NBS) wave functions in quenched lattice QCD. With the use of a method which has been recently developed in the derivation of nuclear forces from lattice QCD, we derive the anti-q-q potentials from the NBS wave functions. We calculate the anti-q-q NBS wave functions in pseudo-scalar and vector channels for several quark masses. The derived potentials at each quark mass in both channels show linear plus Coulomb form. We also discuss the quark-mass and channel dependence of the anti-q-q potentials.