The volume dependence of the long-range two-body potentials in various color channels by lattice QCD

TL;DR

This study uses lattice QCD simulations to analyze how the confining forces between two quarks depend on their color charge, revealing differences in potential strength and divergence behavior across color channels.

Contribution

It provides the first detailed lattice QCD analysis of the volume dependence of two-body potentials across various color channels, highlighting the divergence in non-singlet channels.

Findings

Color-singlet and antitriplet potentials are attractive with a string tension ratio of about 2.

Color-octet and sextet channels contribute minimally to the two-quark potential.

Infrared self-energy diverges in non-singlet channels as volume increases, consistent with color factors.

Abstract

We study the color-dependent confining forces between two quarks by the quenched lattice simulations of Coulomb gauge QCD. The color-singlet and color-antitriplet instantaneous potentials yield attractive forces. The ratio of the string tensions obtained from them is approximately 2 and have little volume dependence. Meanwhile, the color-octet and color-sextet channels give a minor contribution for two-quark system. We finally find that the infrared self-energy of the color-nonsinglet channels diverges in the infinite volume limit; however, the degree of the divergence on the finite lattice can be understood in terms of color factors.