Bethe-Salpeter equation at leading order in Coulomb gauge

TL;DR

This paper studies the Bethe-Salpeter equation for mesons in Coulomb gauge using a linear potential, revealing insights into chiral symmetry breaking and heavy quark limits through numerical solutions.

Contribution

It introduces a leading order Coulomb gauge approach with a linear potential and contact term, providing a finite formulation and numerical solutions for meson properties.

Findings

Demonstrates how to write equations in terms of finite functions despite infrared singularities.

Shows the pattern of dynamical chiral symmetry breaking.

Reveals the leading order heavy quark limit in the solutions.

Abstract

The Bethe-Salpeter equation and leptonic decay constants for pseudoscalar and vector quark-antiquark mesons with arbitrary quark masses are studied in Coulomb gauge, under a leading order truncation. As input, we use a pure linear rising potential, supplemented by a contact term arising from the conservation of total color charge. It is shown how the equations can be written in terms of manifestly finite functions, despite the infrared singular interaction. The resulting equations are solved numerically. Both the pattern of dynamical chiral symmetry breaking and the leading order heavy quark limit are visible.