Mass spectra of heavy pseudoscalars using instantaneous Bethe-Salpeter equation with different kernels

TL;DR

This paper calculates the mass spectra of heavy pseudoscalar mesons using the instantaneous Bethe-Salpeter equation with various kernels derived from different gauge choices, revealing gauge-dependent mass splitting patterns.

Contribution

It introduces a comparative analysis of mass spectra obtained from Bethe-Salpeter equations with different gauge-based kernels for heavy pseudoscalars.

Findings

Smallest mass splitting in time-component Coulomb gauge.

Largest mass splitting in Feynman and Coulomb gauges.

Intermediate splitting in Landau gauge.

Abstract

We solved the instantaneous Bethe-Salpeter equation for heavy pseudoscalars in different kernels, where the kernels are obtained using linear scalar potential plus one gluon exchange vector potentials in Feynman gauge, Landau gauge, Coulomb gauge and time-component Coulomb gauge. We obtained the mass spectra of heavy pseudoscalars, and compared the results between different kernels, found that using the same parameters we obtain the smallest mass splitting in time-component Coulomb gauge, the similar largest mass splitting in Feynman and Coulomb gauges, middle size splitting in Landau gauge.