A New Basis Function Approach to 't Hooft-Bergknoff-Eller Equations

TL;DR

This paper introduces a new basis function method to analytically and numerically solve the 't Hooft-Bergknoff-Eller equations, providing accurate mass predictions for the lightest mesonic bound state in gauge theories.

Contribution

It proposes a novel basis function approach that improves the approximation of wavefunctions and yields an analytic formula for meson mass in light-front gauge theories.

Findings

Wavefunctions are well approximated by new basis functions

Analytic formula for the lightest meson mass obtained

Results are consistent with previous studies

Abstract

We analytically and numerically investigate the 't Hooft-Bergknoff-Eller equations, the lowest order mesonic Light-Front Tamm-Dancoff equations for U(N_C) and SU(N_C) gauge theories. We find the wavefunction can be well approximated by new basis functions and obtain an analytic formula for the mass of the lightest bound state. Its value is consistent with the precedent results.