A New Basis Function Approach to 't Hooft Equation

TL;DR

This paper introduces new basis functions for solving the 't Hooft equation in SU(N_C) gauge theories, providing accurate approximations of wave functions and an analytic formula for the lightest bound state mass, aligning with previous findings.

Contribution

The paper proposes a novel basis function approach to solve the 't Hooft equation, enhancing analytical and numerical understanding of mesonic bound states in gauge theories.

Findings

Wave functions are well approximated by the new basis functions.

An analytic formula for the lightest bound state mass is derived.

Results are consistent with previous studies.

Abstract

We present the new basis functions to investigate the 't Hooft equation, the lowest order mesonic Light-Front Tamm-Dancoff equation for $\rm SU(N_C)$ gauge theories. We find the wave function 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.