Two-Fermion Bound States within the Bethe-Salpeter Approach

TL;DR

This paper introduces a new hyperspherical harmonic-based method to solve the Bethe-Salpeter equation for two-fermion bound states, providing detailed analysis and comparisons with non-relativistic and light-front results.

Contribution

A novel hyperspherical harmonic approach for solving the Bethe-Salpeter equation with a new basis of spin-angular harmonics and an efficient numerical algorithm.

Findings

Successful solution of the Bethe-Salpeter equation for various meson exchange kernels.

Analysis of bound state stability across different interaction types.

Comparison showing relativistic and non-relativistic results align in certain regimes.

Abstract

To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is suitable for a representation of the vertex functions. We present a numerical algorithm to solve the Bethe-Salpeter equation and investigate in detail the properties of the solution for the scalar, pseudoscalar and vector meson exchange kernels including the stability of bound states. We also compare our results to the non relativistic ones and to the results given by light front dynamics.