A Novel Approach in Solving the Spinor-Spinor Bethe-Salpeter Equation

TL;DR

This paper introduces a new numerical method using hyperspherical harmonics to solve the spinor-spinor Bethe-Salpeter equation in Euclidean space, enabling detailed analysis of meson exchange kernels and bound state stability.

Contribution

It presents a novel basis of spin-angular harmonics and a numerical algorithm for solving the Bethe-Salpeter equation, advancing the computational techniques in relativistic bound state problems.

Findings

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

Analysis of bound state stability across scalar, pseudoscalar, and vector channels.

Comparison with non-relativistic and light front dynamics results shows consistency and differences.

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.