Solving the Bethe-Salpeter equation for a pseudoscalar meson in Minkowski space

TL;DR

This paper introduces a novel method to solve the Bethe-Salpeter equation for pseudoscalar mesons directly in Minkowski space using integral representations, allowing for more realistic modeling of quark-antiquark bound states.

Contribution

It presents a new approach that incorporates Green's function dressing and potential running coupling effects directly in Minkowski space.

Findings

Initial numerical results in ladder approximation

Method naturally includes Green's function dressing

Potential to incorporate running coupling constants

Abstract

A new method of solution of the Bethe-Salpeter equation for a pseudoscalar quark-antiquark bound state is proposed. With the help of an integral representation, the results are directly obtained in Minkowski space. Dressing of Green's functions is naturally taken into account, thus providing the possible inclusion of a running coupling constant as well as quark propagators. First numerical results are presented for a simplified ladder approximation.