Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

TL;DR

This paper advances the calculation of light meson masses by incorporating complex corrections into the Dyson--Schwinger and Bethe--Salpeter equations, surpassing traditional rainbow-ladder truncation for more accurate results.

Contribution

It introduces a Bethe-Salpeter kernel that includes dominant non-Abelian, Abelian, and pion cloud effects, going significantly beyond the rainbow-ladder approximation.

Findings

Sub-leading Abelian corrections are dynamically suppressed.

Results improve upon early qualitative predictions.

Spectrum of light mesons calculated with enhanced accuracy.

Abstract

We investigate masses of light mesons from a coupled system of Dyson--Schwinger (DSE) and Bethe--Salpeter equations (BSE), taking into account dominant non-Abelian, sub-leading Abelian, and dominant pion cloud contributions to the dressed quark-gluon vertex. The axial-vector Ward-Takahashi identity preserving Bethe-Salpeter kernel is constructed and the spectrum of light mesons calculated. Our model goes significantly beyond the rainbow-ladder. We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions from simple truncation schemes.