# Bethe-Salpeter studies of mesons beyond rainbow-ladder

## TL;DR

This study advances the understanding of light meson masses by solving coupled Dyson-Schwinger and Bethe-Salpeter equations beyond rainbow-ladder approximation, including complex momentum dependencies and unquenching effects, revealing the impact of various corrections.

## Contribution

It introduces a comprehensive numerical approach that fully incorporates momentum dependencies and corrections beyond rainbow-ladder, improving meson mass predictions.

## Key findings

- Sub-leading Abelian corrections are dynamically suppressed.
- Results surpass early qualitative predictions with simpler schemes.
- Inclusion of unquenching effects influences meson properties.

## Abstract

We investigate the masses of light mesons from a coupled system of Dyson-Schwinger and Bethe-Salpeter equations. The dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex are explicitly taken into account. We also include unquenching effects in the form of hadronic resonance contributions via the back-reaction of pions. We construct the corresponding Bethe--Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the relative impact of different corrections beyond rainbow-ladder on the properties of mesons. We find that sub-leading Abelian corrections are further suppressed dynamically, and that our results supersede early qualitative predictions with significantly simpler truncation schemes.