Six-meson amplitude in QCD-like theories

TL;DR

This paper computes the six-meson scattering amplitude at low energy in QCD-like theories with various symmetry breaking patterns, extending previous work and providing analytical expressions for one-loop six-particle amplitudes.

Contribution

It provides the first analytical expressions for six-meson amplitudes in diverse QCD-like theories at next-to-leading order, extending previous models and enabling detailed amplitude analysis.

Findings

Analytical expressions for six-meson subamplitudes derived

Extension of previous O(N) sigma model results to other symmetry patterns

Facilitates study of six-particle properties at one-loop level

Abstract

We calculate the relativistic six-meson scattering amplitude at low energy within the framework of QCD-like theories with $n$ degenerate quark flavors at next-to-leading order in the chiral counting. We discuss the cases of complex, real and pseudo-real representations, i.e. with global symmetry and breaking patterns $\text{SU}(n)\times\text{SU}(n)/\text{SU}(n)$ (extending the QCD case), $\text{SU}(2n)/\text{SO}(2n)$, and $\text{SU}(2n)/\text{Sp}(2n)$. In case of the one-particle-irreducible part, we obtain analytical expressions in terms of 10 six-meson subamplitudes based on the flavor and group structures. We extend on our previous results obtained within the framework of the $\text{O}(N+1)/\text{O}(N)$ non-linear sigma model, with $N$ being the number of meson flavors. This work allows for studying a number of properties of six-particle amplitudes at one-loop level.