Six-meson amplitude in QCD-like theories

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 $\text{SU}(n)\times \text{SU}(n)\mathrm{/}\text{SU}(n)$ (extending the QCD case), $\text{SU}(2n)\mathrm{/}\text{SO}(2n)$, and $\text{SU}(2n)\mathrm{/}\text{Sp}(2n)$. 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 $\text{O}(N+1)\mathrm{/}\text{O}(N)$ 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.