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 pseudoreal representations, i.e. with global symmetry and breaking patterns SU (n )×SU (n )/SU (n ) (extending the QCD case), SU (2 n )/SO (2 n ), and SU (2 n )/Sp (2 n ). In case of the one-particle-irreducible part, we obtain analytical expressions in terms of ten six-meson subamplitudes based on the flavor and group structures. We extend on our previous results obtained within the framework of the O (N +1 )/O (N ) nonlinear 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.