Meson-meson Scattering in QCD-like Theories

TL;DR

This paper provides analytical calculations of meson-meson scattering amplitudes at high order in chiral perturbation theory for various QCD-like theories with different symmetry breaking patterns, including numerical results and relations between cases.

Contribution

It offers the first complete analytical expressions for meson-meson scattering in QCD-like theories with complex, real, and pseudo-real representations, covering all symmetry breaking patterns.

Findings

Analytical expressions for scattering amplitudes at NNLO.

Derived scattering lengths for different channels.

Identified relations between cases in large n limit.

Abstract

We discuss meson-meson scattering at next-to-next-to-leading order in the chiral expansion for QCD-like theories with general $n$ degenerate flavours for the cases with a complex, real and pseudo-real representation. I.e. with global symmetry and breaking pattern $SU(n)_L\times SU(n)_R\to SU(n)_V$, $SU(2n)\to SO(2n)$ and $SU(2n)\to Sp(2n)$. We obtain fully analytical expressions for all these cases. We discuss the general structure of the amplitude and the structure of the possible intermediate channels for all three cases. We derive the expressions for the lowest partial wave scattering length in each channel and present some representative numerical results. We also show various relations between the different cases in the limit of large $n$.