Three-pion scattering in Chiral Perturbation Theory

TL;DR

This paper calculates the relativistic six-pion scattering amplitude at low energy within Chiral Perturbation Theory, extending previous models to next-to-leading order and providing expressions for related pion properties.

Contribution

It provides the first calculation of the six-pion scattering amplitude at $ ext{O}(p^4)$ in the massive $ ext{O}(N)$ nonlinear sigma model, including for the specific case of two-flavor Chiral Perturbation Theory.

Findings

Relativistic six-pion scattering amplitude derived at $ ext{O}(p^4)$.

Expressions for pion mass, decay constant, and four-pion amplitude at $ ext{O}(p^4)$.

Abstract

We present the results on the relativistic six-pion scattering amplitude at low energy, calculated at $\mathcal{O}(p^4)$ within the framework of the massive $\text{O}(N)$ nonlinear sigma model extended to the next-to-leading order in the chiral counting. For $N=3$, this approach corresponds to the two(-quark)-flavor Chiral Perturbation Theory. We also present the expressions for the pion mass, pion decay constant and the four-pion amplitude in the case of $N$ (meson) flavors at $\mathcal{O}(p^4)$.