Six-pion amplitude

TL;DR

This paper calculates the relativistic six-pion scattering amplitude at low energy within the massive O(N) nonlinear sigma model up to next-to-leading order, providing detailed results for pion properties and four-pion interactions.

Contribution

It extends the chiral perturbation theory calculations to include the six-pion amplitude at next-to-leading order, which was not previously available.

Findings

Six-pion amplitude computed up to p^4 order.

Results for pion mass and decay constant at p^4 order.

Expressions for four-pion amplitude at p^4 order.

Abstract

Within the framework of the massive O($N$) nonlinear sigma model extended to the next-to-leading order in the chiral counting (for $N=3$ corresponding to the two(-quark)-flavor Chiral Perturbation Theory), we calculate the relativistic six-pion scattering amplitude at low energy up to and including terms $\mathcal{O}(p^4)$. Results for the pion mass, decay constant and the four-pion amplitude in the case of $N$ (meson) flavors at $\mathcal{O}(p^4)$ are also presented.