$a \to \pi \pi \pi$ decay at next-to-leading order in chiral perturbation theory

TL;DR

This paper develops a next-to-leading order chiral perturbation theory framework for axion-pion interactions and calculates the decay rate of a GeV-scale axion-like particle into three pions, highlighting the limits of the effective theory.

Contribution

It constructs the NLO axion-pion effective Lagrangian and evaluates the decay rate, revealing the breakdown of the chiral expansion near the kinematic threshold.

Findings

NLO calculation of axion decay rate into three pions.

Chiral expansion breaks down just above the kinematic threshold.

Non-perturbative methods are needed beyond this point.

Abstract

We discuss the construction of the two-flavour axion-pion effective Lagrangian at the next-to-leading order (NLO) in chiral perturbation theory and present, as a phenomenological application, the calculation of the decay rate of a GeV-scale axion-like particle via the channel $a \to \pi\pi\pi$. Through the NLO calculation, we assess the range of validity of the effective field theory and show that the chiral expansion breaks down just above the kinematic threshold. Alternative non-perturbative approaches are called for in order to extend the chiral description of axion-pion interactions.