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

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.

Comments: 21 pages, 2 figures. Mistake in the definition of the quark mass matrix corrected. Main conclusions unchanged