Consistent Treatment of Axions in the Weak Chiral Lagrangian

TLDR: In this paper, the authors present a consistent implementation of weak decays involving an axion or axion-like particle in the context of an effective chiral Lagrangian, and derive model-independent results for the decays with axion couplings and mass.

Abstract: We present a consistent implementation of weak decays involving an axion or axionlike particle in the context of an effective chiral Lagrangian. We argue that previous treatments of such processes have used an incorrect representation of the flavor-changing quark currents in the chiral theory. As an application, we derive model-independent results for the decays ${K}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}a$ and ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{e}a$ at leading order in the chiral expansion and for arbitrary axion couplings and mass. In particular, we find that the ${K}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}a$ branching ratio is almost 40 times larger than previously estimated.