Axion-like particle-meson production in semileptonic $\tau$ decays

Abstract

In this work we explore the semileptonic $\tau$ decays into the axion-like particle ($a$)-meson final states within chiral effective field theory. The next-to-leading-order mixing matrix for the $\pi^0$-$\eta$-$\eta'$-$a$ system with the linear isospin-breaking effects, is exploited and then implemented to calculate the hadronic form factors relevant to the $\tau$ decays. The resonance parameters entering the form factors are determined from fits to the experimental spectra of $\tau^- \to \pi^- \pi^0 \nu_\tau$, $\tau^- \to K_S \pi^- \nu_\tau$, and $\tau^- \to K^- \eta \nu_\tau$. We then focus on the predictions to the branching ratios, invariant-mass distributions, and forward-backward asymmetries from the $\tau^-\to P a \nu_\tau$ processes, with $P=\pi^-$ and $K^-$. Our results provide a quantitative basis for future searches of the axion-like particle signals in semileptonic $\tau$ decays.