Axion-like particle-meson production in semileptonic τ decays

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