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We analyze the second-class current decays$\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$ in the framework of ChiralPerturbation Theory with resonances. Taking into account$\pi^{0}$-$\eta$-$\eta^{\prime}$ mixing, the $\pi^{-}\eta^{(\prime)}$ vectorform factor is extracted, in a model-independent way, using existing data onthe $\pi^{-}\pi^{0}$ one. For the participant scalar form factor, we haveconsidered different parameterizations ordered according to their increasingfulfillment of analyticity and unitarity constraints. We start with aBreit-Wigner parameterization dominated by the $a_{0}(980)$ scalar resonanceand after we include its excited state, the $a_{0}(1450)$. We follow by anelastic dispersion relation representation through the Omn\`{e}s integral.Then, we illustrate a method to derive a closed-form expression for the$\pi^{-}\eta$, $\pi^{-}\eta^{\prime}$ (and $K^{-}K^{0}$) scalar form factors ina coupled-channels treatment. Finally, predictions for the branching ratios andspectra are discussed emphasizing the error analysis. An interesting result ofthis study is that both $\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$ decaychannels are promising for the soon discovery of second-class currents atBelle-II. We also predict the relevant observables for the partner$\eta^{(\prime)}_{\ell 3}$ decays, which are extremely suppressed in theStandard Model.

Predictions on the second-class current decays $\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$