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

Understand

We analyze the second-class current decays $\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$ in the framework of Chiral Perturbation Theory with resonances.

• Taking into account $\pi^{0}$-$\eta$-$\eta^{\prime}$ mixing, the $\pi^{-}\eta^{(\prime)}$ vector form factor is extracted, in a model-independent way, using existing data on the $\pi^{-}\pi^{0}$ one.
• For the participant scalar form factor, we have considered different parameterizations ordered according to their increasing fulfillment of analyticity and unitarity constraints.
• We start with a Breit-Wigner parameterization dominated by the $a_{0}(980)$ scalar resonance and after we include its excited state, the $a_{0}(1450)$.