# Predictions on the second-class current decays τ−→π−η(′)ντ

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  π0ηη mixing, the πη() vector form factor is extracted, in a model-independent way, using existing data on the ππ0one. 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 a0(980) scalar resonance and after we include its excited state, the a0(1450). We follow by an elastic dispersion relation representation through the Omn\`{e}s integral. Then, we illustrate a method to derive a closed-form expression for the πη, πη (and KK0) scalar form factors in a coupled-channels treatment. Finally, predictions for the branching ratios and spectra are discussed emphasizing the error analysis. An interesting result of this study is that both τπη()ντ decay channels are promising for the soon discovery of second-class currents at Belle-II. We also predict the relevant observables for the partner η()l3 decays, which are extremely suppressed in the Standard Model.

 Comments: 34 pages, 17 figures Subjects: High Energy Physics – Phenomenology (hep-ph); High Energy Physics – Experiment (hep-ex) Cite as: arXiv:1601.03989 [hep-ph] (or arXiv:1601.03989v1 [hep-ph] for this version)