Towards the (Mexican) discovery of second class currents at Belle-II

Within the SM, the yet unmeasured $τ^-\toπ^-η^{(\prime)}ν_τ$ decays are predicted as a suppressed, isospin-violating effect with branching ratios $\lesssim\mathcal{O}(10^{-5})$. However, they can also proceed through other mechanisms (such as charged Higgs exchange) at comparable rates. This has motivated several studies of the corresponding QCD predictions for these second class current processes. In this contribution we discuss the prospects for the discovery of these decays at Belle-II emphasizing the Mexican involvement in this project. Our branching ratio prediction $\sim1.7\cdot10^{-5}$ (decay channel with an $η$ meson) is well within the reach of Belle-II. The branching fraction for the decay channel with an $η^\prime$ meson is expected to be between one and two orders of magnitude more suppressed.

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