CP Asymmetry in $τ\to Kπν_τ $ within Non-Minimal $SU(5)$

Abstract: Direct CP asymmetry in semi-leptonic $\tau$ decays is an intriguing hint for new physics beyond the standard model. We investigate the CP asymmetry in $\tau^- \to K_S^0 \pi^- \nu_\tau$ and $\tau^- \to K^- \pi^0 \nu_\tau$ decays in non-minimal SU(5) model, with 45-dimensional Higgs multiplet. We show that the associate color-triplet scalar is a natural example of a scalar leptoquark that mediates the transition $\tau \to s \bar u \nu_\tau$, and accounts for the 2.8 $\sigma$ discrepancy between the $A_{\rm CP}(\tau^- \to K_S^0 \pi^- \nu_\tau)$ experimental results and the SM expectation. Furthermore, it predicts a sizable $A_{\rm CP}(\tau^- \to K^- \pi^0 \nu_\tau)$, of order ${\cal O}(10^{-3})$, which can be accessible in current and near future experiments.