CP Asymmetry in $\tau \to K\pi {\nu }_{\tau }$ 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 $A_{\mathrm{CP}}({\tau }^{-}\to K_S^0{\pi }^{-}{\nu }_{\tau })$ experimental results and the SM expectation. Furthermore, it predicts a sizable $A_{\mathrm{CP}}({\tau }^{-}\to K^{-}{\pi }^0{\nu }_{\tau })$, of order $\mathcal{O}(10^{-3})$, which can be accessible in current and near future experiments.

Comments: 10 pages, 3 figures