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

Abstract

Direct CP asymmetry in semi-leptonic $τ$ decays is an intriguing hint for new physics beyond the standard model. We investigate the CP asymmetry in $τ^- \to K_S^0 π^- ν_τ$ and $τ^- \to K^- π^0 ν_τ$ 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 $τ\to s \bar u ν_τ$, and accounts for the 2.8 $σ$ discrepancy between the $A_{\rm CP}(τ^- \to K_S^0 π^- ν_τ)$ experimental results and the SM expectation. Furthermore, it predicts a sizable $A_{\rm CP}(τ^- \to K^- π^0 ν_τ)$, of order ${\cal O}(10^{-3})$, which can be accessible in current and near future experiments.