CP Violation in the Cabbibo-suppressed Decay Tau->K Pi Nu_tau with Polarized Tau Leptons

CP violation from physics beyond the Standard Model (SM) is investigated in the Cabbibo-suppressed decay $\tau \to K\pi {\nu }_{\tau }$ with polarized $\tau$ leptons, to which both the ${\mathrm{J}}^P=1^{-}$ resonance $K^{\ast }$ and the $J^P=0^{+}$ resonance $K_0^{\ast }$ contribute. In addition to the CP-odd rate asymmetry, $\tau$ polarization enables us to construct three additional CP-odd polarization asymmetries that can be enhanced due to the interference between the $K^{\ast }$ and $K_0^{\ast }$, and whose magnitudes depend crucially on the $K_0^{\ast }$ decay constant, $f_{K_0^{\ast }}$. Taking a QCD sum rule estimate of $f_{K_0^{\ast }}=45$ MeV and the present experimental constraints on the CP-odd parameters into account, we estimate quantitatively the maximally-allowed values for the CP-odd rate and polarization asymmetries in the multi-Higgs-doublet (MHD) model and the scalar-leptoquark (SLQ) models consistent with the SM gauge symmetry where neutrinos are massless and left-handed as in the SM. We find that the CP-odd rate and polarization asymmetries are of a similar size for highly-polarized $\tau$ leptons and, for their maximally-allowed values, CP violation in the MHD model and two SLQ models may be detected with about ${10}^6$ and ${10}^7$ $\tau$’s at the $1\sigma$ level.