CP Violation in the Cabibbo-suppressed Decay $\tau \to K \pi \nu_{\tau}$ with Polarized $\tau$ Leptons

CP violation from physics beyond the Standard Model (SM) is investigated in the Cabibbo-suppressed decay $\tau\to K\pi\nu_{\tau}$ with polarized $\tau$ leptons, to which both the ${\rm J}^{P}=1^-$ resonance $K^*$ and the $ J^{P}=0^+$ resonance $K^*_0$ 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 $K^*$ and $K^*_0$, and whose magnitudes depend crucially on the $K^*_0$ decay constant, $f_{K^*_0}$. Taking a QCD sum rule estimate of $f_{K^*_0}=45$ 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 model and two SLQ models may be detected with about $10^6$ and $10^7$ $\tau$'s at the $1\sigma$ level