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

Abstract

CP violation from physics beyond the Standard Model (SM) is investigated in the Cabbibo-suppressed decay $τ\to Kπν_τ$ with polarized $τ$ 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, $τ$ 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 $τ$ 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 $10^7$ $τ$'s at the $1σ$ level.