The form factors of tau -> K pi(eta) nu and the predictions for CP violation beyond the standard model

Abstract

We study the hadronic form factors of $τ$ lepton decays $τ\to K π(η) ν$. We compute one loop corrections to the form factors using the chiral Lagrangian including vector mesons. The counterterms which subtract the divergence of the one-loop amplitudes are determined by using background field method. In the vector form factor, $K^\ast$ resonance behavior is reproduced because the diagram with a vector meson propagator is included. We fit the data of the hadronic invariant mass spectrum measured by Belle by determining some of the counterterms of the Lagrangian. Besides the hadronic invariant mass spectrum, the forward-backward asymmetry is predicted. We also study the effect of CP violation of a two Higgs doublet model. In the model, CP violation of the neutral Higgs sector generates the mixing of CP even Higgs and CP odd Higgs. We show how the mixing leads to the direct CP violation of the $τ$ decays and predict the CP violation of the forward-backward asymmetry.