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

We study the hadronic form factors of the τ lepton decays τ → K π(η)ν. We compute oneloop corrections to the form factors using the chiral Lagrangian including vector mesons. The counterterms that subtract the divergence of the one-loop amplitudes are determined by using the background field method. In the vector form factor, K ∗ resonance behavior is reproduced because a 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, 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 direct CP violation of the τ decays and predict the CP violation of the forward‐backward asymmetry.