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

D Kimura,T Morozumi,K Y Lee

doi:10.1093/ptep/ptt013

Abstract

We study the hadronic form factors of the τ lepton decays |$\tau \rightarrow K \pi (\eta) \nu $|⁠. We compute one-loop 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.

Highlights

The tau hadronic decays are unique as the decays can be useful for the search for the new CP violation beyond the standard model [1,2,3,4,5,6,7,8,9,10,11,12]
Babar [16] searched CP violation of τ → Ksπ−ν(n)π0 (n > 0) and obtains non-zero CP asymmetry which sign is opposite to the standard model prediction [17],[18]
We show the CP violation of the type II two Higgs doublet model can be probed by the direct CP violation of the τ hadronic decays

Summary

INTRODUCTION

The tau hadronic decays are unique as the decays can be useful for the search for the new CP violation beyond the standard model [1,2,3,4,5,6,7,8,9,10,11,12]. To predict the direct CP violation of the hadronic τ decays, the strong phase shifts are important quantities and the quantitative prediction on the strong phase shifts is necessary when extracting the weak CP violating phases from the experimentally observed CP asymmetries [6, 10, 11] This is a reason why we study the hadronic form factors. One loop corrections to the SU(2) vector form factor are studied with the resonance chiral theory in [21]. By using the chiral Lagrangian including vector resonance [27], we compute the one loop corrections of pseudoscalar mesons to the form factors. We give some details of the derivation of the formulae used in the text

CHIRAL LAGRANGIAN WITH VECTOR MESONS

NUMERICAL ANALYSIS IN THE SM

TWO HIGGS DOUBLET MODEL WITH CP VIOLATION

SUMMARY AND CONCLUSION