τ→ Ｋ πν decays and CP violation

τ→ Ｋπν decays and CP violation Kang Young Lee: KAIST D. Kimura, K. Nakagawa, T. Morozumi: Hiroshima Univ. Oct. 25 (Thu.)

1. Motivation There are a lot of data of τ＋τ－pairs obtained from B experiments, ・ Belle (KEK) ・ BaBar (SLAC) We consider direct CP violation of semileptonic τdecays, ⇔ CP violation ? Finally, we estimate CP asymmetry based on MSSM.

2. Model We pay attention to Tree diagrams } } + } } SM: CP is conserved (g is real) MSSM If g’ (or g’’ ) can be complex, there is a possibility which the CP symmetry is violated.

A. Pilaftsis, C.E.M. Wagner, Nucl. Phys. B553, 3 (1999) Two Higgs doublet model j denotes the generation indices. ξis a global U(1) symmetry which the conformal invariant part of the model possesses. v1 and v2 are the moduli of the vacuum expectation values. v1, v2 and ξcan be determined by the minimum of the potential.

After diagonalization of mass matrices, where me is real, When ξ’ is not 0, there is the possibility which CP asymmetry can be observed. } }

⇒ Four fermi interactions for +

3. Decay amplitude where } F and Fs are the form factors defined as } We use F and Fs as a result of the chiral perturbation theory in the one loop approximation. J. Gasser and H. Leutwyler, Nucl. Phys. B250, 465 (1985)

To compare the CP asymmetry for tau decays we calculate the differential decay rate with the tau spin vector s An eigenvalue for the spin operator is defined as In the τrest frame : The angles α and φ

The squared decay amplitude If one can know the tau spin, CP asymmetry can be extracted. Next we move to the CM frame of K－and π0 to estimate the CP asymmetry.

4. Differential decay rate Here, Wλ has three independent amplitudes corresponding to the angular momentum of Kπ system as (L, |Lz|) : (1, 0) (1, 1) (0, 0) CP asymmetry is caused by the interference between (1,0) and (0,0), (1,1) and (0,0). Where l(Q2) is K－momentum in the CM frame of hadrons.

We want to evaluate CP asymmetry using Wλ When is real, CP is invariant

5. Numerical result of differential decay rate We introduce strong phase δst and CP violating phase θw 1/2π

5. Summary ・ We have studied τ→ Ｋπν decays and it’s CP violation with the two doublet Higgs model. ・ We point out that there is a possibility to observe the CP asymmetry.

τ→ Ｋ πν decays and CP violation