1

τ→ Ｋ πν decays and CP violation

Kang Young Lee: KAISTD. Kimura, K. Nakagawa, T. Morozumi: Hiroshima Univ.

Oct. 25 (Thu.)

2

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.

3

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.

4

Two Higgs doublet model

j denotes the generation indices.

A. Pilaftsis, C.E.M. Wagner, Nucl. Phys. B553, 3 (1999)

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 minimumof the potential.

5

After diagonalization of mass matrices,

where me is real,

}}

When ξ’ is not 0, there is the possibility which CP asymmetrycan be observed.

6

Four fermi interactions for

+

⇒

7

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 theoryin the one loop approximation.

J. Gasser and H. Leutwyler, Nucl. Phys. B250, 465 (1985)

}

}

8

To compare the CP asymmetry for tau decays we calculate the differential decay rate with the tau spin vector s

In the τrest frame :

An eigenvalue for the spin operator is defined as

The angles α and φ

9

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.

10

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.

11

We want to evaluate CP asymmetry using Wλ

When is real, CP is invariant

12

We introduce strong phase δst and CP violating phase θw

5. Numerical result of differential decay rate

1/2π

13

14

5. Summary

・ We point out that there is a possibility to observe the CP asymmetry.

・ We have studied τ→ Ｋ πν decays and it’s CP violation with the two doublet Higgs model.