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### Tauonic B decay in a supersymmetric model

YITP workshop:Progress in Particle Physics 2004.6.30

Hideo Itoh (KEK, Ibaraki univ.)

in collaboration with

S.Komine(KEK), Y.Okada(KEK)

1: Introduction

We want to probe the evidence of new physics

2HDM, SUSY, GUT…

Including two Higgs doublet

Many candidates beyond the SM

If we can probe charged Higgs effects on B physics

Indirect signal of the new physics

Charged Higgs provide large contribution

Contributing diagram

We can probe charged Higgs effect in the

(M.Tanaka:1994, J.A.Coarasa, R.A.Jimenez, J.Sora:1997,

G.H.Wu, K.Kiers, J.N.Ng:1997 …)

It becomes mass correction for the bottom quark mass

Also, if we consider a supersymmetric model

Appear the SUSY corrections for Yukawa sector

After EW symmetry breaking

(K.S.Babu & C.Kolda, M.Carena, et al)

This affects branching ratios for some processes!

(ex. BS→μμ , etc …)

We will probe the super B factory

We also include additional tau mass corr.

We estimated these effects for the following two processes

B￫DτνandB￫τν

Super B factory: The luminosity is 50-100 times more than

the current achieved luminosity.

In this talk

We will show the following contents

SUSY corrections for B￫DτνandB￫τν

in our framework.

Numerical results and Conclusions.

Summary.

Different type of the tree level Yukawa couplings

are induced SUSY effects through 1-loop diagram.

2: Formalism(A.Dedes & A.Pilaftsis)

Tree level Yukawa coupling have the same structure

of the superpotential.

Our framework: MSSM with MFV and large tanβ

negligible

Our calculating flow1:Assumed MFV

2:Calculated the gluino and charged higgsino and bino diagrams.

3:Estimated mass matrices that including SUSY corrections.

4:Diagonalized mass matrices.

5:Derived charged Higgs couplings.

Results

1:

2:higgsino cont. is suppressed by

Therefore, 4-Fermi effective Lagrangian

forB￫Dτυ process

Hadronic matrix elements for

Decay amplitude

Therefore, 4-Fermi effective Lagrangian

forB￫τυ process

Hadronic matrix elements for

Decay width

For correction matrices

We estimated the correction matrices against

several value of the SUSY parameter.

There is parameter region that tau mass correction

becomes comparable with the bottom mass correction.

So if we estimate the branching ratio without tau mass

correction, we mislead the results.

5ab-1 : 7.9%

50ab-1: 2.5%

}

Expected uncertainties in the measured Br.

3: Numerical results

In B￫Dτνprocess

For branching ratio

No experimental data

SM prediction: Br～8×10-3

Form factor is canceled by taking ratio B￫Dτνand B￫τν.

Theoritical uncertainty becomes small.

Branching ratio for B￫Dτν

tanβ=50

tanβ=30

SUSY cor. case at μ = -400GeV

SUSY cor. case at μ = 400GeV

SM pred.

SUSY cor. case at μ = 400GeV

SM pred.

SUSY cor. case at μ = -400GeV

No SUSY cor. case

No SUSY cor. case

We can see that loop correction affects for tree diagram

drasticaly.

In B￫τνprocess

SM prediction: Br = 0.9×10-4

From BaBar : Br < 4.1×10-4

Super B factory will be sensitive to SM rates

Expected 4σ significance at 2 ab-1

tanβ=30

tanβ=50

SUSY cor. case at μ = -400GeV

SUSY cor. case at μ = -400GeV

No SUSY cor. case

SUSY cor. case at μ = 400GeV

SM pred.

SM pred.

No SUSY cor. case

SUSY cor. case at μ = 400GeV

We can see that loop correction affects for tree diagram

drastically too.

We show the correlation between these two processes

μ= - 400GeV

μ= 400GeV

We choose the charged Higgs mass as variable, 150～400GeV.Since we assumed MFV, these correlation appears.

It is important to investigate the both processes.

-20%

-20%

-40%

SM pred.

SM pred.

SM pred.

Contour plot for several cases for B￫Dτν

No SUSY corr.

lowest

-10%

μ=400GeV

μ=-400GeV

-30%

-40%

lowest

-10%

-40%

-30%

-20%

-10%

Contour plot for several cases for B￫τν

No SUSY corr.

Exp. bound

lowest

-10%

SM pred.

10%

20%

30%

}

Exp.bound

μ=-400GeV

μ=400GeV

-80%

lowest

200%

-70%

SM pred.

-90%

-90%

-60%

lowest

-50%

-40%

-30%

4:Summary

TheB￫Dτυ and B￫τυ processes on the MSSM that assumed MFV and large tanβ.

SUSY corrections for the bottom and the tau mass.

SUSY loop correction is very large.

and

There is parameter region where corrections due to tau mass and bottom mass become comparable.

So tau mass correction is important.

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