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

Many candidates beyond the SM

We want to probe the evidence of new physics

Including two Higgs doublet

2HDM, SUSY, GUT…

If we can probe charged Higgs effects on B physics

Indirect signal of the new physics

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 …)

Contributing diagram

Charged Higgs provide large contribution

It becomes mass correction for the bottom quark mass

This affects branching ratios for some processes!

Also, if we consider a supersymmetric model

Appear the SUSY corrections for Yukawa sector

After EW symmetry breaking

(ex. BS→ μμ , etc …)

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

We also include additional tau mass corr.

We estimated these effects for the following two processes

B ￫ Dτν and B ￫τν

We will probe the super B factory

Super B factory: The luminosity is 50-100 times more than the current achieved luminosity.

In this talkWe will show the following contents

SUSY corrections for B ￫ Dτν and B ￫ τνin our framework.

Numerical results and Conclusions.

Summary.

2: FormalismOur framework: MSSM with MFV and large tanβ

Tree level Yukawa coupling have the same structureof the superpotential.

Different type of the tree level Yukawa couplings are induced SUSY effects through 1-loop diagram.

(A.Dedes & A.Pilaftsis)

are 1-loop induced coupling constant

1-loop diagram for

1-loop diagram for

Our calculating flow

1:Assumed MFV2:Calculated the gluino and charged higgsino a

nd bino diagrams.3:Estimated mass matrices that including SUS

Y corrections.4:Diagonalized mass matrices. 5:Derived charged Higgs couplings.

Results1: negligible

2:higgsino cont. is suppressed by negligible

Charged Higgs couplings

Contribution of the loop diagrams

Therefore, 4-Fermi effective Lagrangian for B ￫ Dτυ process

Hadronic matrix elements for

Decay amplitude

Differential partial width for

Therefore, 4-Fermi effective Lagrangian for B ￫ τυ process

Hadronic matrix elements for

Decay width

3: Numerical results

For correction matricesWe estimated the correction matrices againstseveral value of the SUSY parameter.

There is parameter region that tau mass correctionbecomes comparable with the bottom mass correction.

So if we estimate the branching ratio without tau masscorrection, we mislead the results.

For correction matrices

μ=-400GeV

μ=400GeV

In B ￫ Dτν process

3: Numerical results

No experimental dataFor branching ratio

SM prediction: Br～ 8×10-3

Super B factory

5ab-1 : 7.9%50ab-1: 2.5%Expected uncertainties in the measured Br.}

Branching ratio for B ￫ Dτν

We can see that loop correction affects for tree diagramdrasticaly.

Form factor is canceled by taking ratio B ￫ Dτν and B ￫ τν . Theoritical uncertainty becomes small.

tanβ=50 tanβ=30

SM pred.

SUSY cor. case at μ = -400GeV

SUSY cor. case at μ = 400GeV

No SUSY cor. case

SM pred.

SUSY cor. case at μ = -400GeV

SUSY cor. case at μ = 400GeV

No SUSY cor. case

In B ￫ τν process

SM prediction: Br = 0.9×10-4

From BaBar : Br < 4.1×10-4

Super B factory will be sensitive to SM ratesExpected 4σ significance at 2 ab-1

Decay constant :

Branching ratio for B ￫ τν

We can see that loop correction affects for tree diagramdrastically too.

tanβ=50 tanβ=30

SM pred.

SUSY cor. case at μ = 400GeV

SUSY cor. case at μ = -400GeV

No SUSY cor. caseSM pred.

No SUSY cor. case

SUSY cor. case at μ = 400GeV

SUSY cor. case at μ = -400GeV

We show the correlation between these two processes

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.

μ= - 400GeV

μ= 400GeV

No SUSY corr.

μ=400GeV μ=-400GeV

Contour plot for several cases for B ￫ Dτν

SM pred.

-10%

-20%-30%-40%lowest

SM pred.

-10%-20%-30%-40%

SM pred.

-10%-20%-30%

-40%lowest

No SUSY corr.

μ=400GeV μ=-400GeV

Contour plot for several cases for B ￫ τν

lowest} -10%

SM pred.10%20%30%

Exp. bound

lowest

-30%

-40%

-50%

-60%

-70%-80%

-90% SM pred.

lowest

200%Exp.bound

-90%

4:Summary

The B ￫ 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.