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### Tauonic B decays in the MSSM

arXiv : hep-ph/0409228

YITP : 2005.1.13

Hideo Itoh (Ibaraki univ., KEK)

in collaboration with

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

0: Overview of the physics of the B and SuperB Factory

The current experiments

Asymmetric B factory experiments(1999～)

KEKB(KEK) : Belle experiment (～340fb-1)

PEPⅡ(SLAC) : BaBar experiment (～250fb-1)

The first purpose of the B factories

Precise test of the CKM picture

for the CPV

It succeeded!

Ex.

What is the next purpose of the B factories?

We look for deviation from the SM:

Correction from new physics beyond the SM

We need more Luminosity and far precise test.

In particular:

Processes of the final state including

more than two neutrinos

tauonic B decays : B→Dτν, B→τν

To identify these processes, we have to accumlate

more luminosity.

Necessity of the SuperB

LC

LHC

EDM

LFV

K physics

Muon g-2

Charm physics

Motivation of the SuperB Factory(Letter of Intent for KEK Super B Factory, hep-ex/0406071)

SuperB Factory : Goal of the luminosity is 50-100 times more

than the current achieved luminosity.

・SuperB is focused on studies for new physics (NP).

・LHC may find NP, but the information from LHC are not

enough to distinguish between NP models.

・SuperB provides much information for the NP models

from following measurements.

- New CP phase

- LFV (τ→μγ, τ→eγ,…)

- Tauonic B decays

- etc…

These results are useful to

combine with the LHC results.

(Okada san)

KEKB Upgrade Scenario

Lpeak (cm-2s-1)

Lint

5x1034

1 ab-1

1.4x1034

280 fb-1

5x1035

10 ab-1

5x109 BB

/year !!

& alsot+t-

Super-KEKB

(major upgrade)

1. Introduction

Two types of the SUSY effects on B physics

1. For the FCNC processes (b→sγ, Bs→μμ, B→φKs…)

Ex.)

SUSY (loop)

SM (loop)

2. For the Tauonic B decays (B→Dτν, B→τν)

Ex.)

SM (tree)

SUSY (tree)

Important features of the tauonic B decays

・Charged Higgs boson can contribute to the decay

amplitude at the tree level in the MSSM.

・At least two neutrinos are present in the final state

in the signal side.

Full-reconstruction is required for

the B decay in the opposite side.

It is difficult to probe the tauonic B decays.

However we may probe the charged Higgs effects on the B physics if we can probe the tauonic B decays.

Full-reconstruction efficiency is 10-3.

So we need more and more luminosity to probe the tauonic B decays.

SM prediction and current experimental results

The branching ratio of the tauonic B decays at the SM

・B→Dτν : 8×10-3

・B→τν : 9×10-5

・B→Dτνis larger branching ratio.

There is no experimental data.

We have not probed B→Dτνat both B factories.

・B→τνis smaller branching ratio due to helicity suppression.

Experimental data

- Upper bound from Belle : 2.9×10-4

- Upper bound from BaBar : 3.3×10-4

These processes are important target of the SuperB Factory.

Also there are SUSY corrections to the Yukawa couplings

SUSY correction to yd is induced due to 1-loop diagrams.

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

Contributing diagrams

SUSY corrections

The b→c(u)τυ processes in the MSSM

This correction affects the branching ratios

for some other processes too.

Ex. BS→μμ(A.Dedes & Pilaftsis, et al)

b→sγ (G.Degrassi & P.Gambino & G.F.Giudice, et al)

…

We study B￫Dτνand B￫τν in MSSM

・Assume the Minimal Flavor Violation case

Explain later・・・

・SUSY correction to H±-c (u )-b and H±-τ-νvertex

・Correlation between b￫sγ, Bs￫μ+μ- and tauonic

B decays.

Different types of the tree level Yukawa couplings

are induced by SUSY effects through 1-loop diagram.

(A.Dedes & A.Pilaftsis)

2: FormalismTree level Yukawa couplings have the same structure

as that of the superpotential.

Framework: MSSM with MFV and large tanβ

MSSM with Minimal Flavor Violation (MFV)

Minimal Flavor Violation

Squarks have the same flavor structure as one of the quarks.

In other words, the flavor changing source is only the KM matrix.

・Not MFV case

The large deviation from SM is possible generally.

Because there are many flavor mixing parameters.

・MFV case

The large deviation from SM is possible for large tanβ.

tanβ is the ratio of the two vacuum expectation values

of the neutral Higgs.

This assumption comes from mSUGRA, GMSB, AMSB ・・・.

Under the Minimal Flavor Violation

Loop function

The SUSY corrections at b→u,c are given by

SUSY corrections to the charged Higgs couplings

Charged Higgs coupling including SUSY correction :

(“

“ denotes a diagonal matrix.)

For the correction to the down-type Yukawa coupling

In Minimal Flavor Violation case

・gluino-sbottom contribution

・higgsino-stop contribution

at MFV

Higgsino contribution becomes too small

in comparison with gluino contribution.

For the correction to the lepton Yukawa coupling

These SUSY corrections appear via the following combina

-tion of the parameters in the branching ratio formulas.

SUSY effects are absorbed into

the value of tanβ. I will explain later.

If there are no SUSY corrections (Ex. 2HDM case)

SUSY

2HDM

Intuitively, these SUSY corrections become the vertex correction like below.

Also we can see the following results.

B→Dτν

B→τν

There is a correlation between the tauonic B decays at MFV!

SUSY parameters for the tauonic B decays at MFV

・Tree-level charged Higgs effect depends on the following parameters.

・The SUSY corrections to the Yukawa couplings depend on the follow

-ing parameters with tanβ.

3: Numerical results

The SUSY correction matrix elements

3: Numerical results

The SUSY correction matrix elements

At above parameter space, the SUSY correction to the

lepton Yukawa coupling becomes sizable in comparison

with the down-type Yukawa’s one.

μ = 400GeV

μ = -400GeV

μ = 400GeV

No SUSY cor. case

SM

SM

No SUSY correction case

Branching ratio for B￫Dτν and B￫τν at tanβ = 50

B￫Dτν

B￫τν

μ is the higgsino mass parameter.

The SUSY corrections drastically contribute to the branching ratio.

・Vertical error :

25

・Horizontal error :

・SuperKEKB : 5ab-1

Sensitivity to reach to 11

SM

5

20

10

15

The correlation itself is the same as the 2HDM,

and so one cannot distinguish them.

The correlation of the two processes as a function of

In MFV, SUSY effect can be absorbed into an effective tanβ.

It is thus interesting to compare it with other experiments.

no SUSY corr.

Au=Ad=100GeV

Au=Ad=-100GeV

no SUSY corr.

Au=Ad=100GeV

Effect on other process: b￫sγAu and Ad are trilinear scalar couplings

・Charged Higgs and chargino-stop diagrams contribute.

・For μ<0 case, fine-tuning of parameters is necessary.

Upper bound from exp.

Au=Ad=-100GeV

Upper bound from exp.

Au=Ad=100GeV

Au=Ad=100GeV

Effect on other process: Bs￫μ+μ-・SM prediction : 3.4×10-9

・Receive the large SUSY corrections

・μ<0 case is strongly restricted by b￫sγ

4. Summary

Receive large correction via SUSY loops.

MSSM with MFV at large tanβ : B￫Dτνand B￫τν

The correlation between Br[B￫Dτν] and Br[B￫τν] in MFV

SUSY loop effect

absorbed into the effective tanβ

Correlation is same as the 2HDM

Important to compare : measurements of Br[B￫Dτν] and Br[B￫τν]

(SuperB Factory )

: measurements of tanβ (LHC )

Ex. ・heavy Higgs direct production

・chargino/neutralino mixing

・stau decay

b￫sγ and Bs￫μ+μ- :receive large correction generally

in the same parameter space

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