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YITP : 2005.1.13 Hideo Itoh (Ibaraki univ., KEK) in collaboration with

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

arXiv : hep-ph/0409228

Tauonic B decays in the MSSMTauonic B decays in the MSSM

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

Asymmetric B factory experiments(1999 ～ )

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

PEP (SLAC) : Ⅱ BaBar experiment ( ～ 250fb-1)

The current experiments

The first purpose of the B factories

Precise test of the CKM picture for the CPV It succeeded!

Ex.

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The history of the integrated luminosity

2004 summer

2003 summer

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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 accumlatemore luminosity.

Necessity of the SuperB

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Motivation of the SuperB Factory

SuperB Factory : Goal of the luminosity is 50-100 times more than the current achieved luminosity.

B physics

LHC LC

LFVEDM

Muon g-2K physics

Charm physics

・ 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)

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

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KEKB Upgrade Scenario

Super-KEKB(major upgrade)

1.4x1034

280 fb-1

5x1034

1 ab-1

5x1035

10 ab-1

Lpeak (cm-2s-1)Lint

5x109 BB/year !!

& also +-

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1. IntroductionTwo types of the SUSY effects on B physics

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

Ex.)

SM (loop) SUSY (loop)

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

SM (tree) SUSY (tree)

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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.

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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.

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The b→c(u)τυ processes in the MSSM 　

Contributing diagrams

SUSY correction to yd is induced due to 1-loop diagrams. (K.S.Babu & C.Kolda, M.Carena, et al)

Also there are SUSY corrections to the Yukawa couplings

SUSY corrections

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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) …

・ Assume the Minimal Flavor Violation case 　　　 Explain later ・・・・ SUSY correction to H±-c (u )-b and H±-τ -ν vertex・ Correlation between b ￫ sγ, Bs ￫ μ+μ- and tauonic B decays.

We study B ￫ Dτν and B ￫ τν in MSSM

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2: FormalismFramework: MSSM with MFV and large tanβTree level Yukawa couplings have the same structureas that of the superpotential.

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

(A.Dedes & A.Pilaftsis)

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MSSM with Minimal Flavor Violation (MFV)

Minimal Flavor Violation

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

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 caseThe large deviation from SM is possible generally.Because there are many flavor mixing parameters.

・ MFV caseThe large deviation from SM is possible for large tanβ.tanβ is the ratio of the two vacuum expectation valuesof the neutral Higgs.

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Under the Minimal Flavor Violation

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Under the Minimal Flavor Violation

Loop function

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Charged Higgs coupling including SUSY correction :

SUSY corrections to the charged Higgs couplings

“ denotes a diagonal matrix.)(“

For the correction to the down-type Yukawa coupling

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

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at MFV

Higgsino contribution becomes too smallin comparison with gluino contribution.

・ gluino-sbottom contribution

・ higgsino-stop contribution

In Minimal Flavor Violation case

For the correction to the lepton Yukawa coupling

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These SUSY corrections appear via the following combina-tion of the parameters in the branching ratio formulas.

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

SUSY effects are absorbed intothe value of tanβ. I will explain later.

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2HDM SUSY

In MFV caseB→DτνB→τν

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

Also we can see the following results.

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

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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.

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3: Numerical results The SUSY correction matrix elements

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3: Numerical results

The SUSY correction matrix elements

At above parameter space, the SUSY correction to thelepton Yukawa coupling becomes sizable in comparisonwith the down-type Yukawa’s one.

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

The SUSY corrections drastically contribute to the branching ratio.

SM

μ = -400GeV

μ = 400GeV

No SUSY correction case

SM

μ = -400GeV μ = 400GeV

No SUSY cor. case

B ￫ Dτν B ￫ τν

μ is the higgsino mass parameter.

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In MFV, SUSY effect can be absorbed into an effective tanβ .The correlation itself is the same as the 2HDM,and so one cannot distinguish them.

SM5

1015

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The correlation of the two processes as a function of

・ Vertical error :

・ Horizontal error :

Theoretical uncertainties :

・ SuperKEKB : 5ab-1

　 Sensitivity to reach to 11

It is thus interesting to compare it with other experiments.

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Effect on other process: b ￫ sγ

Au=Ad=100GeV

Au=Ad=-100GeV

no SUSY corr.Au=Ad=-100GeV

Au=Ad=100GeV

no SUSY corr.

・ Charged Higgs and chargino-stop diagrams contribute.・ For μ<0 case, fine-tuning of parameters is necessary.

Au and Ad are trilinear scalar couplings

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Effect on other process: Bs ￫ μ+μ-

Au=Ad=100GeV

Au=Ad=-100GeV

Upper bound from exp. Au=Ad=-100GeV

Au=Ad=100GeV

Upper bound from exp.

・ SM prediction : 3.4×10-9

・ Receive the large SUSY corrections ・ μ<0 case is strongly restricted by b ￫ sγ

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MSSM with MFV at large tanβ : B ￫ Dτν and B ￫ τν

Receive large correction via SUSY loops.

4. Summary

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

SUSY loop effect absorbed into the effective tanβCorrelation is same as the 2HDM

Important to compare : measurements of Br[B ￫ Dτν ] and Br[B ￫ τν ] (SuperB Factory )

b ￫ sγ and Bs￫ μ+μ- : receive large correction generally in the same parameter space

: measurements of tanβ (LHC )Ex. ・ heavy Higgs direct production ・ chargino/neutralino mixing ・ stau decay