Phenomenological aspects of Generation TwPhenomenological aspects of Generation Twisted Supersymmetric Unificationisted Supersymmetric Unification

Aug. 30, 2006, SI2006 @ APCTPAug. 30, 2006, SI2006 @ APCTP

Kentaro KojimaKentaro Kojima

Department of Physics, Kyushu University

Based on Based on 　　 Kenzo Inoue, K.K., Koichi Yoshioka, JHEP 0607032; and in preparationKenzo Inoue, K.K., Koichi Yoshioka, JHEP 0607032; and in preparation

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• SUSY is one of the most promising candidates for TeV scale new physics– solves hierarchy problem in the SM Higgs potential– naturally includes DM candidates– MSSM predicts gauge coupling unification!

Supersymmetric GUT is well motivated Supersymmetric GUT is well motivated

• Neutrino gives important information to the SUSY-GUTvery heavy RH neutrinos:SU(3)×SU(2)×U(1) singlets

This seems to prefer SO(10) or higher GUT theoriesThis seems to prefer SO(10) or higher GUT theories

But GUTs naively have difficulties about flavor structure

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Several quarks and leptons are unified into a multiplet:

e.g. minimal SU(5) GUT　

Several types of Yukawa coupling unification are predicted:

SU(5) relation Symmetric Yukawa matrices

Minimal SO(10) GUT

Good for third generation,Good for third generation, Completely false for the others;Completely false for the others;

SU(5) relation must be modified…SU(5) relation must be modified…

Diagonalizationmatrices

Same contributions to CKM and MNS;Same contributions to CKM and MNS;naively conflict with experimental resultsnaively conflict with experimental results

Asymmetric matrices are useful…Asymmetric matrices are useful…

GUTs need nontrivial extensions for the flavor sectorGUTs need nontrivial extensions for the flavor sector

Identified to RH ν

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Contents of the talkContents of the talk

• SO(10) unification with generation twistingSO(10) unification with generation twisting

• Third generation fermion masses and sparticle spectrumThird generation fermion masses and sparticle spectrum• Radiative EWSB and bottom mass predictionRadiative EWSB and bottom mass prediction

• b→sγ and τ→μγ processesb→sγ and τ→μγ processes

• LSP nature and cosmological constraintLSP nature and cosmological constraint• Neutralino relic densityNeutralino relic density

• SummarySummary

SO(10) unification SO(10) unification with generation twistingwith generation twisting

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hierarchicalhierarchical

same ordersame order

Asymmetric Yukawa matrices seem to be suitable for CKM and MNS in GUTsAsymmetric Yukawa matrices seem to be suitable for CKM and MNS in GUTs

MSSM+RHν 　 (assuming the seesaw mechanism)

SU(5) relaltionSU(5) relaltion

Symmetric contributionSymmetric contributionto Yukawa matricesto Yukawa matrices

How can we realize the lopsided forms in SO(10)?How can we realize the lopsided forms in SO(10)?

But naïve SO(10) GUT cannot accommodate to the asymmetryBut naïve SO(10) GUT cannot accommodate to the asymmetry

Highly asymmetric matrices,Highly asymmetric matrices,so-calledso-called lopsided forms, lopsided forms,

[Babu, Barr 95]

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Generation twistingGeneration twisting

In generally, there are many candidates for SU(5) 5* in SO(10) (or higher as E6) multiplets:

e.g.

10+5*+1 5+5*

10+5*+1 5+5*

10+5*+1 5+5*

16i 10M

. . .

[Sato, Yanagida (98); Bando, Kugo, Yoshioka (99)]

SU(2) rotation in E6

Note: Hd (5*H) should be mixed states of 10H and others

Naturally embedded into E6 GUTNaturally embedded into E6 GUT

1

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In the following, we consider the scenario whereIn the following, we consider the scenario where

• Large top Yukawa coupling mainly comes from Large top Yukawa coupling mainly comes from

• Difference between CKM and MNS is the result of twisted 5*Difference between CKM and MNS is the result of twisted 5*

Small VSmall VCKMCKM

Large VLarge VMNSMNS

LopsidedLopsidedYYdd and Y and Yee

Twisted 5*Twisted 5*structurestructure

It is generally difficult to see or test the flavor It is generally difficult to see or test the flavor structure of the GUT since Mstructure of the GUT since MGG is very high. is very high. But we may probe into the flavor structure of But we may probe into the flavor structure of the GUT throughthe GUT through SUSY particle spectrum. SUSY particle spectrum.

Third generation fermion masses Third generation fermion masses and sparticle spectrumand sparticle spectrum

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Yukawa structure at the GUT scaleYukawa structure at the GUT scale

Considered Yukawa matrices (up to relatively small entries)

• Nearly maximal atmospheric mixing angle comes from YNearly maximal atmospheric mixing angle comes from Yee

• The angle θ parametrizes down-type Higgs mixingThe angle θ parametrizes down-type Higgs mixing

• SU(5) relation is modified by SU(5) relation is modified by

Includes SU(5) :Includes SU(5) :Contributions to Ye and Contributions to Ye and Yd are different: Yd are different: 1:-1/31:-1/3 [Georgi-Jarlskog(79)]

tanβ is decreased with Increasing θ

b-τmass ratio depends on Xd

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Fermion masses in the MSSMFermion masses in the MSSM

In large tanβ, Δb can be very largeIn large tanβ, Δb can be very large

Depend onDepend onSUSY spectrumSUSY spectrum

Sign of μSign of μ 　⇔　　⇔　 Sign of Sign of ΔΔ ｂｂ

(PQ sym. limit)(PQ sym. limit)

(R sym. limit)(R sym. limit)

•

•

[Hall, Rattazzi, Sarid (94); Blazek, Raby, Pokorski (95); Tobe, Wells (03)]

<<Induced bySUSY

(cf. non-renorm.theorem)

““Threshold Threshold corrections”corrections”

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Inclusion of radiative EWSBInclusion of radiative EWSB

μ and　 B are fixed by the following two equations at MSUSY

GUT scaleGUT scaleSUSY breakingSUSY breakingparameters parameters

Solving theSolving theMSSM (+RHν) RGEMSSM (+RHν) RGE

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Includes Includes SU(5)SU(5)

SO(10) motivated boundary conditions SO(10) motivated boundary conditions for SUSY breaking parametersfor SUSY breaking parameters

Now, SO(10) representations of the theory areNow, SO(10) representations of the theory are

Independent SUSY breaking parameters at the GUT scale:Independent SUSY breaking parameters at the GUT scale:

mixed Hd

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Bottom quark mass prediction for different XBottom quark mass prediction for different Xdd

green: excluded by b→sγ decay

blue: excluded by τ→μγ decay

gray: excluded by Higgs mass bound

xxdd= 1 : μ<0, hierarchical spectrum (M= 1 : μ<0, hierarchical spectrum (M1/21/2, |μ|<<m, |μ|<<m00))xxdd=-1/3: μ>0, hierarchy must be weakened=-1/3: μ>0, hierarchy must be weakened

different Xd → different size of Δb→different Xd → different size of Δb→ different sign of μdifferent sign of μdifferent sparticle spectrumdifferent sparticle spectrum

(Xd=1) (Xd=-1/3)

LSP nature and cosmological LSP nature and cosmological constraintconstraint

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Suppression of the neutralino relic density Suppression of the neutralino relic density

In our scenario, LSP is neutralino;

Xd=1 case: Xd=1 case: RRχ χ can be smallcan be small(Suppressed μ is consistent with mb)

Contribution tends to be too largeContribution tends to be too large

Suppressed Xd case: Suppressed Xd case: RRχ χ should be nearly 1should be nearly 1(only bino-like LSP is allowed)(only bino-like LSP is allowed) CP-odd Higgs resonance can suppresses the density

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• XXd d = 1 case= 1 case

• Higgsino-like LSP suppresses Higgsino-like LSP suppresses

• CP-odd Higgs resonance also suppreCP-odd Higgs resonance also suppre

sses the density, but where correct sses the density, but where correct mmbb cannot be achieved.cannot be achieved.

[Calculated by DarkSUSY]

• XXd d = -1/3 case= -1/3 case

• CP-odd Higgs mass is relatively CP-odd Higgs mass is relatively light and insensitive to light and insensitive to mm00

• Suppression of the density is Suppression of the density is enough supplied by enough supplied by

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Parameter scan for Xd=1 case:Parameter scan for Xd=1 case:

Constraints for bottom mass, b→sγ, superparticle masses are included

•Relic density has strong correlation with gaugino fraction•Higgsino components effectively suppress the density•LSP should have negligible higgsino components

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Parameter scan for Xd=-1/3 case:Parameter scan for Xd=-1/3 case:

Constraints for bottom mass, b→sγ, sparticle masses are included

• The relic density has strong correlation with CP-odd Higgs mass• LSP mass should be near the half of the CP-odd Higgs mass: • Sizable τ→μγ ratio is expected for relatively light SUSY spectrum; It may be observed near future experimental searches

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SummarySummary

• We study low energy remnants of the generation twistinWe study low energy remnants of the generation twisting.g.

• Typical sparticle mass spectrum is changed depending oTypical sparticle mass spectrum is changed depending on the breaking degree of SU(5) relation, n the breaking degree of SU(5) relation,

• Future searches of SUSY particles and flavor violations Future searches of SUSY particles and flavor violations

may be the probe into flavor sector of the unified theorymay be the probe into flavor sector of the unified theory

: heavy scalars, LSP should have higgsino components: heavy scalars, LSP should have higgsino components

: : relatively light spectrum is allowed; large LFV ratio;relatively light spectrum is allowed; large LFV ratio; masses of LSP and CP-odd Higgs should be correlatedmasses of LSP and CP-odd Higgs should be correlated

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AppendixAppendix

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Largely broken SU(5) relationLargely broken SU(5) relation

• SU(5) relation must be broken to reproduce observed SU(5) relation must be broken to reproduce observed mass pattern of 1mass pattern of 1stst and 2 and 2ndnd generation. generation.

• In generally the breaking appears in large asymmetrical entriesIn generally the breaking appears in large asymmetrical entries

• EvenEven if the 3-3 entries are unified, if the 3-3 entries are unified, bottom-tau mass ratio hasbottom-tau mass ratio has a large deviation from 1a large deviation from 1; e.g. ; e.g.

[Georgi, Jarlskog (79); Ellis, Gaillard (79)]due to group-theoretical factor, non-renorm. o.p.

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Large threshold correction to the bottom massLarge threshold correction to the bottom massin large or moderate tanβ regimein large or moderate tanβ regime

ΔΔbb can be easily large as O(0.5) for tanβ can be easily large as O(0.5) for tanβ ～～ 5050

Sign of μSign of μ 　⇔　　⇔　 Sign of Sign of ΔΔ ｂｂ

(PQ sym. limit)(PQ sym. limit)

(R sym. limit)(R sym. limit)

•

•

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Bottom mass prediction without the correctionBottom mass prediction without the correction

Experimental range

tanβ and θ are correlatedtanβ and θ are correlated

Input parameters

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Implications for superparticle spectrumImplications for superparticle spectrum

Bottom mass prediction and allowed range of Bottom mass prediction and allowed range of ΔΔbb

SU(5) breaking factor SU(5) breaking factor xxdd

strong correlation; due to the strong correlation; due to the lopsided Ylopsided Ydd

Various SUSY spectra are expected depends on Various SUSY spectra are expected depends on xxdd and θ and θ ((tantanββ))

e.g.

xd=1 μ<0 and relatively hierarchical spectrum are expected for a large value of tanβ

xd=-1/3 μ>0 and scalars cannot be much heavier thangauginos and higgsisnos

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Radiative EWSB conditionsRadiative EWSB conditions

Solving the RGESolving the RGE

•　 positive D-term reduce the size of μ

• increasing θ, CP-odd Higgs mass tends to be large

at MSUSY

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b b s γ rare decay process s γ rare decay process

When tanβ is not small, three diagrams give important contributions:

Consistent Consistent with exp.with exp. The both must be suppressedThe both must be suppressed

orEach of them must be canceled outEach of them must be canceled out

(allowed only for μ>0; suppresed Xd case)(allowed only for μ>0; suppresed Xd case)

XXdd=1 case: =1 case:

Suppressed Suppressed XXdd case: case:

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Lepton flavor violating processLepton flavor violating process

Large 2-3 entry of YeRGE between RGE between induces irreducible 2-3 mixing induces irreducible 2-3 mixing in the mass matrix for scalar in the mass matrix for scalar lepton doubletlepton doublet

For suppressed Xd case, where relatively light scalars For suppressed Xd case, where relatively light scalars are allowed, sizable B(τare allowed, sizable B(τμγ) is expectedμγ) is expected

D-term contributions amplify non-degeneracy of D-term contributions amplify non-degeneracy of the scalar leptons:the scalar leptons:

Non-zero D-term contributions enhances B(τNon-zero D-term contributions enhances B(τμγ)μγ)

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• XXd d = 1 case = 1 case (preliminary)(preliminary)

• Higgsino-like LSP suppresses Higgsino-like LSP suppresses

• The s-channel pole also suppresses theThe s-channel pole also suppresses the

density, but where correct density, but where correct mmbb cannot be achieved. cannot be achieved.

[Calculated by DarkSUSY]

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• XXd d = -1/3 case= -1/3 case

• CP-odd Higgs mass is relatively light and insensitive to CP-odd Higgs mass is relatively light and insensitive to mm00

• Suppression of the density is enough suppliedSuppression of the density is enough supplied