Review of the present status of SO(10) GUT

Universitry of SouthamptonMarch 7, ‘08

Takeshi Fukuyama (Ritsumeikan University)

Why GUT ?Beyond Standard model is not necessarily GUT.

GUT does not necessarily mean ultra high energy.

• Experimental observations Asymptotic freedom in strong interactions natural to extend Electro-weak to incorpolate strong interactionNeutrino oscillations high energy scales via SeesawMuon g-2

Theoretical implications (aesthetic displeasure of SM)The unification of so many parameters in the SMHiggs mass hierarchy problem->new physics above TeVIntermediate energy scales of axion and Heavy (right-handed) neutrino

etc.Confrontation with CosmologyDark Matters, Dark Energy

Why 　ＳＵＳＹ？• Gauge coupling unification (MSSM)(Non-SUSY with Pati-Salam, threshold corrections)• Mass hierarchy problem(Little Higgs, Randall-Sandrum Extra dimension,..)• Dark Matters (Modified gravity, axion, sterile neutrinos)• SUSY resolves the problems, but gives rise to ot

her problems like Susy breaking mechanism, Mu-problem, gravitino

problem, …..

What is the gauge group ?

• SU(5)• SO(10)=5bar+10+1, anomaly free*• E_6, E_8* Anomalous<->unrenormalizable, nonunitary(Anomalous but consistent theory was attacked by us: T.F and K.Kami

mura 1988 Phys.Lett.)

• These are the (vertical) symmetries of one family (?).

How about the (horizontal) symmetry of inter-families ?

Can GUT be consistent in 4 D ?

• The relation with the alternative approach• Extra dimension is not opposed to SUSY

but may be necessary for its consistency via SUSY breaking mechanism and others.

How about the relation with Hosotani mechanism ?

Orbifold GUT

What does the string theory impose on GUT ?

And the relation with the Cosmology, sepecially with Inflation model.

Overview of experimental data

• Neutrino masses & mixings Since the discovery of neutrino oscillations in SuperK (1998), Since the discovery of neutrino oscillations in SuperK (1998),

we have a first evidence of physics beyond the SM. we have a first evidence of physics beyond the SM. Now is in the era of precision measurement for atmospheric & Now is in the era of precision measurement for atmospheric &

solar neutrino oscillations in SuperK, K2K, SNO and KamLand.solar neutrino oscillations in SuperK, K2K, SNO and KamLand.

Future prospect is to measure the remaining mixing angle, Future prospect is to measure the remaining mixing angle, CHOOZ angle, and the CP violation in the lepton sector!CHOOZ angle, and the CP violation in the lepton sector!

These data show that we have These data show that we have two large mixing anglestwo large mixing angles plus plus one small angleone small angle in the lepton sector. (cf. quark sector have in the lepton sector. (cf. quark sector have three small mixing anglesthree small mixing angles. ). )

• Why lepton sector have so Why lepton sector have so large mixings in large mixings in comparison to quark comparison to quark sector?sector?

• Which mass patterns do Which mass patterns do

neutrinos favor?neutrinos favor?

Theoretical open question

• Because we really see LFV as neutrino oscillations, we naturally Because we really see LFV as neutrino oscillations, we naturally expect LFV can also be seen in the charged lepton sector! expect LFV can also be seen in the charged lepton sector!

• Current experimental bound: Current experimental bound:

• How well motivated from theoretical point of view?How well motivated from theoretical point of view?

In the Standard Model (+ Right-handed neutrinos): too small rate In the Standard Model (+ Right-handed neutrinos): too small rate ( GIM suppression well works).∵( GIM suppression well works).∵

In SUSY models:In SUSY models: New sourceNew source ofof LFV, soft SUSY breaking terms LFV, soft SUSY breaking terms (with No GIM suppression, in general) exist.(with No GIM suppression, in general) exist.LFV processes are important sources for low-energy SUSY LFV processes are important sources for low-energy SUSY

search!search!

Lepton Flavor Violation (LFV)

Muon g-2

• There exist a 2.8σ discrepancy between the recent BNL There exist a 2.8σ discrepancy between the recent BNL result and the Standard Model predictions. result and the Standard Model predictions.

• If this is real, it may be a first evidence of supersymmetry.If this is real, it may be a first evidence of supersymmetry.

Motivation of SO(10) GUT

• SUSY ＋ GUT Experimental evidence:Experimental evidence: three gauge couplings unificationthree gauge couplings unification with MSSM particle contents.with MSSM particle contents.• SO(10) GUTSO(10) GUT SO(10) fundamental representation include all the matter in the SO(10) fundamental representation include all the matter in the

MSSM plus MSSM plus right-handed neutrinosright-handed neutrinos. .

Experimental evidence:Experimental evidence: very tiny neutrino massesvery tiny neutrino masses. It can be explained via the “It can be explained via the “seesaw mechanismseesaw mechanism”, and it works ”, and it works

well in SO(10) GUT in the presence of the well in SO(10) GUT in the presence of the right-handed right-handed neutrinosneutrinos. (. (Yanagida, Gell-Mann et al. (79’) )

16x16=10+120+126

So Higgs which can couple via Yukawa

10, 120, 126bar

10 is essential for b-tau unification and

126 bar is also essential for type I seesaw and R-symmetry

SO(10) GUT• Renormalizable SUSY SO(10)Based on the works in collaboration with T. Kikuchi, N. Okada, A.Ilakovac and S. Meljanac, References: JHEP 0211 (2002); Phys. Rev. D 68 (2003); Int. J. Mod. Phys. A19 (20

04); JHEP 0409 (2004); J. Math. Phys. 46 (2005); JHEP 0505 (2005); Phys.Rev.D75 (2007)

With N.Okada: works in preparation

Predictive,

• Perturbative (to the Planck scale) SUSY SO(10)

• After the symmetry breakings, we have

Yukawa couplings

Below the GUT scale, we assume MSSM is realized, and we have two Higgs doublet which are linear combinations of original

fields.

Mass relation

• All the mass matrices are descried by only two fundamental All the mass matrices are descried by only two fundamental matrices. matrices.

• 1313 inputs : inputs : 66 quark masses, quark masses, 33 angles + angles + 11 phase in CKM matrix, phase in CKM matrix, 33 charged-lepton masses. charged-lepton masses. ⇒ ⇒ fix and fix and ⇒ ⇒ predictions in the parameters in the neutrino sector!predictions in the parameters in the neutrino sector!

Predictions in neutrino sector

• We have only one parameter We have only one parameter 　　　　　　　 　　　　　　　 , left free. So, , left free. So, we can make definite predictions. we can make definite predictions.

Input data @ EW scale

• Now, all the mass matrices have been determined!Now, all the mass matrices have been determined!• For example, Neutrino Dirac Yukawa coupling matrix (in the For example, Neutrino Dirac Yukawa coupling matrix (in the

basis where charged lepton mass matrix is diagonal): basis where charged lepton mass matrix is diagonal):

• We must check this model by proving the other phenomena We must check this model by proving the other phenomena related to the Yukawa couplings! (related to the Yukawa couplings! (LFVLFV, , muon g-2muon g-2, , EDMEDM, , neutrino magnetic dipole moment (MDM), proton decayneutrino magnetic dipole moment (MDM), proton decay, etc.), etc.)

Yukawa’s are determined!

Soft SUSY breaking terms

• We consider the general soft SUSY breaking mass parameters at We consider the general soft SUSY breaking mass parameters at low-energylow-energy

• Because we really see LFV as neutrino oscillations, we naturally Because we really see LFV as neutrino oscillations, we naturally expect LFV can also be seen in the charged lepton sector! expect LFV can also be seen in the charged lepton sector!

• Current experimental bound: Current experimental bound:

• How well motivated from theoretical point of view?How well motivated from theoretical point of view?

In the Standard Model (+ Right-handed neutrinos): too small rate In the Standard Model (+ Right-handed neutrinos): too small rate ( GIM suppression well works).∵( GIM suppression well works).∵

In SUSY models:In SUSY models: New sourceNew source ofof LFV, soft SUSY breaking terms LFV, soft SUSY breaking terms (with No GIM suppression, in general) exist.(with No GIM suppression, in general) exist.LFV processes are important sources for low-energy SUSY LFV processes are important sources for low-energy SUSY

search!search!

Lepton Flavor Violation (LFV)

Estimations of LFV and g-2

• LFV and g-2 are originated from the same dipole moment operatorLFV and g-2 are originated from the same dipole moment operator

• include the SUSY partners in the loop.include the SUSY partners in the loop. Chargino –sneutrino & Neutralino -charged-slepton loop

Hisano et al. PRD53 (1996)

Formula for LFV, g-2 and EDM

• For the estimation of LFV the decay rate is given byFor the estimation of LFV the decay rate is given by

• For the estimation of g-2 the SUSY contribution is estimated byFor the estimation of g-2 the SUSY contribution is estimated by

• For the estimation of EDM the SUSY contribution is estimated For the estimation of EDM the SUSY contribution is estimated byby

mSUGRA boundary condition

• We impose the universal boundary conditions at the GUT scale We impose the universal boundary conditions at the GUT scale

• So we have three free parameters in the soft mass terms, So we have three free parameters in the soft mass terms,

RG induced Flavor mixings

• Flavor mixing is induced by RG running from the GUT scale to the Flavor mixing is induced by RG running from the GUT scale to the EW scaleEW scale

• In the basis where the charged lepton mass matrix is diagonal, LFV In the basis where the charged lepton mass matrix is diagonal, LFV is induced through the neutrino Dirac Yukawa coupling matrix. is induced through the neutrino Dirac Yukawa coupling matrix.

The prediction about • For fixedFor fixed

• Very close to the current experimental upper bound.Very close to the current experimental upper bound. →It is →It is testable in near future experiments. testable in near future experiments.

２． Problems of 4D SO(10) GUT

• Thus the theory enter into the precision calculation phase, where some problems give arise:

• Fast Proton Decay.

• Many intermediate energy scales break the gauge coupling unification since we have five directions which are singlet under G_{321}.

Superpotential was fully analyzed

• Fukuyama et.al. hep-ph/0401213 v1

gave the symmetry breaking pattern

from minimal SO(10) to Standard Model,starting from

210,126,10 H

Proton decay in SUSY GUT

• In the minimal SO(10) model, we have two kinds of Yukawa In the minimal SO(10) model, we have two kinds of Yukawa matrices, and the Wilson coefficients can be written as: matrices, and the Wilson coefficients can be written as:

• In SUSY models, the In SUSY models, the color triplet Higgsinoscolor triplet Higgsinos mediate the proton mediate the proton decay induced by the following baryon and lepton number decay induced by the following baryon and lepton number

violating violating dimension five operatordimension five operator

• Proton Decay ResultsProton Decay Results: The decay rate in our model is within the : The decay rate in our model is within the experimental upper bound if we take the small tan β = 2.5, experimental upper bound if we take the small tan β = 2.5, assuming the color triplet Higgs mass to be at the usual GUT assuming the color triplet Higgs mass to be at the usual GUT scale. scale.

• Note added: It’s possible to completely cancel out the proton decay rate Note added: It’s possible to completely cancel out the proton decay rate by tuning the parameters in the Higgs sector (3 +1 or 5+1 parameters). by tuning the parameters in the Higgs sector (3 +1 or 5+1 parameters).

Our SO(10) Model is very testable in the near future Our SO(10) Model is very testable in the near future experiments!experiments!

Proton decay rate formula

Parameters in Higgs sector-(i)

Parameters in Higgs sector-(ii)

Proton decay in SO(10) GUT-(i)

The green region is the allowed region. In case of , there is large enough parameter space which cancels the proton decay rate, though it is very tiny region in case of .

Doublet-doublet problem

Minimal model (10+126+126+210 Higgses) is disfavored.(Bertolini-Schwetz-Malinsky, …)

___

1. is a function of vacua .

2. Neutrino scale is a function of .

Experimentally allowed solution :

But, gauge coupling unification spoils on the vacuum.

Many vacua (STD singlets)

• (1234)

• (5678+5690+7890)

• (1256+1278+1290+3456+3478+3490)

• (13579)

• (24680)

The gauge coupling unification

From Bertolini-Scwetz-Malinsky hep-ph/0605006

How to repair it in non-minimal SO(10) models

1. Add additional 10 or 120 Higgs.

2. Add additional 126+126, or 54 Higgs for neutrino scale.___

Type I seesaw Type II seesaw

The detail does not affect to the following discussion.

Alternative Higgs choices :

(Babu-Gogoladze-Nath-Syde)

First part summary

• We estimated We estimated neutrino oscillation parametersneutrino oscillation parameters, , LFV rates,LFV rates, Muon Muon g-2g-2 and and Proton decayProton decay in the in the Minimal SO(10) ModelMinimal SO(10) Model

• Results:Results: Neutrino masses & mixingsNeutrino masses & mixings can be well much described. can be well much described. LFV ratesLFV rates can be well exceed the future bounds can be well exceed the future bounds Muon g-2Muon g-2 can be suitable for can be suitable for BNL E821BNL E821 resultresult Combining withCombining with WMAP dataWMAP data → → Cosmologically allowed region existsCosmologically allowed region exists Using these unambiguous Yukawa couplings, we have also analyzed the proton decay rate in detail.

Solution by warped extra dimension-First approach-

1. A variety of Higgs mass spectra destroys the successful gauge coupling unification in the MSSM. Especially, the existence of the intermediate mass scale for the right-handed neutrino cause a problem.

2. This model has a cut off scale at the GUT scale. It means that a concrete UV completion of the model is necessary to be considered.

We explore to solve these problems by changing the 4D flat space to the 5D Randall-Sundrum type warped background.

1. This model can easily provide a natural suppression for the Yukawa couplings by a wave function localization.

2. UV completion is provided by a strong gravity. (cf. AdS/CFT)

.

How to solve this mild hierarchy problem?

In order to realize the gauge coupling unification, the simplest way is to put all the VEV’s at the GUT scale.

It is necessary to have an additional suppression as follows

On the other hand, neutrino oscillation data shows the existence of the intermediate mass scale, which may destabilize the successful gauge coupling unification in the MSSM

World of Extra Dimension

A solution to the mass hierarchy problem

In these days, there is a natural solution to provide a large mass hierarchy.In the Randall-Sundrum scenario, the exponentially warped metric can be used to explain any mass hierarchy.

The Setup We assume a 5D warped space:

In SUSY models in 5D, any chiral multiplets become a part of hypermultiplet and vector multiplet is extended to include an adjoint scalar.

By assigning an even/odd parity for , only has a zero mode wave function. This assignment also allows a bulk mass term for them.

Lagrangian for the Hypermultiplet in bulk

Effect of the VEV for the adjoint scalarIf we take into account of the VEV for the adjoint scalar in the vector multiplet, the bulk mass term is shifted as follows [Kitano-Li (03’)] :

In the context of the Left-Right symmetric gauge theory, providing the VEV only for the right-handed part provides an explanation for the mild hierarchy.

So we can determine the profile of wave function from group propery.

Solution by orbifold-Second Approah-

• Kawamura(’01),Hall-Nomura(’01),Dermisek-Mafi(’01)

Proton decay is suppressed by BC.

BC breaks SU(5) into MSSM with direct no coupling with triplet, wheras SO(10) into Pati-Salam included it in general, inducing large proton decay ratio.

)/( '22

1 ZZS

• For SO(10), there are many set ups even in .

• y=0 visible and

vev of PS singlet at y=pi/2 brane destroys SUSY.• y=pi/2 visible and vev of SO(10) singlet at y=0 branes d

estroys SUSY – today’s talk.• In both cases, PS invariance play the crucial role to prot

ect the fast proton decay.• We can exclude (6,1,1) which was harmful which was in

cluded in full SO(10) invariant theory.

)/( '22

1 ZZS

Our Setup

　 SO(10) 　 inv 　　　　　　　　　　　 PS 　 inv

　　　　　　　　　　　　　　　　　　　 vev 　 of (10,1,3)

　　 Standard

ｙ＝０　　　　　　　　　　　ｙ＝ pi/2 　Inviible Visible

Only gauge multiplet resides in bulk

SU(4)xSU(2)_LxSU(2)_R

Gauge coupling unification

P-S inv Higgs superpotential

Doublet-doublet (mu-term) problm

Gravitino mass escapes Problem

The relation with the other world

• Inflation theory in the framework of GUT

• Gauge Higgs unification-Hosotani Mechanism

• Landau’s conjecture:

QED may be consistent iff it is incorporated with gravitation.

Summary• The explicit construction of Higgs superpotetial revealed the precise sp

ectra of intermediate enrgy specta to standard.• It led to the destruction of gauge coupling unification.• It may lead to the incompatibility with proton stability• In order to circumvent these pathologies, we are forced to put it in extr

a dimensions.

• We considered SO(10) in 5 D in two ways.• One is to break SO(10) by the vev of bulk, which may explain tha mas

s spectra.• Another is to break SO(10) by using both the boundary conditions and

vev. This preserves the advantageous points of SO(10) (mass relations of

Dirac fermions and saves the disadvantageous points of SO(10) (Proton decay and gauge unification) .

4D

5D