# Presentation: 175889

## SO(10) SUSY GUT in 5 D.   September 21 @LBNL

**Takeshi Fukuyama (Ritsumeikan University)**

- 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 (2004); JHEP 0409 (2004); J. Math. Phys. 46 (2005); JHEP 0505 (2005); **Phys.Rev.D75 (2007)**
- With N.Haba and N.Okada: works in preparation

## Table of Contents

- 1. Breif review of the minimal SO(10) model.
- 2. Problems in the model as a 4D GUT
- 3. Embedding the model in flat or warped
-     5D space
- 4. Summary

## Minimal SO(10) model

- Two kinds of symmetric Yukawa couplings

- Two Higgs fields are decomposed to

- SU(4) adjoint **15** have a basis,                                   so as to satisfy the traceless condition.  Putting leptons into the 4th color, we get,  so called, ‘Georgi-Jarslkog’ factor,           for leptons.

- (Babu-Mohapatra (93’); Fukuyama-Okada (01’))

## Mass relation

- All the mass matrices are descried by only two fundamental matrices.
- 13 inputs : 6 quark masses, 3 angles + 1 phase in CKM matrix,
-                         3 charged-lepton masses.
-        ⇒ fix           and
-        ⇒ _**predictions in the parameters in the neutrino sector!**_

## Predictions in neutrino sector

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

## Now, all the mass matrices have been determined!
For example, Neutrino Dirac Yukawa coupling matrix (in the basis where charged lepton mass matrix is diagonal): 

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

- For example, Neutrino Dirac Yukawa coupling matrix (in the basis where charged lepton mass matrix is diagonal):
- We must check this model by proving the other phenomena related to the Yukawa couplings! (LFV, muon g-2, EDM, neutrino magnetic dipole moment (MDM), proton decay, etc.)

- Yukawa’s are determined!

## The prediction about 

- For fixed

## For fixed 

Input parameters providing                         close to the present upper bound predict suitable magnitude for muon g-2.

- Input parameters providing                         close to the present upper bound predict suitable magnitude for muon g-2.

- The prediction about muon g-2

## Superpotential was fully analyzed

- Fukuyama et.al. hep-ph/0401213 v1
- gave the symmetry breaking pattern
- of minimal SO(10) to Standard Model,starting from

## 2.Problems of 4D SO(10) GUT

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

## Proton decay in SUSY GUT

- In the minimal SO(10) model, and the Wilson coefficients can be written as:

- In SUSY models, the color triplet Higgsinos mediate the proton decay induced by the following baryon and lepton number violating dimension five operator

## Slide 12

## Discard (6,1,1) in the PS model

## 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                       .

## Proton decay in SO(10) GUT-(ii)

- 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                       .

## The gauge coupling unification

- From Bertolini-Scwetz-Malinsky hep-ph/0605006

## Solution by warped  extra dimension-First approach-

- 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.
- 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.

- This model can easily provide a natural suppression for the Yukawa couplings by a wave function localization.
- UV completion is provided by a strong gravity. (cf. AdS/CFT)

## How to solve this mild hierarchy problem?

- 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.

- 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

## 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.

## Effect of the VEV for the adjoint scalar

- If 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’)] :

- For the parity conservation, the adjoint VEV which has an odd parity should have the following form:

- 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)
- Raby-H.D.Kim
- Proton decay is suppressed by BC.
-  BC breaks SU(5) into MSSM with direct no coupling with triplet, but does SO(10) into Pati-Salam which includes it in general,

## 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 destroys SUSY – today’s talk.
In both cases, PS invariance play the crucial role for the protect from the fast proton decay.
We can exclude (6,1,1) which was harmful, included in full SO(10) invariant theory.

- 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 destroys SUSY – today’s talk.
- In both cases, PS invariance play the crucial role for the protect from the fast proton decay.
- We can exclude (6,1,1) which was harmful, included in full SO(10) invariant theory.

## Our Setup

-  SO(10) inv           PS inv
-                    vev of (10,1,3)
-                                                 Standard
-         y=0           y=pi/2
- Inviible                                visible

## Slide 29

## Slide 31

##         Gauge coupling unification

-         Gauge coupling unification

## Slide 33

## Summary

- The explicit construction of Higgs superpotetial revealed the precise spectra 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 extra 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 mass 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