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Summary of my work on the minimal SO(10) modelPresentation Transcript
1.
Phenomenology of the m inimal SO(10) model and its extensions Tatsuru Kikuchi (KEK) based on the works in collaboration with T. Fukuyama, N. Okada, A. Ilakovac and S. Meljanac References: LFV, g-2 & EDM: Phys. Rev. D68 (2003); P-decay: JHEP 0409 (2004); CG coefficients: Eur. Phys. J. C42 (2005); J. Math. Phys. 46 (2005); Leptogenesis: JCAP 0506 (2005); Warped x-dim.: Phys. Rev. D75 (2007) Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
Some applications -LFV, g-2, EDM, leptogenesis, p-decay
Problems in the model as a 4D GUT
M R <<M GUT versus gauge coupling unification
Use of large dimensional representation breaks perturbativity
Embedding the model in a mini-warped 5d space
Warp factor can be used to explain the mass hierarchy between the GUT scale and Planck scale (M GUT /M PL ) as well as that of the intermediate scale and the GUT scale (MR/M GUT ).
Summary
Table of Contents Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
SO(10) is the most attractive GUT candidate since it includes all the matter in the SM plus right-handed neutrino .
Experimental evidence beyond the Standard Model: very tiny neutrino masses . It can be explained via the see-saw mechanism which works well in SO(10) GUT due to the natural existence of the right-handed neutrino .
“ Minimal SO(10) model” is the theory which includes two Higgs multiplets { 10 + 126 } in the Yukawa coupling with matter multiplet 16
In this model, all the Yukawa coupling matrices for quarks & leptons are written in terms of two basic matrices (Y 10 and Y 126 ).
Brief review of m inimal SO(10) model Babu-Mohapatra ( ' 93), Fukuyama-Okada ( ' 01), Dutta-Mimura-Mohapatra ( ' 04),… Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
Recent WMAP satellite data show the very precision measurement of the cold dark matter (CDM) relic density
In MSSM with R-parity, we have a natural candidate of the CDM, the lightest sparticle (LSP) or the lightest neutralino ( ).
In minimal SO(10) model, R-parity is automatically conserved since the Majorana mass term for the right-handed neutrino violates the lepton number by two units, and then the LSP becomes stable to provide a natural candidate for the CDM.
Baryogenesis through the leptogenesis mechanism also works well in SO(10) GUT due to the presence of the right-handed neutrinos.
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
5.
Fermion Mass matrices
In minimal SO(10) model, all the fermions mass matrices are written in terms of two basic mass matrices
This leads to some simple relations for the quark and lepton mass matrices:
13 inputs for the charged fermion data: 6 quark masses, 3 angles + 1 phase in CKM matrix, 3 charged-lepton masses
⇒ fix and
⇒ predictions on the neutrino sector!
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
6.
Solving the GUT relation
By using trace and determinant, we obtain two independent equations from the GUT relation.
They can be solved by inputting the experimental data at the weak scale.
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy The phase of c d remains undetermined. July 22-26, 2007
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Mass relation for the neutrino sector:
Type-I See-saw mass matrix:
All lepton mass matrices are determined by only the quark mass matrices!
Predictive theory for the neutrino oscillation data!
Other phenomena related to the Yukawa couplings can be evaluated precisely. ( LFV, muon g-2, EDM, proton decay )
Predictions for the Neutrino mass matrices in Minimal SO(10) model Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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We have only one parameter left free. So, we can make definite predictions.
Predictions in neutrino sector Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy Fukuyama-Okada (‘01) July 22-26, 2007
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Other predictions on LFV, g-2, EDM
LFV, g-2 and EDM are originated from the same dipole moment operator
include the SUSY partners in the loop. Chargino-sneutrino and Neutralino-charged slepton in the loop. Hisano et al. (‘96)
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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Cosmologically favored parameters
The mSUGRA parameter region is very restricted.
J. Ellis et al (‘03) Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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The numerical results on LFV, g-2, EDM Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy Fukuyama-T.K.-Okada (‘03) mu e gamma Electron EDM Exp. bound g-2 July 22-26, 2007
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Neutrino magnetic moments Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy Imaginary part of the chargino –sneutrino vertices contribute Fukuyama-T.K.-Okada (’04) July 22-26, 2007
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Non-thermal leptogenesis
is produced as a decay product of the inflaton, and then decays into a charged lepton-Higgs pair producing B-L asymmetry.
Numerically, we find the following explicit expression
We make use of a minimal SO(10) result to evaluate this formula.
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy Fukuyama-T.K. (‘05) July 22-26, 2007
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The produced baryon asymmetry and the inflaton mass Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy Kinematically excluded region (M inf < MR) Cosmologically allowed region Type-I see-saw Type-II see-saw (no allowed region for non-thermal leptogenesis) Fukuyama-T.K. (‘05) July 22-26, 2007
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Proton decay in SUSY GUT s
In SUSY models, Color Triplet Higgsinos (H C ) mediate the proton decay inducing the following baryon and lepton number violating dimension five operator
In the minimal SO(10) model, we have two types of Yukawa matrices, and the Wilson coefficients can be written as a matrix form
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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Proton decay rate in minimal SO(10) model Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy The green region is the allowed region . In case of , there is a large enough parameter space where all the proton decay models are canceled out although it is very tiny region in case of Fukuyama-Ilakovac-T.K.-Meljanac-Okada (‘05) July 22-26, 2007
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To realize the gauge coupling unification, the simplest way is to put all the VEV’s at the GUT scale.
On the other hand, neutrino oscillation data shows the existence of an intermediate mass scale, which may destabilize the successful gauge coupling unification in the MSSM.
To keep all the VEV’s at the GUT scale, it is necessary to have an additional suppression in MR:
Mild mass hierarchy problem: M R < M GUT Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy Question: Can we realize vR = M GUT while keeping the successful data fitting of the fermion masses and mixings? This is a key point of this work which is realized by considering the model in a warped extra dimension. July 22-26, 2007
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Suppose a minimal Higgs sector which enable to break SO(10) to MSSM
The minimal Higgs potential constructed from the above Higgs is given by
Note that minimal SO(10) model utilizes large representations of the Higgs, it means the gauge coupling is easy to blow up soon after the GUT scale! i.e. t he cutoff scale of the model is just the GUT scale!
Question: How we can achieve a theory with a low cutoff scale well below the Planck scale? This can easily be realized in extra-dimensional set up.
Further consideration to the problems: Higgs sector in minimal SO(10) model Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy (A detailed potential analysis with CG: Fukuyama-Ilakovac-T.K.-Meljanac-Okada (’05)) July 22-26, 2007
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One example
Blows up before unify!
Intermediate scale (<< M GUT ) threshold causes a trouble.
Gauge coupling unification Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy Bertolin-Scwetz-Malinsky (06’) July 22-26, 2007
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Ways to avoid problems
For blowing up problems, there are basically two ways to avoid it.
Use small dimensional rep. of Higgs instead of large one.
Consider a low cut off theory (mini-warped SO(10) model)
In the 1 st approach, we may loose some predictivity on the neutrino sector. However, it is still non-trivial issue if we can fit the charged fermion data with a minimal set of Higgs sector. An example: {10 + 120} is used for fitting the charged fermion data. D. Chang-T. Fukuyama-T.K.-N. Okada (‘05) . “Perturbative SO(10) model”
We found it’s possible to fit all the charged fermion masses and mixings in this scheme.
2 nd approach will be considered in the last part of this talk.
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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1 st option –Perturbative SO(10) model
The model has used the small representations of Higgs multiplets to keep the perturbativity up to the Planck scale.
For the color triplet Higgsinos , we put them at the GUT scale M GUT = 2 x 10 16 [GeV]. However, we still have 3 parameters characterizing the mass matrix for the color triplet, which we vary them freely. Then, we can parameterize the 2x2 mass matrix as
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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Two parameters are enough to cancel out the dominant proton decay mode.
Actually, we found a set of the parameters which cancels out the dominant proton decay mode.
This corresponds to the mass matrix of the from,
Parameter choice to cancel out the dominant proton decay mode Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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When we choose the parameters to cancel out the dominant decay mode ( decay mode) at the same time, we must check the other modes ( and ) are safe or not.
Subdominant proton decay modes D. Chang-T. Fukuyama-T.K.-N. Okada (‘05). Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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Tuning the bulk and brane cosmological constant, RS found the solution of Einstein equation
We will put all matter on the IR brane while Higgs live in the bulk.
2 nd option –minimal SO(10) model in a mini- warped extra dimension Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy 4D Minkowski part Model free parameters : 5D Planck scale : AdS curvature : warp factor or Fukuyama-T.K.-Okada (’07) July 22-26, 2007
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Lagrangian for the bulk field:
We assume χ obtains non-vanishing VEV to give different wave function suppression factors for different charge bulk fields.
N=2 vector multiplet is decomposed into N=1 vector and adjoint scalar multiplet.
Basic setup of the 5D warped SUSY model Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
26.
Solution of the bulk field EOM
Suppose that an adjoint scalar, Σ , which can be arisen from the N=2 vector multiplet, develops the VEV as
This provides a shift of the bulk mass term
A solution for the bulk field’s equation of motion is given
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
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Matter lives on the IR brane (“GUT brane”) while Higgs are in the bulk.
Our setup- wave function profile for the bulk Higgs and brane matter Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy y=0 y= IR brane (GUT brane) UV brane (Planck brane) Δ H u , H d
GUT scale as a 4D cutoff scale: GUT scale is obtained from Planck scale via mini-warping , and is found to be the cutoff scale of the 4D effective theory.
Higgs doublets (H u , H d ) are localized toward IR brane, this enable to produce O(1) Yukawa couplings.
Singlet Higgs ( Δ ), which gives a right-handed neutrino mass, is localized toward UV brane, hence is well separated to the matter on the IR brane.
July 22-26, 2007
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4D effective action on the IR brane Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy
After rescaling of brane field, , the resultant Yukawa coupling could be unsuppressed or suppressed depending on the choice of the bulk mass parameters
Lagrangian for a chiral multiplet on the IR brane ( Φ ) is given by
The interaction between brane field ( Φ ) and bulk field (H) is given by
July 22-26, 2007
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Effects of the VEV of adjoint scalar
This gives an additional contribution to the bulk mass term, which is determined by the charge of each bulk field:
Basically, the wave function get suppressed from the bulk mass in the following manner:
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy
Suppose adjoint scalar gets a non-zero VEV, then it is always possible to have a mass term for the bulk field as follows:
July 22-26, 2007
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Hence, the more charge fields have U(1) charge, the more the wave function of the bulk field receives suppression.
Due to the large U(1) charge for the singlet, it will be suppressed on the IR brane, that is really what we needed to suppress the Yukawa coupling for the right-handed neutrino.
For example, two mass hierarchy can be explained at the same time:
Effects of the VEV of adjoint scalar Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
31.
Summary
We considered a minimal SO(10) model, and estimated neutrino oscillation parameters, LFV rates, muon g-2 and proton decay in detail.
Results:
Neutrino masses & mixings can be well much described.
LFV rates can be well exceed the future bounds.
Muon g-2 can be suitable for BNL E821 result.
Combining with WMAP data -> Cosmologically allowed region exists
Proton decay has also been analyzed in detail.
However, it has some troubles in the Higgs sector.
To fit the neutrino oscillation data, the right-handed neutrinos must lie at the intermediate scale. Such a new scale below the GUT scale may spoil the gauge coupling unification . And there is a blowing up problem in minimal SO(10) model.
Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007
32.
We have considered the minimal SO(10) model in a warped extra dimension. The warped geometry leads to a low scale effective cutoff in effective four dimensional theory, and we fix it at the GUT scale:
The effective right-handed neutrino Yukawa couplings can be lowered while keeping any VEV’s at the GUT scale. A suppression factor can be achieved by localizing the Higgs in the bulk :
For an appropriate choice of parameters, both mass scales can be explained at the same time:
Summary Workshop on Grand Unification and Proton Decay, ICTP, Miramare, Trieste, Italy July 22-26, 2007