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Review of the present status of SO(10) GUT

This review discusses the motivations behind Grand Unified Theories (GUTs), focusing on SO(10) GUT, experimental observations, theoretical implications, gauge group SU(5), SUSY, dark matter, neutrino masses, and mixings. It also explores theoretical questions and the relationship with cosmology.

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Review of the present status of SO(10) GUT

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  1. Review of the present status of SO(10) GUT Universitry of Southampton March 7, ‘08 Takeshi Fukuyama (Ritsumeikan University)

  2. 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 interaction Neutrino oscillations high energy scales via Seesaw Muon g-2 Theoretical implications (aesthetic displeasure of SM) The unification of so many parameters in the SM Higgs mass hierarchy problem->new physics above TeV Intermediate energy scales of axion and Heavy (right-handed) neutrino etc. Confrontation with CosmologyDark Matters, Dark Energy

  3. 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 other problems like Susy breaking mechanism, Mu-problem, gravitino problem, …..

  4. 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.Kamimura 1988 Phys.Lett.) • These are the (vertical) symmetries of one family (?). How about the (horizontal) symmetry of inter-families ?

  5. 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.

  6. Overview of experimental data • Neutrino masses & mixings • Since the discovery of neutrino oscillations in SuperK (1998), we have a first evidence of physics beyond the SM. • Now is in the era of precision measurement for atmospheric & solar neutrino oscillations in SuperK, K2K, SNO and KamLand. • Future prospect is to measure the remaining mixing angle, CHOOZ angle, and the CP violation in the lepton sector! • These data show that we have two large mixing angles plus one small angle in the lepton sector. (cf. quark sector have three small mixing angles. )

  7. Theoretical open question • Why lepton sector have so large mixings in comparison to quark sector? • Which mass patterns do neutrinos favor?

  8. Lepton Flavor Violation (LFV) • Because we really see LFV as neutrino oscillations, we naturally expect LFV can also be seen in the charged lepton sector! • Current experimental bound: • How well motivated from theoretical point of view? • In the Standard Model (+ Right-handed neutrinos): too small rate (∵GIM suppression well works). • In SUSY models:New sourceofLFV, soft SUSY breaking terms (with No GIM suppression, in general) exist. LFV processes are important sources for low-energy SUSY search!

  9. Muon g-2 • There exist a 2.8σ discrepancy between the recent BNL result and the Standard Model predictions. • If this is real, it may be a first evidence of supersymmetry.

  10. Motivation of SO(10) GUT • SUSY ＋ GUT • Experimental evidence:three gauge couplings unification with MSSM particle contents. • SO(10) GUT • SO(10) fundamental representation include all the matter in the MSSM plus right-handed neutrinos. • Experimental evidence:very tiny neutrino masses. It can be explained via the “seesaw mechanism”, and it works well in SO(10) GUT in the presence of the right-handed neutrinos. (Yanagida, Gell-Mann et al. (79’))

  11. 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

  12. 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 (2004); 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)

  13. Yukawa couplings • After the symmetry breakings, we have • Below the GUT scale, we assume MSSM is realized, and we have two Higgs doublet which are linear combinations of original fields.

  14. 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!

  15. Predictions in neutrino sector • We have only one parameter , left free. So, we can make definite predictions.

  16. Input data @ EW scale

  17. Yukawa’s are determined! • 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.)

  18. Soft SUSY breaking terms • We consider the general soft SUSY breaking mass parameters at low-energy

  19. Lepton Flavor Violation (LFV) • Because we really see LFV as neutrino oscillations, we naturally expect LFV can also be seen in the charged lepton sector! • Current experimental bound: • How well motivated from theoretical point of view? • In the Standard Model (+ Right-handed neutrinos): too small rate (∵GIM suppression well works). • In SUSY models:New sourceofLFV, soft SUSY breaking terms (with No GIM suppression, in general) exist. LFV processes are important sources for low-energy SUSY search!

  20. Estimations of LFV and g-2 • LFV and g-2 are originated from the same dipole moment operator • include the SUSY partners in the loop. Chargino –sneutrino & Neutralino -charged-sleptonloop Hisano et al. PRD53 (1996)

  21. Formula for LFV, g-2 and EDM • For the estimation of LFV the decay rate is given by • For the estimation of g-2 the SUSY contribution is estimated by • For the estimation of EDM the SUSY contribution is estimated by

  22. mSUGRA boundary condition • We impose the universal boundary conditions at the GUT scale • So we have three free parameters in the soft mass terms,

  23. RG induced Flavor mixings • Flavor mixing is induced by RG running from the GUT scale to the EW scale • In the basis where the charged lepton mass matrix is diagonal, LFV is induced through the neutrino Dirac Yukawa coupling matrix.

  24. The prediction about • For fixed • Very close to the current experimental upper bound. →It is testable in near future experiments.

  25. 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}.

  26. 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

  27. Proton decay in SUSY GUT • In the minimal SO(10) model, we have two kinds of Yukawa matrices, 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

  28. Proton Decay Results: The decay rate in our model is within the experimental upper bound if we take the small tan β = 2.5, assuming the color triplet Higgs mass to be at the usual GUT scale. • 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). Our SO(10) Model is very testable in the near future experiments!

  29. Proton decay rate formula

  30. Parameters in Higgs sector-(i)

  31. Parameters in Higgs sector-(ii)

  32. 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 .

  33. Doublet-doublet problem

  34. ___ 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.

  35. Many vacua (STD singlets) • (1234) • (5678+5690+7890) • (1256+1278+1290+3456+3478+3490) • (13579) • (24680)

  36. The gauge coupling unification From Bertolini-Scwetz-Malinsky hep-ph/0605006

  37. How to repair it in non-minimal SO(10) models • Add additional 10 or 120 Higgs. ___ 2. Add additional 126+126, or 54 Higgs for neutrino scale. Type II seesaw Type I seesaw The detail does not affect to the following discussion. Alternative Higgs choices : (Babu-Gogoladze-Nath-Syde)

  38. First part summary • We estimated neutrino oscillation parameters, LFV rates,Muon g-2 and Proton decay in the Minimal SO(10) Model • Results: Neutrino masses & mixings can be well much described. LFV rates can be well exceed the future bounds Muon g-2 can be suitable forBNL E821result Combining withWMAP data → Cosmologically allowed region exists Using these unambiguous Yukawa couplings, we have also analyzed the proton decay rate in detail.

  39. 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. Solution by warped extra dimension-First approach- 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)

  40. In order 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 the intermediate mass scale, which may destabilize the successful gauge coupling unification in the MSSM . How to solve this mild hierarchy problem? It is necessary to have an additional suppression as follows

  41. World of Extra Dimension

  42. 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.

  43. Lagrangian for the Hypermultiplet in bulk

  44. 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’)] : 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.

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

  46. 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.

  47. 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 to protect the fast proton decay. • We can exclude (6,1,1) which was harmful which was included in full SO(10) invariant theory.

  48. Our Setup SO(10)invPSinv vevof (10,1,3) Standard ｙ＝０　　　　　　　　　　　ｙ＝pi/2 Inviible Visible Only gauge multiplet resides in bulk

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