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SUSY SO(10) GUT Next Generation Standard Model ?

SUSY SO(10) GUT Next Generation Standard Model ?. T.Fukuyama(Ritsumeikan University) March 17 ’07 Yonsei University. Based on the works in collaboration with N. Okada, T.Kikuchi 、 A. Ilakovac and S. Meljanac. References:

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SUSY SO(10) GUT Next Generation Standard Model ?

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  1. SUSY SO(10) GUTNext Generation StandardModel? T.Fukuyama(Ritsumeikan University) March 17 ’07 Yonsei University Based on the works in collaboration with N. Okada, T.Kikuchi、A. Ilakovacand 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); and the work in preparation.

  2. Contents • 1. There are four fundamental interactions • 2. They are not constants and unified to one at verrry high enery or at verrry early Universe. • 3.Theory beyond the Standard Model-GUT • 4. Neutrino is the key word for it. • 5. Gravitation saves GUT. Space-time is Not 4 dimensions.

  3. WhyGrand UnifiedTheory　？ • We have four fundamental forces: macroscopic electromagnetic and gravitational interactions, and microscopic strong and weak interactions. Their strengths are very hierarchical at present. That is, strong force is much stronger than electromgnetic force： atomic fusion and fission are much more violent than chemical reaction. However, electromagnetic force ( strong force) increases (decreases) as the energy scale gets laｒge. So we may expect these three forces coincides at some high energy scale, which is indeed the case. This scale is called Grand Unified Theory (GUT) Scale

  4. Grand unification • In the presence of supersymmetry at the EW scale, we can realize the gauge couplings unification. This may indicate the presence of low-energy supersymmetry and a grand unified theory.

  5. Thus gauge coupling unification indeed occurs- MSSM (Minimum SUSY Standard Model). This scale is called Grand Unified Theory (GUT) Scale and GeV • However, recently it is found that neutrinos have masses and we hope to know how and why neutrinos have such and such tiny masses. • Tiny mass indicates the very high energy New Physics • -Next Generation Standard Model. • SO(10) GUT is the most promising candidate for it.

  6. Unification of forces

  7. What is Gauge Theory ? Given a Lagrangian, dynamic is determined. Lagrangian is determined by the gauge principle. Noether, Utiyama. This is crucial for the renormalizability. However Physical observables are NOT determined solely by Lagrangian. Observables are the expectation values of state. States is deviated from symmetry (SSB) and the world is asymmetric though dynamics is symmetric. Gauge Principle and SSB are two ingredients.

  8. Standard Model • Standard model is the gauge theory of SU(3)xSU(2)xU(1). • SU(3) color and represents strong int. Color was found by Han(韓）and Nambu(南部） • SU(2), weak charge. and U(1), hyper charge, constitute electroweak int., which is broken to U(1) electromagnetic charge. Gravitation appears later in this talk.

  9. Is Standard Model complete ? • All theories (may) have their application limits. • Newton’s dynamics is NOT applicable where constituents have fast velocities of O( light velocity). Standard model may be modified when constituents have very high energy. Modified to what theory ? Is there any evidence ?

  10. There are several experimental evidences. • Neutrino has mass. • Muon g-2 • There are several theoretical motivations. • Coupling constants are unified. • Standard model includes so many parameters. • It can not explain why they have such and such values • Hierarchy problem

  11. Mass hierarchｙ problem

  12. In order to remedy Hierarchy problem • SUPER SYMMETRY • Extra Dimension • Little Higgs—Higgs Field is Nambu-Goldstone Boson

  13. Structure needs Dark Matter • Fluctuation grows proportionally to scale factor • Hubble’s law • Fluctuation was in CMB • After a becomes 3000 times larger at present but still

  14. DM is free from the electromagnetic int. • DM made a potential well before CMB and baryon was attracted to this well after CMB and now • That is, the Universe has structure. • SUSY gives the candidate of DM, neutralino, gravitino,…..

  15. Neutrino oscillation • Neutrino oscillates if it has mass • Neutrino mass is very tiny but its smallness indicates opens the window to new high energy physics

  16. Seesaw Mechanism • Why is neutrino mass so small? • Need right-handed neutrinos to generate neutrino mass, but nR SM neutral To obtainm3~(Dm2atm)1/2, mD~mt, M3~1015GeV (GUT!)

  17. Why SO(10) and not SU(5) ? • Standard Model is SU(3)xSU(2)xU(1) Gauge Theory, whose rank is four. • New theory must include this as subgroup. • The minimum such group is SU(5) but SO(10) (rank 5) is more preferable • Fundamental representation of SO(10) is 16, which includes all matter contents • =16 • 16=10+5bar+1 under SU(5) decomposition. • SO(10) satisfies Anomaly free condition.

  18. 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’))

  19. Theory consists of two ingredients: • Gauge Invariance and Spontaneous Symmetry Breaking. • Mass of fermion is generated by the Yukawa coupling with Higgs: • However, • So Higgs H must belong to either 10,120,126bar. • We have found that the minimum SO(10) GUT • where 10 and 126bar Higgs couple with matters.

  20. Minimal SO(10) model (Babu-Mohapatra (93’); Fukuyama-Okada (01’)) • 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.

  21. 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.

  22. Low-energy superpotential • Then the low-energy Yukawa couplings are given by

  23. 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!

  24. 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. )

  25. Current Data Here and • Strumia-Vissani hep-ph/060654

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

  27. 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!

  28. 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.

  29. Cosmological constraint on Fig. The shaded red region is ruled out by WMAP observation alone. The shaded orange region is ruled out when adding SDSS galaxy clustering information and the yellow region is ruled out when including SDSS Lyman-alpha Forest information as well. The five curves correspond to the sum of the neutrino masses, equaling 1, 2, 3, 4 and 5 eV, respectively. This figure shows that the WMAP CMB-measurements alone tell us almost nothing about neutrino masses and are consistent with neutrinos making up 100 % of the dark matter. Tegmark, hep-ph/0503257

  30. Gravitino problem Fig. Upper bounds on the reheating temperature as a function of the gravitino mass for the case where the gravitino dominantly decays into gluon-gluino pair. • This result indicates that the thermal leptogenesis cannot work if we keep the gravitino mass at the weak scale. • Then we should consider some alternative mechanism: non-thermal leptogenesis, AD- baryo- (lepto-) genesis, ….. Kawasaki-Kohri-Moroi, astro-ph/0408426

  31. Charged lepton sector • By making some linear combinations, we get a “GUT relation”, e.g. • Cf. GUT relation in minimal SU(5): • This is a good relation for 3rd generation. So we can naively expect that is small.

  32. Neutrino sector • Dirac neutrino mass matrix: • Right-handed Majorana mass matrix: • Light Majorana neutrino mass matrix is obtained by using a seesaw formula: All lepton mass matrices are determined by only the quark mass matrices!

  33. Seesaw mass matrix • Type-I seesaw formula: • When we choose parameters to cancel the second line, this reduces to the type-II seesaw formula.

  34. Bi-large mixing mass matrix • Bi-large mixing mass matrix is naturally obtained as a result of the fact that the bottom-tau mass unification at the GUT scale. • “33” element is suppressed by choosing a parameter near the value σ= π. It’s an essential point to produce the bi-large mixing structure of the neutrino mass matrix.

  35. Solving the GUT relation • By using “trace” and “determinant”, we obtain two independent equations.

  36. Input data @ EW scale

  37. Solution of the GUT relation • We vary the input values of and to find a solution. • For we find a crossing point as in the figure:

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