1. March 2005 Theme Group 2 Perspectives on Grand Unification in View of Neutrino Mass R. N. Mohapatra University of Maryland

2. March 2005 Theme Group 2 S. Sakata and MNSP Neutrino Mixing matrix -1956-Sakata model (p, n, ) -led to SU(3) symmetry and to quark model -concept of weak isospin used in modern gauge theories

3. March 2005 Theme Group 2 Baryon-Lepton Symmetry Baryon-Lepton Symmetry-inspired by Sakata Model Gamba, Marshak, Okubo (1959) -Sakata called it ``Kiev Symmetry '‘

4. March 2005 Theme Group 2 Isospin Unification and Electric Charge GMO proposed generalized Gell-Mann- Nishijima Formula based on Baryon- Lepton Symmetry: Q = I + -``Baryon-Lepton Unification’’- Key ingredient of modern grand unified theories.

5. March 2005 Theme Group 2 From Sakata Model to Nagoya Model 1960: Maki-Nakagawa-Ohnuki-Sakata propose composite model with B-matter: -Precursor of modern composite models; -1962: Brookhaven expt discovers second neutrino - Problem for Nagoya model.

6. March 2005 Theme Group 2 Birth of Neutrino Mixing Idea To fit two neutrinos into Nagoya model, Maki, Nakagawa, Sakata introduce neutrino mixings: true neutrino and weak neutrinos

7. March 2005 Theme Group 2 Maki-Nakagawa-Sakata-Pontecorvo Matrix For 3 generation, Majorana neutrinos, MNSPmatrix is U = VK, where v = (Thanks to Chlorine, S-K,Gallex,Sage,SNO,KamLand,K2K,MINOexpts)

8. March 2005 Theme Group 2 A Hidden symmetry of Leptons ? Possible symmetries being discussed: S3,S4, A4.

9. March 2005 Theme Group 2 Neutrino Masses

10. March 2005 Theme Group 2 Puzzles of Neutrino Mass Physics Why Why are neutrino mixings so much larger than quark mixings ? How does neutrino mass physics fit into the big picture of grand unification, supersymmetry (and/or extra dimensions )? In any case, neutrino mass is first evidence of new physics beyond the standard model !!

11. March 2005 Theme Group 2 New standard model: Seesaw Paradigm Add right handed neutrinos to the standard model and give them a large mass: Minkowski (77), Yanagida; Gell-Mann, Ramond, Slansky; Glashow; RNM, Senjanovic (79)

12. March 2005 Theme Group 2 Seesaw Mechanism Implies neutrinos are Majorana fermions. Predicts neutrinoless double beta decay.

13. March 2005 Theme Group 2 Why Seesaw Theoretically Appealing ? Adding RH neutrino makes Standard model quark lepton symmetric; (unlike standard model) It makes B-L cubic anomaly free and expands the gauge group to the left-right symmetric group:

14. March 2005 Theme Group 2 Other Implications: 1.Weak interactions become asymptotically parity conserving; 2. Marshak and RNM (79); A. Davidson (79). 3. Implies lepton number violation and Majorana neutrino mass, since

15. March 2005 Theme Group 2 Neutrino Mass Parity Violation Connection Low energy weak interaction V-A type because neutrino mass is so small:

16. March 2005 Theme Group 2 GRAND UNIFICATION (Pati,Salam; Georgi, Glashow,73) Grand unification: An important and interesting concept ; says that all matter (quarks and leptons) and all forces are one and the same Two simple theories : (A) Supersymmetric minimal standard model (with SUSY at TeV)- couplings unifiy; (B) G_{SM}->SU(2)_LX SU(2)_R X SU(4)_c (no susy)-> SO(10)

17. March 2005 Theme Group 2 Unification of Couplings: two examples Weak scale susy Non SUSY SO(10) with seesaw

18. March 2005 Theme Group 2 Advantages of High Scale in GUT Superheavy GUT scale goes well to address cosmological issues e.g inflation and baryon asymmetry etc. Coupling unification perhaps means a grand unifying symmetry and a predicitve theory for quark and lepton masses. Superheavy scale : just what one needs to suppress proton decay predicted by GUT that unify quarks and leptons. Present limit: implies (Close to the GUT scale.)

19. March 2005 Theme Group 2 Simplest GUT Model: SU(5)

20. March 2005 Theme Group 2 SUSY GUT: Why SUSY ? 1. Stabilizes gauge hierarchy; 2.Explains EWSB; 3. Provides dark matter; lightest SUSY particle if stable.

21. March 2005 Theme Group 2 SUSY NEEDS NEW PHYSICS For the lightest SUSY particle to be dark matter, a new symmetry (in addition to Supersymmetry) called R-parity must be imposed !.Where does this symmetry come from ? Neutrino mass may throw light on this. Recall: seesaw mechanism generates the B-L symmetry- If B-L is broken, it can leave R- parity as a gauge symmetry of MSSM.

22. March 2005 Theme Group 2 Neutrino mass: a hint of grand unification ? Seesaw explanation of neutrino mass has put grand unification back on center stage again ! Why ? Atmospheric mass measured by Super-K using the seesaw formula implies SEESAW SCALE CLOSE TO GUT SCALE-:

23. March 2005 Theme Group 2 Minimal GUT Group for neutrinos: SO(10) Georgi; Fritzsch, Minkowski (75) 1.{16}-dim spinor contains contains all std model fermions plus RH neutrino; 2. It contains B-L symmetry, which can lead to R-parity in MSSM and hence a naturally stable dark matter. 3. B-L explains why Seesaw scale is so much less than the Planck scale-

24. March 2005 Theme Group 2 From SO(10) down to the Std Model SO(10) Nu mass Left-Right Sym. Theory Standard Model-> seesaw

25. March 2005 Theme Group 2 NEW SEESAW FORMULA IN SO(10) 1. New contribution due to Higgs triplet (Fig. b) The first term can dominate for some parameter range:

26. March 2005 Theme Group 2 Fermion Masses in SO(10): Matter in 16-spinor: 16 X 16 = 10 + 126 + 120 Matter Higgs Minimal model: one each of 10+126+ 120. A REALISTIC PREDICTIVE MODEL : Better than minimal SU(5) and testable in neutrino sector.

27. March 2005 Theme Group 2 Large neutrino mixings in minimal SO(10) How large mixings arise naturally in the minimal models : Simple Example: Model with only one {10} and {126} Higgs: Has only 12 parameters (for CP conserving case)- all determined by quark masses and mixings and charged leptons; all neutrino mixings are predicted. Babu, RNM (92); Bajc, Senjanovic, Vissani (2003); Goh, Ng, RNM (2003).

28. March 2005 Theme Group 2 A New sumrule for neutrino mass: Type II seesaw assumption leads to the sum rule at GUT scale: Note

29. March 2005 Theme Group 2 Including CP violation: In the 10+126 model, CP violation can arise from complex Yuakawas- (but works only for a narrow range of parameters) In the full minimal 10+126+120 model, CP is more natural.

30. March 2005 Theme Group 2 Some predictions of the final model: Prediction for U_e3:

31. March 2005 Theme Group 2 Predictions for long baseline experiments:

32. March 2005 Theme Group 2 Predictions for lepton flavor violation

33. March 2005 Theme Group 2 Conclusion Seesaw explanation of neutrino mass has several specific predictions for physics beyond the standard model: A. B-L symmetry B. Left-right symmetry of weak int. C. High seesaw scale- a hint of SO(10) Grand Unification; A minimal SO(10) model with 126-Higgs predicts neutrino mixings and natural dark matter and is testable.

34. March 2005 Theme Group 2 POSTSCRIPT Sakata legacy very much manifest in today’s neutrino physics !!