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Perspectives on Grand Unification in View of Neutrino Mass

Perspectives on Grand Unification in View of Neutrino Mass. R. N. Mohapatra University of Maryland. 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.

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Perspectives on Grand Unification in View of Neutrino Mass

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

  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 Theme Group 2

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

  4. 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. Theme Group 2

  5. 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. Theme Group 2

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

  7. 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) Theme Group 2

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

  9. Neutrino Masses Theme Group 2

  10. 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 !! Theme Group 2

  11. 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) Theme Group 2

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

  13. 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: Theme Group 2

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

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

  16. 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) Theme Group 2

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

  18. 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.) Theme Group 2

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

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

  21. 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. Theme Group 2

  22. 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-: Theme Group 2

  23. Minimal GUT Group for neutrinos: SO(10) • Georgi; Fritzsch, Minkowski (75) • {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- Theme Group 2

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

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

  26. 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. Theme Group 2

  27. 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). Theme Group 2

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

  29. 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. Theme Group 2

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

  31. Predictions for long baseline experiments: Theme Group 2

  32. Predictions for lepton flavor violation Theme Group 2

  33. 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. Theme Group 2

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

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