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Neutrino Mass and Grand Unification

Neutrino Mass and Grand Unification. R. N. Mohapatra University of Maryland LAUNCH, 2007 Heidelberg. Hypothesis of Grand unification.

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Neutrino Mass and Grand Unification

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  1. Neutrino Mass and Grand Unification R. N. Mohapatra University of Maryland LAUNCH, 2007 Heidelberg Theme Group 2

  2. Hypothesis of Grand unification • Grand unification is an interesting hypothesis which says that all forces and all matter become one at high energies no matter how different they look at low energies. • Two examples of theories where simple renormalization group analysis of the low energy couplings do indeed lead to coupling unification at high energies: (A). MSSM at TeV scale-> GUC (B) Theme Group 2

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

  4. Other advantages of GUTs • (i) Higher symmetry could give better understanding of fermion masses ; (ii) Explains charge quantization; (iii) High scale explains proton stability; (iv) High scale goes well with cosmological issues such as inflation and baryogenesis. Theme Group 2

  5. Simplest example: SUSY SU(5) Theme Group 2

  6. Lessons from SU(5): Learning from failure • Does not mean the idea of GUTs is dead. • Key to predictivity is to keep the model renormalizable; e.g. the 10.10.10.5 coupling in SU(5) has to have a coupling < 10^-7 – also indicating that non-ren. Couplings have tiny couplings for whatever reason. • Neutrino mass has again put new life into the GUT idea- perhaps best to use theories with ren. Yukawas (as we do here). Theme Group 2

  7. to GUTs via seesaw • Simplest way to understand small neutrino masses : why ? Add right handed neutrinos to the SM with large Majorana mass: MR is the new physics scale. [Minkowski; Gell-Mann, Ramond, Slansky; Yanagida; RNM, Senjanovic;Glashow] Theme Group 2

  8. What is the seesaw scale, MR? • Using Atmospheric mass measured by Super-K and in the seesaw One gets (i) SEESAW SCALE CLOSE TO GUT SCALE- (ii) If is suppressed (by symmetries), seesaw scale could be lower (even TeV). Case (i) seesaw another indication for SUSY GUT since the GUT scale is GeV ? Theme Group 2

  9. Minimal GUT group for neutrinos • Seesaw provides the answer: • The fact that is most easily understood if there is a new symmetry associated with RH neutrino mass generation. • The obvious symmetry is B-L, which is broken by which gives RH neutrino mass. GUT group must have B-L as the subgroup. Theme Group 2

  10. SO(10) Grand unified theory • Natural GUT group is SO(10) since its spinor rep contains all 16 needed fermions (including RH neutrino) in a single rep. • Georgi; Fritzsch, Minkowski (74) • Contains B-L needed to understand why MR<< M_Planck . • B-L if properly broken also allows a naturally stable dark matter in MSSM. (RNM, 1986) Theme Group 2

  11. From SO(10) down to the Std Model • SO(10) Nu mass • Left-right sym. theory • Standard Model-> seesaw Theme Group 2

  12. How is B-L Broken ?{16} vs {126} • B-L can either be broken by {16}- Higgs by itscomponent. In which case M_R arises from non-renormalizable terms; Leads to R-parity breaking and hence no stable dark matter without extra assumptions. Theme Group 2

  13. Alternatively Break B-L by 126-Higgs • SM singlet in 126 is which has B-L=2; • Leaves R parity unbroken in MSSM and gives stable dark matter. • Also 16 X 16 = 10 + 126 + 120 Matter Higgs Minimal model: one each of 10+126+ 120. 126 gives mass to charged fermions as well as RH neutrinos relating RH neutrino spectrum to charged fermion spectrum. Also uses only renormalizable couplings. (not true for 16- Higgs models.) Theme Group 2

  14. 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

  15. Details of minimal SO(10) • Yukawa: h16.16 10+f 16 .16.126-bar • Leads to fermion mass formulae Theme Group 2

  16. Neutrino mass and seesaw in SO(10) • SO(10) model (and all LRS) models modify seesaw as follows: Type II Type I with [Magg, Wetterich; Lazaridis, Shafi, Wetterich; RNM, Senjanovic; 80] For first term to be significant, triplet mass must be around 10^14 GeV. Does it affect unification ? Theme Group 2

  17. A New sumrule for neutrino mass: • Dominant Type II Theme Group 2

  18. Including CP violation: • In the 10+126 model, CP violation can arise from complex Yukawas- (but works only for a narrow range of parameters) • In the full minimal 10+126+120 model, CP is more natural. • Grimus and Kuhbock, 2006 Theme Group 2

  19. Restrictions from P-decay for all tan Theme Group 2

  20. Some predictions of the 120 model: • Prediction for U_e3: Theme Group 2

  21. Predictions for the MNSP Phase Dirac phase can be predicted = 0.5-0.7 Theme Group 2

  22. Predictions for lepton flavor violation Theme Group 2

  23. Beyond Flavor Issues • Realization of type II seesaw dominance in the models: (i) Higher B-L scale (ii) together with lower triplet mass • Coupling Unification and avoiding early non-perturbativity; • Proton decay Theme Group 2

  24. What happens in the truly minimal model: • {10}+{126}+{210}: Implies • Needs modification: Two possibilities: • (i) Add extra {54} to lower Triplet mass by a mini-seesaw; also overcomes large thershold effect objection. • (ii) Use mini-warping- Physics above GUT scale strongly coupled. Theme Group 2

  25. Coupling Unification with type II seesaw Usual allegation of large threshold effects FALSE !! Could have higher unif. scale with SO(10)-> SU(5) and Triplet, {15 } of SU(5) at 10^13 GeV; Goh, RNM, Nasri,04 Theme Group 2

  26. Another way to achieve Type II dominance • Use mini-warped 5-D model: • Idea: (Fukuyama, Kikuchi, Okada(2007); Okada, Yu, RNM-in prep.) • Consider warped 5-D model with warping from Planck to GUT: • Locate Higgs in the Bulk so that their effect on the 4-D brane depends on location and U(1) charge. That way one can ensure lighter {15} and also unification. • No large Threshold effect since theory non-perturbative after M_U. Theme Group 2

  27. True test of GUT hypothesis • Coupling unification, often cited as evidence for GUTs are not really so. True test of GUTs is proton decay; In particular no proton decay to the level of 10^36-37 years will be evidence against GUTs. Theme Group 2

  28. Nucleon Decay in SUSY GUTs • Gauge Boson exchange: Theme Group 2

  29. SUSY changes GUT scale dependence Theme Group 2

  30. Predictions for proton decay in SO(10)-16 • B-L could be broken either by {16}-H or {126}-H. • SU(5) type problem avoided due to cancellation between diagrams. • Proton decay in {16} models: model dependent: in one class of models (Babu, Pati and Wilczek (2000)) Theme Group 2

  31. Proton decay in SO(10)-126 • Minimal SO(10) model with 10+126 which predict neutrino mixings: • 4 parameter model: predicts • For large tan the model is incompatible with proton decay (Goh, R.N. M, Nasri, Ng (2004)) Theme Group 2

  32. Are GUTs the only choice for seesaw ? • It could be that B-L scale is lower : How to test for that possibility ? • Searching for neutron-anti-neutron oscillation is one way. • Few questions: N-N-bar operator: Leads to Osc. Time Since seesaw scale is >10^11 GeV, any chance to see it ? Theme Group 2

  33. YES SINCE NEW OPERATORS CAN APPEAR • New operators appear with SUSY as well as unexplored TeV scale spectrum!! • Examples: With SUSY: If there is SUSY + diquark fields: SUSY+ /M Weaker suppression Even weaker suppression Theme Group 2

  34. 224 models do lead to such operators • New Feynman diagrams lead to observable N-N-bar transition time with high seesaw scale of 10^11 GeV: Theme Group 2

  35. Comparision P-decay vs N-N-bar Theme Group 2

  36. Proposal to search for N-N-bar at DUSEL • Dedicated small-power TRIGA • research reactor with cold neutron • moderator  vn ~ 1000 m/s •  Vertical shaft ~1000 m deep with • diameter ~ 6 m at DUSEL •  Large vacuum tube, focusing • reflector, Earth magnetic field • compensation system •  Detector (similar to ILL N-Nbar • detector) at the bottom of the shaft • (no new technologies) • Kamyshkov et al. (2005) Theme Group 2

  37. Proton decay vs N-N-bar oscillation Theme Group 2

  38. SUMMARY • Neutrino mass introduces B-L as a symmetry of Nature. What is its scale ? • Very interesting possibility is that B-L scale is GUT scale: Minimal SO(10) realizations with 10+120+126 Higgs are realistic and predictive. Can be tested by forthcoming neutrino experiments ! • Lower B-L scales can be tested by neutron-anti-neutron oscillation using current reactor fluxes. Urge a renewed effort to search for this process. Theme Group 2

  39. Unification scenario with S_4 sym. Y Parida,RNM,07 B-L 2L 3c Theme Group 2

  40. Theme Group 2

  41. Predictions for long baseline experiments: Theme Group 2

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