March 2005 Theme Group 2 Neutrino Mass and Grand Unification R. N. Mohapatra University of Maryland LAUNCH, 2007 Heidelberg

March 2005 Theme Group 2 Hypothesis of Grand unification (i)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. (ii)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)

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

March 2005 Theme Group 2 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.

March 2005 Theme Group 2 Simplest example: SUSY SU(5)

March 2005 Theme Group 2 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 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).

March 2005 Theme Group 2 to GUTs via seesaw 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]

March 2005 Theme Group 2 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 ?

March 2005 Theme Group 2 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.

March 2005 Theme Group 2 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)

March 2005 Theme Group 2 From SO(10) down to the Std Model SO(10) Nu mass Left-right sym. theory Standard Model-> seesaw

March 2005 Theme Group 2 How is B-L Broken ? {16} vs {126} B-L can either be broken by {16}- Higgs by its component. In which case M_R arises from non- renormalizable terms; Leads to R-parity breaking and hence no stable dark matter without extra assumptions.

March 2005 Theme Group 2 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 = Matter Higgs Minimal model: one each of 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.)

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).

March 2005 Theme Group 2 Details of minimal SO(10) Yukawa: h f bar Leads to fermion mass formulae

March 2005 Theme Group 2 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 ?

March 2005 Theme Group 2 A New sumrule for neutrino mass: Dominant Type II

March 2005 Theme Group 2 Including CP violation: In the model, CP violation can arise from complex Yukawas- (but works only for a narrow range of parameters) In the full minimal model, CP is more natural. Grimus and Kuhbock, 2006

March 2005 Theme Group 2 Restrictions from P-decay for all tan

March 2005 Theme Group 2 Some predictions of the 120 model: Prediction for U_e3:

March 2005 Theme Group 2 Predictions for the MNSP Phase = Dirac phase can be predicted

March 2005 Theme Group 2 Predictions for lepton flavor violation

March 2005 Theme Group 2 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

March 2005 Theme Group 2 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.

March 2005 Theme Group 2 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

March 2005 Theme Group 2 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.

March 2005 Theme Group 2 Type II seesaw and Higgs Profiles

March 2005 Theme Group 2 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.

March 2005 Theme Group 2 Nucleon Decay in SUSY GUTs Gauge Boson exchange:

March 2005 Theme Group 2 SUSY changes GUT scale dependence

March 2005 Theme Group 2 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))

March 2005 Theme Group 2 Proton decay in SO(10)-126 Minimal SO(10) model with 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))

March 2005 Theme Group 2 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 ?

March 2005 Theme Group 2 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

March 2005 Theme Group 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:

March 2005 Theme Group 2 Comparision P-decay vs N-N-bar

March 2005 Theme Group 2 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)

March 2005 Theme Group 2 Proton decay vs N-N-bar oscillation

March 2005 Theme Group 2 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 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.

March 2005 Theme Group 2 Unification scenario with S_4 sym. Parida,RNM,07 Y B-L 2L 3c

March 2005 Theme Group 2

March 2005 Theme Group 2 Predictions for long baseline experiments: