Neutrino Mass and Grand Unification R N Mohapatra

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

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 Te. V scale -> GUC (B) Theme Group 2 March 2005

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

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 March 2005

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

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. 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 March 2005

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 March 2005

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 Te. V). Case (i) seesaw another indication for SUSY GUT since the GUT scale is Ge. V ? Theme Group 2 March 2005

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 March 2005

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 March 2005

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

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 nonrenormalizable terms; Leads to R-parity breaking and hence no stable dark matter without extra assumptions. Theme Group 2 March 2005

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 March 2005

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 March 2005

Details of minimal SO(10) • Yukawa: h 16. 16 10+f 16. 126 -bar • Leads to fermion mass formulae Theme Group 2 March 2005

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 Ge. V. Does it affect unification ? Theme Group 2 March 2005

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

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 March 2005

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

Some predictions of the 120 model: • Prediction for U_e 3: Theme Group 2 March 2005

Predictions for the MNSP Phase Dirac phase can be predicted = 0. 5 -0. 7 Theme Group 2 March 2005

Predictions for lepton flavor violation Theme Group 2 March 2005

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 March 2005

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 March 2005

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 Ge. V; Goh, RNM, Nasri, 04 Theme Group 2 March 2005

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 nonperturbative after M_U. Theme Group 2 March 2005

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 March 2005

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

SUSY changes GUT scale dependence Theme Group 2 March 2005

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 March 2005

Proton decay in SO(10)-126 • Minimal SO(10) model with 10+126 which predict neutrino mixings: • 4 parameter model: predicts • For large tan proton decay the model is incompatible with (Goh, R. N. M, Nasri, Ng (2004)) Theme Group 2 March 2005

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 Ge. V, any chance to see it ? Theme Group 2 March 2005

YES SINCE NEW OPERATORS CAN APPEAR • New operators appear with SUSY as well as unexplored Te. V scale spectrum!! • Examples: With SUSY: If there is SUSY + diquark fields: Weaker suppression SUSY+ /M Theme Group 2 Even weaker suppression March 2005

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 Ge. V: Theme Group 2 March 2005

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

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 March 2005

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

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+126 Higgs are realistic and predictive. Can be tested by forthcoming neutrino experiments ! • Lower B-L scales can be tested by neutronanti-neutron oscillation using current reactor fluxes. Urge a renewed effort to search for this process. Theme Group 2 March 2005

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

Theme Group 2 March 2005

Predictions for long baseline experiments: Theme Group 2 March 2005