1. Neutrino Mass and Flavor Physics R. N. Mohapatra

2. Neutrino Mass- What do we know ? Masses: ; Mixings: ; Overall mass scale: <.1- 1 eV (roughly) To be determined (expts in progress or planning) (i) Majorana or Dirac ? (ii) Mass ordering: NH or IH (iii) Value of (iv) Any possible CP violation ? (v) Leptonic unitarity

3. Many experiments on the way (i) Majorana or Dirac (ii) Absolute mass scale: (iii) Mass ordering: (iv) Value of (v) CP phase

4. Plan of the talk Neutrino mass  New physics beyond SM: Raises two new issues: New mass scale to explain why Is it accessible at the LHC ? New approach to flavor : Can we have a unified understanding quark- lepton mixings ?

5. Why ? Seesaw Paradigm: Add heavy right handed neutrinos to SM and play seesaw: Seesaw scale is the new physics scale !! Two different seesaws depending on whether N Majorana or Dirac

6. Type I seesaw Majorana Breaks B-L : New scale and new symmetry beyond SM. After EWSB -Neutrino majorana key parameter to test seesaw type I Minkowski,Gell-Mann, Ramond Slansky,Yanagida, Mohapatra,Senjanovic,Glashow

7. Inverse Seesaw Mostly Dirac i.e. add another singlet Seesaw parameter testing or larger (RNM’86; RNM, Valle’86)

8. New physics signal for simplest seesaw Strength given by or mixing: e.g. collider production: Leptonic non-unitarity: Both negligible for type I seesaw but observable for inverse seesaw M N ~ TeV Situation different with gauge forces !!

9. 1. Seesaw (B-L) scale Neutrino masses do not determine seesaw scale  ; M U ~ GeV Both and high seesaw scale indication for SUSYGUTs; No collider signals ! (Common Lore)  B-L scale at TeV LHC signals with only gauge forces; No GUTs with type I.  B-L at TeV and GUTs can co-exist: since possible (Dev, RNM’09) Inverse seesaw

10. A concrete realization: Low scale B-L in Left-Right N R  Gauge group : New W’ and Z’ Fermion assignment Two Avatars of LR: type I Inverse seesaw +

11. Bound on SUSYLR scale from Low energy data M_WR > 2 TeV from a combination of KL-KS, epsilon, d_n together.(uncertainty from long distance contribution ); (An,Ji,Zhang’07)

12. Bounds from Nu-less double beta decay New contributions from WR-N exchange (only for Case I) (RNM, 86; Hirsch, Klapdor, Panella 96) Diagram:  From Ge76:

13. Seesaw signal from Nu contribution: Inverse hierarchy Normal hierarchy Punch line: Suppose long baseline  and nonzero signal for (+ RP if susy )  TeV WR and type I

14. Constraints on Seesaw scale from coupling unification: TeV type I does not grand unify: Landau Pole (Kopp, Lindner, Niro, Underwood’09) (Parida, Sarkar, Majee, Raichaudhuri’09) Discovery of type I signal at LHC will rule out GUTs.

15. TeV Inverse Seesaw (LR) Inverse seesaw does unify and give realstic model: with both WR and Z’ in TeV range; MSSM GUT SUSYLR GUT Look for not only susy but also WR, Z’, N at LHC: (Dev, RNM, 09; PRD);

16. SO(10) as the GUT theory {16 }- spinor for all matter Type I: only unification route: Inverse seesaw:

17. Radiative Breaking of B-L and SM Positive spartner mass square at GUT scale- RGE turns them negaitve much like SM with large t-mass (Dev, RNM’10)

18. LHC Signals for seesaw LHC production of WR : ; N-decay: type I Inv. Seesaw: Type I case: (Keung, Senjanovic;  Han, Perez,Huang,Li, Wang; Del Aguila, Aguilar-Saavedra; Azuelos,..) Inverse seesaw: Only Trileptons; no same sign dileptons(30 fb^-1) (del Aguila,Aguilar-Saavedra, de Blas) 

19. Other TeV scale Type I Signals TeV type I Seesaw requires B-L=2 Higgs: Doubly charged Higgs can have sub-TeV mass. Decays to lepton pairs Four lepton signals at LHC LHC signals for type I seesaw will rule out simple GUTs

20. New Dark matter in TeV scale Inverse seesaw: If super-partner of RH neutrino is the lightest, it will be stable due to R-parity- become DM. Soft breaking: Lightest linear combination is dark matter: Minimal Type I case: Usual Bino-Higgsino

21. Dark matter in type I GUT vs TeV scale Inverse seesaw: Inverse seesaw case: (Fornengo, Arina, Bazzochi, Romao, Valle’08) New DM New DM : : Two contributions to relic density: Z’ exchange (Matchev, Lee, Nasri) No or small Z’ effect

22. 2. Understanding Flavor (i) Mass hierarchies (ii) Strange mixing patterns: Leptons: Quarks: U PMNS = U CKM = (Harrison, Perkins, Scott; He, Zee,Wolfenstein; Xing,..)

23. Mass Texture Up-quark and charged lepton diagonal basis: = Cabibbo angle

24. Strategy for texture Key idea: SM has a large sym for zero fermion masses : [SU(3)]^5; Choose subgroup: Discrete subgroup with 3-d. rep. Replace Yukawa’s by scalar fields (flavons); Minima of the flavon theory determines Yukawas:

25. Application to Neutrinos Successful Family symmetries for TBM : Flavon fields are triplets: (Ma, Rajasekaran; Babu, Ma, Valle, King, Ross; Altarelli, Feruglio, Chen, Mahanthappa; Everett, Ramond; Luhn, Nasri, Yu, RNM, Hagedorn, Morissi,…..) Grand unified theories: SU(5) How can we unify with quarks ?

26. High scale Ansatz for unifying quark-lepton flavor (Dutta, Mimura, RNM’PRD-09) f diagonal. Anarchic M 0, quark mixings small while lepton mixings large.  explains mass hierarchies + Rank 1 M 0 A B

27. SUSY SO(10) realization Fermions in {16}: 16 m x16 m ={10} H +{120} H +{126} H Fermion masses from Yukawas as in SM: (Babu, Mohapatra, 93)

28. Neutrino mass formula in GUT scale B-L in SO(10): Type II seesaw: Lazaridis, Shafi, Wetterich; R.N.M.,Senjanovic’81

29. SO(10) with GUT scale B-L  unified approach to flavor  fermion mass formulae: (Babu, Mohapatra’92) Bajc, Senjanovic, Vissani’03 For f, h’ << h,  yields ansatz part A at M U ; Rank from flavor symmetry: e.g.

30. An S 4 xSO(10)- example Solar mass Dutta, Mimura, RNM arXiv:0911.2242 Bottom-tau: and Leading order PMNS: U (Harrison, Perkins, Scott; He, Zee, Xing; Wolfenstein) Corrections: Testable Bjorken, King, Pakvasa Ferrandis; Chen, Mahanthappa Double beta mass 3 meV.

31. Prospects for measuring Reactor, Long base line e.g. T2K, NoVA: (Lindner, Huber,Schwetz,Winter’09) Our prediction

32. Conclusion: TeV scale WR compatible with SO(10) GUT ; Can be tested at LHC; New dark matter candidate: New unified approach to flavor based on typeII+ SO(10)- testable via theta_13.

33. WR, Z’ at LHC_ 14 Production : WR Z’

34. Signals for Type I case Two and three lepton signals in colliders N-decay gives signal: Like sign dilepton plus trilepton+ (Han, Perez, Li, Del Aguila, Aguilar Saavedra,…)

35. Inverse seesaw case N is mostly Dirac  Collider leptonic signal from WR production: No like sign dilepton but only trileptons +

36. Distinguishing between seesaws Observation of relative abundance of like sign dileptons vs trileptons can distinguish between TeV scale Inverse seesaw vs type I seesaw (Aguilar-Saavedra)  Type I Inverse