Neutrino Mass and New Physics Roadmap Beyond MSSM

1. Neutrino Mass andNew Physics Roadmap Beyond MSSM R. N. Mohapatra University of Maryland Beijing Flavor workshop, September, 2008.

2. Plan of the talk: Lecture 1.Neutrino mass from TeV scale Physics: -SM and MSSM:Hopes and problems -SUSYLeft-right model: Resolving of problems -SUSYLR: An LHC friendly incarnation -TeV scale baryogenesis: In SUSYLR extension Lecture 2.Neutrino Mass and Grand Unification -SU(5): An illustrative model -SO(10) GUT:fermion masses and mixings; proton decay and strong CP -Beyond SO(10):

3. Recap. of SM: • Fermions: ; ; • Higgs boson: ; ; • 17 parameter theory; Higgs mass arbitrary. • Successful but naturalness issues !!

4. Why to go beyond SM ? • Major puzzles of SM: (i) Origin of Mass: origin and value of <H>: LHC to throw light on it: (ii)Origin of Flavor: Generations;Fermion masses, mixings, CP and P-violation in SM; CP violation in strong interaction; Neutrino mass physics, LFV searches and B-physics will elucidate their origin ! (iii) Cosmological Issues: Dark matter, Origin of matter (also related to flavor puzzle), inflation etc.

5. Origin of Mass • Higgs boson elementary or composite ? • Elementary::Supersymmetry Rules are usual QFT; calculable quantum corrections and precision test possible!!Cosmology easier to visualize in model. • Composite::Technicolor or warped extra dimensions . Conceptually beautiful, analogy to QCD attractive but hard to do precise calculations. Hard to do cosmology !!

6. Supersymmetric Route • Use supersymmetry to solve the mass problem; • Extend it to solve flavor problem e.g. neutrino mass, Dark matter, CP, Strong CP problem etc. • Immediately beyond MSSM: SUSYLR motivated by nu-mass; solves all these problems-

7. Gauge Hierarchy and Supersymmetry • To every SM particle - a superpartner: • Minimal Model -MSSM • Cancels selfmass divergence of Higgs and solves the gauge hierarchy problem: • Bonus 1: Lightest sparticle stable if R-parity exact and becomes dark matter.

8. Bonus 2: Coupling Unification and GUTs • MSSM does not predict coupling unification; Need to assume no new physics till high scale: • Proton decay key test ! • For colliders, gaugino unif. important test:

9. Bonus 3:Electroweak symmetry breaking • MSSM provides a simple way to understand the origin of EWSB and hence the origin of mass !

10. Light Higgs mass bound: • Key test of MSSM is upper bound on light neutral Higgs mass: • Implementing EW baryogenesis puts stronger limits < 120 GeV and light stop < 200 GeV. Testable soon at LHC.

11. Problems: MSSM needs fixing-I • SM has stable proton- but MSSM takes a step backward !! protons decay in an instant in MSSM. • Culprit: R-parity breaking terms • Also no stable dark matter-one of the much touted virtues of susy !!

12. How to naturally get an R-P conserving MSSM ? • Recall • A natural way to have automatic RP conservaing MSSM is to have a higher scale theory with built in local B-L symmetry and break B-L by 2 units. • (RNM,86; Font,Ibanez,Quevedo,89; Martin,92) • (R-parity is often assumed as an adhoc symmetry just to guarantee dark matter and stop proton decay- but we may be missing some important clues to new physics that way !!)

13. MSSM needs fixing-Part II • MSSM has other problems too ! • Too many parameters (~105 or so); • Large flavor changing neutral current effects- • Too large edm problem (SUSY CP problem), no solution to strong CP problem: • Mu-problem

14. Flavor Problems of MSSM • In general, • 5 3x3 hermitean sparticle mass matrices; 15 phases • 3 3x3 arbitrary A matrices; 27 phases • 3 gaugino mass phases; mu-phase,B-mu phase; 5 phases; • 32 phases for squarks in addition to CKM phase; SM only one phase.

15. SUSY breaking- hope for some type II problems: • SUSY breaking mechanism may cure the FCNC and too many parameter problem: • Gravity mediated (MSUGRA) : -FCNC problem ! • Gauge Mediated SUSY Breaking: many fewer parameters: - Mu-Bmu problem; gravitino LSP KeV dark matter only for low reheating temp ! (ii) Anomaly Med. SUSY Breaking: many fewer parameters -Howeverwithoutnew physics beyond MSSM breaks electric charge ! Going beyond MSSM clearly indicated for various reasons !

16. A New beyond MSSM roadmap inspired by nu- mass • MSSM SUSY LEFT RIGHT • Gauge group: • Solves many problems of SM and MSSM in addition to explaining small neutrinos masses: • (i) Proposed to explain origin of parity violation: (ii) No SUSY CP and strong CP problems; (iii) Automatic R-parity- stable DM; (iv) Predicts new kinds of light Higgs bosons.

17. Why nonzero -mass suggests LR sym. • Starting point for simple understanding of neutrino mass: add RH neutrino to MSSM :

18. Seesaw: type I and RH neutrinos: Large Majorana mass for the RH neutrinos: Note just like R-parity, Seesaw also requires B-L=2; Could there be a common theory for both ? Minkowski’77; Gell-Mann, Ramond, Slansky; Yanagida; Glashow R. N. M.; Senjanovic 79

19. An important property of -MSSM • A new cubic triangle anomaly free quantum number is B-L unlike MSSM i.e. • MSSM: • Whereas with nu^c added B-L is gaugeable sym. And minimal such theory is LR model.

20. LR Model-A natural framework for seesaw and gauged B-L • Gauge group: • Fermion assignment • Higgs fields • Nu-R and new scale automatic ! (RNM,Senjanovic,79)

21. Parity Violation out of Spontaneous Breaking • The weak Lagrangian of model: • Weak Lagrangian Parity Inv. • Low energy parity violation due to

22. A Much more physical formula for electric charge • SM: • What is Y ?- a free parameter. • LR model: • Implies that: ; • Parity violation implies that neutrino is a Majorana fermion-

23. Detailed Higgs content and Sym Breaking Break symmetry- and in particular B-L by 2 units as required to guarantee R-parity and seesaw

24. Quark and lepton masses: • SM: • 13 parameters; • LR: • For u,d,e sector same 13 parameters except now Yukawa coupling matrices are hermitean due to LR symmetry.

25. Symmetry breaking and seesaw for neutrinos I+IIseesaw : Or as weak int becomes V-A

26. Origin of type II term Lazaridis, Shafi, Wetterich; R.N.M.,Senjanovic Formula important for determining the scale of B-L;

27. Summary of bounds on LR Scale: Non-SUSY case • Collider limits on WR and Z’:around 780 GeV- 800 GeV. • Low energy limits:K-K-bar, CPV, edm etc: WR mass > 2.5 TeV. (Zhang,An,Ji,RNM,2008) • Limits from Neutrinoless double beta decay+ vacuum stability: WR mass > 1.5 TeV. • Limits are lower for SUSYLR due to sparticle FCNC effects. (Zhang,An,Ji 2008)

28. What is the Seesaw (LR) scale ? GUT vs sub-GUT • Type I term; so can allow WR anywhere from TeVs up. To right nu masses. • Type II term; sub-eV neutrino mass would then imply suggest standard standard GUT scenario e.g. SO(10) with 126 Higgs . Has issues- (see Part 2 of talk) • Two questions arise: (i) Why contemplate lower scale LR sym ? -unlike GUT seesaw, TeV and other sub-GUT scale seesaw testable in colliders; (ii) Doesn’t the type II term need extreme fine tuning ? -SUSYLR solves this problem.

29. SUSY ESSENTIAL FOR LOW SCALE LR SEESAW • In Non-susy left-right models, the relation arises from the term • SUSY LR does not allow such terms and hence implies and thus no restriction on the seesaw scale from type II seesaw. • We will contemplate seesaw (left-right) scales anywhere from TeV up.

30. Type II seesaw magnitude from SUSY breaking: • Susy breaking does induce from diagrams: Magnitude: Can be small making type II contribution of right order.

31. Defining Left-Right symmetry • Non-SUSY: • SUSYLR: New coordinate • Under parity: • But since ; • This implies under parity etc.

32. SUSYLR and Strong CP: • Parity definition ( both susy, nonsusy) • ; etc; • Implies that the Yukawa coupling matrices defined by: h are hermitean to be parity invariant. • This implies that the quark mass matrices are hermitean provided the vacuum expectation values are real. • This has several consequences:

33. Consequences of Hermitean M • Left and Right CKM angles are equal. (less parameters in weak currents) • Solves Strong CP problem – no axion • by parity symmetry • by hermiticity RNM, Senjanovic,78; RNM, Rasin; 95; Kuchimanchi,95; Babu, Dutta, RNM, 2000.

34. Again SUSY essential for strong CP • Mass matrices: • h hermitean even for SUSY with given definition of parity; so M is hermitean if <phi> is real. • In non-susy <phi> is not real due to the presence of arbitrary phases in pot. • Again SUSY does not allow such terms- parity makes all couplings in super-pot real and all vevs real real. • Radiative corrections small; Higher Dim operators must be small.

35. Phase counting in SUSYLR • Mass matrices, A-terms hermitean. • Gluino mass real; • Left and right wino has only one phase; • 2 squark mass matrices related: 3 phases • One A matrix diagonal and another with 1 phases. • Total of Only 5 phases in addition to the CKM phase:down from 32 in MSSM • No large edm contribution naturally !!

36. Model Details and Phenomenology: • (i) Minimal Model: • Matter: • Higgs: • Superpotential:

37. Implications of Minimal SUSYLR: A TeV Scale Theory (i)In the minimal model, all symmetry breakings related to soft SUSY breakings: (ii) Ground state breaksparity only if it breaksR-parity : (iii) There is an upper limit on the WR scale in the TeV range- so predicts the seesaw scale.(kuchimanchi, RNM, 93,95) • With , neutrino masses OK. • Induced CP phase is small and maintains the strong CP solution.

38. Two ways to restore R-parity: • (ii) Add non-renormalizable terms: (SUSYLRN) • Requires(Aulakh,Melfo,Senjanovic) • (iii) Model with a singlet S: (SUSYLR+) and include one loop corrections: Also requires (Babu,RNM,08) Yet they have visible signatures at LHC.

39. Why is R-parity breaking mandatory ? • Treat Delta part separately since phi and Delta parts are decoupled (No singlet) • Similar to MSSM, but different in the sense that D-term has a peculiar property: For the ground state , , For ground state, , for arbitrary v and v-bar. Different from MSSM.

40. More D-flat Directions compared to MSSM • MSSM, only D-flat direction is: • For SUSYLR many: • E.g. (i) with • (ii) ; • (iii) ; • etc. ->more constraints on parameters

41. No Parity Violation without R-parity Violation • Potential for the system with • V + • Compare with MSSM Potential: very similar: • Difference: MSSM positivity constraint : :sym br. Cond: • For SUSYLR: as in MSSM; but for QED breaking direction another constraint: • implying i.e. NO PARITY VIOLATION !!

42. Situation is more interesting: No EWSB either • The most general potential for bidoublets: • Unlike MSSM, there are more D-flat directions in SUSYLR bidoublets thereby giving new positivity constraints which imply that the global minimum is No EWSB without R-P breaking at the tree level !!

43. Why not add a singlet ? • Consider the Higgs sector to have: • The superpotential: • This theory breaks parity and SU(2)_R but has a problem: • Since charge breaking ground state has D-term zero, it is the global minimum at tree level. • V > V • HOW TO CURE THESE PROBLEMS ?

44. With R-parity breaking parity and EWS break ! • If , there are new contributions to potential in the VS and VD terms and both parity breaking and EWSB occur in QED vacuum. • Second: Parity breaking scale has an upper limit: • About 3-4 TeV for f=0.1. Testable at LHC. • Low energy bound on WR mass for susyLR: > 2 TeV. (Zhang, Ji, An, 07) • Several Implications of this R-P breaking Th.

45. Numerical Search for minimum • Global minimum with spontaneous R-parity breaking:

46. One Loop Effects: • One loop effects: (Babu,RNM’08) + • If loop contribution is asymptotically smaller, thenNo parity violation without R-P violation; same result persists. • If not in a narrow range of parameters R-parity can be conserved:

47. (i) Unstable gravitino dark matter and SUSY LR • Getting neutrino masses from TeV scale seesaw implies that R-P breaking couplings are of the form: • If gravitino is the LSP with m <10 GeV, its lifetime is > sec. naturally and hence it can be a dark matter. • Decay mode: (Ji,RNM, Nussinov, Zhang:arXiv:0808.1904) • Idea of unstable gravitino dark matter: Ibarra et al; Takayama, Yamaguchi;…)

48. Cures problems with stable Gravitinos in Cosmology • Gravitino density of universe with inflation • DM gravitino mass around 100 GeV. • If not LSP and DM, decay ruins BBN; • If LSP, NLSP decays ruin BBN’s successes. • Longlives Unstable gravitino better for dark matter cosmology ! • Possibility that it can explain some cosmic ray anomalies e.g. EGRET gamma ray excess, HEAT positron excess etc.

49. (ii) New upper bound on light Higgs mass: • MSSM: • SUSYLR with TeV scale WR (Zhang, An,Ji and RNM, 2008, PRD)

50. LHC signals of low mass WR • Looking for TeV scaleat LHC : Signal: Very little background; already used in D0, CDF ; Present limits: 780 GeV (Does not depend on ) (Keung, Senjanovic, 83; del Aguila and Augilar-Savedra)