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Neutrino Mass and New Physics Roadmap Beyond MSSM. R. N. Mohapatra University of Maryland Beijing Flavor workshop, September, 2008. Plan of the talk:. Lecture 1. Neutrino mass from TeV scale Physics: - SM and MSSM : Hopes and problems
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Neutrino Mass andNew Physics Roadmap Beyond MSSM R. N. Mohapatra University of Maryland Beijing Flavor workshop, September, 2008.
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):
Recap. of SM: • Fermions: ; ; • Higgs boson: ; ; • 17 parameter theory; Higgs mass arbitrary. • Successful but naturalness issues !!
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.
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 !!
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-
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.
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:
Bonus 3:Electroweak symmetry breaking • MSSM provides a simple way to understand the origin of EWSB and hence the origin of mass !
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.
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 !!
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 !!)
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
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.
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 !
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.
Why nonzero -mass suggests LR sym. • Starting point for simple understanding of neutrino mass: add RH neutrino to MSSM :
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
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.
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)
Parity Violation out of Spontaneous Breaking • The weak Lagrangian of model: • Weak Lagrangian Parity Inv. • Low energy parity violation due to
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-
Detailed Higgs content and Sym Breaking Break symmetry- and in particular B-L by 2 units as required to guarantee R-parity and seesaw
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.
Symmetry breaking and seesaw for neutrinos I+IIseesaw : Or as weak int becomes V-A
Origin of type II term Lazaridis, Shafi, Wetterich; R.N.M.,Senjanovic Formula important for determining the scale of B-L;
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)
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.
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.
Type II seesaw magnitude from SUSY breaking: • Susy breaking does induce from diagrams: Magnitude: Can be small making type II contribution of right order.
Defining Left-Right symmetry • Non-SUSY: • SUSYLR: New coordinate • Under parity: • But since ; • This implies under parity etc.
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:
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.
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.
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 !!
Model Details and Phenomenology: • (i) Minimal Model: • Matter: • Higgs: • Superpotential:
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.
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.
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.
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
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 !!
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 !!
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 ?
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.
Numerical Search for minimum • Global minimum with spontaneous R-parity breaking:
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:
(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;…)
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.
(ii) New upper bound on light Higgs mass: • MSSM: • SUSYLR with TeV scale WR (Zhang, An,Ji and RNM, 2008, PRD)
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)