Neutrino Mass Models Neutrino Mass Models Why BSM? Neutrino mass - PowerPoint PPT Presentation

Neutrino Mass Models Neutrino Mass Models Why BSM? Neutrino mass models roadmap Survey of approaches TBM, A 4 , CSD Family symmetry and GUTs Sum rules and predictions 29/05/2008 Steve King, Neutrino'08, Christchurch 1

Great interest in neutrino theory, e.g. Melbourne Participants: Kev Abazajian (Maryland) Steve King (Southhampton) Carl Albright (Fermilab) Archil Kobakhidze (Melbourne) Evgeny Akhmedov (Max Planck, Heidelberg) Sandy Law (Melbourne) Matthew Baring (Rice) Manfred Lindner (Max Planck, Heidelberg) Pasquale Di Bari (Padova) Ernest Ma (UC Riverside) Nicole Bell (Melbourne) Kristian McDonald (TRIUMF) Mu-Chun Chen (UC Irvine) Bruce McKellar (Melbourne) Vincenzo Cirigliano (LANL) Hitoshi Murayama (UC Berkeley) Roland Crocker (Monash) Sandip Pakvasa (Hawaii) Basudeb Dasgupta (Tata Institute) Sergio Palomares-Ruiz (Durham) Amol Dighe (Tata Institute) Stephen Parke (Fermilab) Andreu Esteban-Pretel (Valencia) Sergio Pastor (Valencia) Ferruccio Feruglio (Padua/INFN) Nadine Pesor (Melbourne) Robert Foot (Melbourne) Serguey Petcov (SISSA/INFN, Trieste) George Fuller (UC San Diego) Michael Pluemacher (Max Planck, Munich) Alex Friedland (LANL) Tatsu Takeuchi (Virginia Tech.) Julia Garayoa Roca (Valencia) Ricard Tomas (Hamburg) Vladimir N. Gavrin (Moscow, INR) Timur Rashba (Max Planck, Munich) Damien George (Melbourne) Ray Sawyer (UC Santa Barbara) Andre de Gouvea (Northwestern) Alexei Smirnov (ICTP, Trieste) Tom Griffin (Melbourne) Gerard Stephenson (UNM) Gary Hill (Madison) Alexander Studenikin (Moscow State University) Martin Hirsch (Valencia) Jayne Thompson (Melbourne) Thomas Jacques (Melbourne) Shoichi Uchinami (Tokyo Metropolitan U.) Girish Joshi (Melbourne) Raoul Viollier (Cape Town) Sin Kyu Kang (Seoul National University of Technology) Ray Volkas (Melbourne) Renata Zukanovich-Funchal (S ão Paulo) Boris Kayser (Fermilab)

Why Beyond Standard Model?  1. There are no right-handed neutrinos R 2. There are only Higgs doublets of SU(2) L 3. There are only renormalizable terms In the Standard Model these conditions all apply so neutrinos are massless, with  e ,   ,   distinguished by separate lepton numbers L e , L  , L  Neutrinos and anti-neutrinos are distinguished by the total conserved lepton number L=L e +L  +L  To generate neutrino mass we must relax 1 and/or 2 and/or 3 Staying within the SM is not an option – but what direction? 29/05/2008 Steve King, Neutrino'08, Christchurch 3

Neutrino mass models roadmap True Sterile  or CPTV ? LSND True or False? False Dirac Extra dims? Dirac or Majorana? Majorana Higgs Triplets, Loops, RPV, See-saw mechanisms Normal or Inverted? Inverted Symmetry e.g. L e – L  – L  ? Normal No Very precise TBM? Anarchy, see-saw, etc … Yes No Family symmetry? Alternatives? Yes Degenerate Type II see-saw? Hierarchical or deg? Hierarchy GUTs and/or Strings? Type I see-saw?

LSND True or False? MiniBoone does not support LSND result does support three neutrinos For steriles see Shaposhnikov talk In this talk we assume that LSND is false 29/05/2008 Steve King, Neutrino'08, Christchurch 5

Dirac or Majorana? CP conjugate Majorana masses   c m LL L L Violates L M   , , L L L c Violates   e RR R R Neutrino=antineutrino m   Conserves L LR L R , , L L L Violates   e  Neutrino antineutrino Dirac mass 29/05/2008 Steve King, Neutrino'08, Christchurch 6

1 st Possibility: Dirac       H     e , ,  Recall origin of electron mass in SM with L   e H  R 0   e   H L       0 LHe H e e e R e L R Yukawa coupling  e must be small since <H 0 >=175 GeV        0 6 0.5 3.10 m H MeV e e e Introduce right-handed neutrino  eR with zero Majorana mass       0 c LH H   eR eL eR then Yukawa coupling generates a Dirac neutrino mass Why so small?         0 12 0.2 10 m H eV – extra dimensions   LR 29/05/2008 Steve King, Neutrino'08, Christchurch 7

Flat extra dimensions with RH neutrinos in the bulk Dienes, Dudas, Gherghetta; Arkhani-Hamed, Dimopoulos, Dvali, March-Russell For one extra dimension y the  R wavefunction spreads out over the extra dimension, leading to a volume suppressed Yukawa coupling at y=0  R in bulk  0 H M      0 string m H LR M V Planck 7 M 10    12 string . . 10 e g 19 10 M y Planck 29/05/2008 Steve King, Neutrino'08, Christchurch 8

Warped extra dimensions with SM in the bulk  Randall-Sundrum; Rubakov, Gherghetta, … e Overlap wavefunction of fermions with Planck TeV Higgs gives brane brane exponentially suppressed Dirac masses, depending on the fermion profiles 29/05/2008 Steve King, Neutrino'08, Christchurch 9

2 nd Possibility: Majorana   where  is light Higgs triplet with Renormalisable LL  L =2 operator  VEV < 8GeV from  parameter   2 Non-renormalisable      0 c LLHH H  L =2 operator eL eL Weinberg M M This is nice because it gives naturally small Majorana neutrino masses m LL » <H 0 > 2 /M where M is some high energy scale The high mass scale can be associated with some heavy particle of mass M being exchanged (can be singlet or triplet) • Loop models H H H H M • RPV SUSY M • See-saw mechanisms L L L L 29/05/2008 Steve King, Neutrino'08, Christchurch 10

• Loop models Introduce Higgs singlets and triplets with couplings to leptons Zee (one loop) Babu (two loop) 29/05/2008 Steve King, Neutrino'08, Christchurch 11

• RPV SUSY Another way to generate Majorana masses is via SUSY Scalar partners of lepton doublets (slepton doublets) have same quantum numbers as Higgs doublets If R-parity is violated then sneutrinos may get (small) VEVs inducing a mixing between neutrinos and neutralinos      2   2 MeV     m eV LL M TeV       Also need loops   Drees,Dreiner, Diaz, Hirsch, Porod, L L Romao,Valle, … 29/05/2008 Steve King, Neutrino'08, Christchurch 12

See Senjanovic talk for type III • Type I and II see-saw mechanism P.Minkowski, Type I see-saw mechanism Type II see-saw mechanism Lazarides, Gell-Mann, Magg, Ramond, Mohapatra, Slansky, Yanagida; Senjanovic, Mohapatra,   Shafi, Senjanovic, Wetterich Schechter,  (1981) Valle, … R Heavy triplet   L L   Y  L L M   c RR R R 2 v    1    I T II m m M m u m Y M  LL LR RR LR LL  29/05/2008 Steve King, Neutrino'08, Christchurch 13

• Type II upgrade of type I models Antusch, SFK 1 0 0     m m 0 1 0 m M m II 1 T       LL LR RR LR   0 0 1   Hierarchical type I contribution Unit matrix type II controls the neutrino mixings and contribution from an mass splittings  i  i SO(3) family symmetry L L Type II contribution governs the neutrino mass scale and renders neutrinoless double beta | | m decay observable ee II m 29/05/2008 Steve King, Neutrino'08, Christchurch 14

Very precise Tri-bimaximal mixing (TBM) ? Harrison, Perkins, Scott          5 , 0 . 35 , 4 12 23 13 c.f. data              33.8 1.4 , 45 3 , 1 2 12 2 3 1 3 • Current data is consistent with TBM • But no convincing reason for exact TBM – expect deviations 29/05/2008 Steve King, Neutrino'08, Christchurch 15

It is useful to consider the following parametrization of the PMNS mixing matrix in terms of deviations from TBM SFK; see also Pakvasa, Rodejohann, Wyler; Bjorken, Harrison, r = reactor s = solar a = atmospheric s = solar Scott, Parke, … For a list of oscillation formulae in terms of r,s,a see SFK arXiv:0710.0530 29/05/2008 Steve King, Neutrino'08, Christchurch 16

Perturbing the TBM neutrino mass matrix Albright, Rodejohann 2 Smaller  13 U 3 e Larger  13 2 U 3 e . . 29/05/2008 Steve King, Neutrino'08, Christchurch 17