Neutrino Mass Models
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1 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
2 Great interest in neutrino theory, e.g. Melbourne Participants: Kev Abazajian (Maryland) Carl Albright (Fermilab) Evgeny Akhmedov (Max Planck, Heidelberg) Matthew Baring (Rice) Pasquale Di Bari (Padova) Nicole Bell (Melbourne) Mu-Chun Chen (UC Irvine) Vincenzo Cirigliano (LANL) Roland Crocker (Monash) Basudeb Dasgupta (Tata Institute) Amol Dighe (Tata Institute) Andreu Esteban-Pretel (Valencia) Ferruccio Feruglio (Padua/INFN) Robert Foot (Melbourne) George Fuller (UC San Diego) Alex Friedland (LANL) Julia Garayoa Roca (Valencia) Vladimir N. Gavrin (Moscow, INR) Damien George (Melbourne) Andre de Gouvea (Northwestern) Tom Griffin (Melbourne) Gary Hill (Madison) Martin Hirsch (Valencia) Thomas Jacques (Melbourne) Girish Joshi (Melbourne) Sin Kyu Kang (Seoul National University of Technology) Boris Kayser (Fermilab) Steve King (Southhampton) Archil Kobakhidze (Melbourne) Sandy Law (Melbourne) Manfred Lindner (Max Planck, Heidelberg) Ernest Ma (UC Riverside) Kristian McDonald (TRIUMF) Bruce McKellar (Melbourne) Hitoshi Murayama (UC Berkeley) Sandip Pakvasa (Hawaii) Sergio Palomares-Ruiz (Durham) Stephen Parke (Fermilab) Sergio Pastor (Valencia) Nadine Pesor (Melbourne) Serguey Petcov (SISSA/INFN, Trieste) Michael Pluemacher (Max Planck, Munich) Tatsu Takeuchi (Virginia Tech.) Ricard Tomas (Hamburg) Timur Rashba (Max Planck, Munich) Ray Sawyer (UC Santa Barbara) Alexei Smirnov (ICTP, Trieste) Gerard Stephenson (UNM) Alexander Studenikin (Moscow State University) Jayne Thompson (Melbourne) Shoichi Uchinami (Tokyo Metropolitan U.) Raoul Viollier (Cape Town) Ray Volkas (Melbourne) Renata Zukanovich-Funchal (São Paulo)
3 Why Beyond Standard Model? 1. There are no right-handed neutrinos 2. There are only Higgs doublets of SU(2) L 3. There are only renormalizable terms R 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
4 Neutrino mass models roadmap LSND True or False? False Dirac or Majorana? Majorana True Dirac Sterile or CPTV? Extra dims? Higgs Triplets, Loops, RPV, See-saw mechanisms Normal or Inverted? Normal Very precise TBM? Yes Family symmetry? Yes Hierarchical or deg? Hierarchy Type I see-saw? Inverted Symmetry e.g. L e L L? No No Degenerate Anarchy, see-saw, etc Alternatives? Type II see-saw? GUTs and/or Strings?
5 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
6 Dirac or Majorana? Majorana masses CP conjugate mll M L c L c RR R R Violates L Violates L,, e L L Neutrino=antineutrino Dirac mass m LR L R Conserves L Violates L,, e L L Neutrino antineutrino 29/05/2008 Steve King, Neutrino'08, Christchurch 6
7 1 st Possibility: Dirac e Recall origin of electron mass in SM with L, er, H 0 LHe H e e 0 e R e L R Yukawa coupling e must be small since <H 0 >=175 GeV m H 0.5 MeV e e e Introduce right-handed neutrino er with zero Majorana mass c 0 LH er H el er H e H L then Yukawa coupling generates a Dirac neutrino mass 0 12 Why so small? mlr H 0.2 ev 10 extra dimensions 29/05/2008 Steve King, Neutrino'08, Christchurch 7
8 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 H 0 0 M string mlr H V M Planck y 7 M string 10 e. g M 10 Planck 12 29/05/2008 Steve King, Neutrino'08, Christchurch 8
9 Planck brane Warped extra dimensions with SM in the bulk e TeV brane Randall-Sundrum; Rubakov, Gherghetta, Overlap wavefunction of fermions with Higgs gives exponentially suppressed Dirac masses, depending on the fermion profiles 29/05/2008 Steve King, Neutrino'08, Christchurch 9
10 2 nd Possibility: Majorana Renormalisable L =2 operator Non-renormalisable L =2 operator LL M LLHH where is light Higgs triplet with VEV < 8GeV from parameter M H 0 2 c el el Weinberg 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) H L M H L H L M H L Loop models RPV SUSY See-saw mechanisms 29/05/2008 Steve King, Neutrino'08, Christchurch 10
11 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
12 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 m LL MeV M TeV Also need loops ev L L Drees,Dreiner, Diaz, Hirsch, Porod, Romao,Valle, 29/05/2008 Steve King, Neutrino'08, Christchurch 12
13 See Senjanovic talk for type III Type I and II see-saw mechanism P.Minkowski, Gell-Mann, Ramond, Slansky, Yanagida; Mohapatra, Senjanovic, Schechter, Valle, Type I see-saw mechanism L R c M RR R R L m m M m I 1 T LL LR RR LR Type II see-saw mechanism m L II LL Y L 2 vu Y M Heavy triplet Lazarides, Magg, Mohapatra, Senjanovic, Shafi, Wetterich (1981) 29/05/2008 Steve King, Neutrino'08, Christchurch 13
14 Type II upgrade of type I models Antusch, SFK i L i L m m m M m II 1 T LL LR RR LR Unit matrix type II contribution from an SO(3) family symmetry Hierarchical type I contribution controls the neutrino mixings and mass splittings Type II contribution governs the neutrino mass scale and renders neutrinoless double beta decay observable m ee II m 29/05/2008 Steve King, Neutrino'08, Christchurch 14
15 Very precise Tri-bimaximal mixing (TBM)? Harrison, Perkins, Scott 12 35, 45, c.f. data , 45 3, Current data is consistent with TBM But no convincing reason for exact TBM expect deviations 13 29/05/2008 Steve King, Neutrino'08, Christchurch 15
16 It is useful to consider the following parametrization of the PMNS mixing matrix in terms of deviations from TBM r = reactor s = solar a = atmospheric SFK; see also Pakvasa, Rodejohann, Wyler; Bjorken, Harrison, Scott, Parke, For a list of oscillation formulae in terms of r,s,a see SFK arxiv: /05/2008 Steve King, Neutrino'08, Christchurch 16
17 Perturbing the TBM neutrino mass matrix Albright, Rodejohann U e3 2 Smaller 13 U e3 2 Larger /05/2008 Steve King, Neutrino'08, Christchurch 17
18 TBM mass matrices in three different bases 1. Diagonal charged lepton basis m E LR me m m 2. Cabibbo-Wolfenstein basis m m m e E 2 mlr me m m 2 me m m, m m LL m m m LL m m 3.Diagonal neutrino basis m LL 2 m 2 U MNS m m m 3 U U E V L V MNS MNS E L V L E L L V V 2 / 3 e i L V 1 1 2, i i Low energy physics doesn t care about the choice of basis, but the high scale theory does 29/05/2008 Steve King, Neutrino'08, Christchurch 18
19 Family symmetry t e u d s c b e The basic idea of family symmetry is to assign each family a new type of charge
20 The magic symmetry A 4 A 4 is symmetry group of the tetrahedron (Plato s ``fire ) reproduces the TBM form of the charged lepton mass matrix in the Cabibbo-Wolfenstein basis 2 Ma, Rajasakaran TBM form of the neutrino mass matrix then requires a delicate Higgs vacuum alignment Ma; Altarelli,Feruglio A 4 may also be used to give the TBM neutrino mass matrix in the Flavour basis 1 Altarelli,Feruglio A 4 may arise from 6D orbifolding Altarelli,Feruglio,Lin 29/05/2008 Steve King, Neutrino'08, Christchurch 20
21 Deriving TBM from see-saw mechanism Diagonal RH nu basis columns SFK See-saw I Sequential dominance m LL Dominant m 3 AA BB CC X Y Z T T T Subdominant m 2 Decoupled m 1 m LL m m Constrained SD TBM mass matrix (» 2RHN) 29/05/2008 Steve King, Neutrino'08, Christchurch 21
22 This requires a non-abelian family symmetry Need 0 B YLR A B A B with 2$ 3 symmetry (from maximal atmospheric mixing) 1$ 2 $ 3 symmetry (from tri-maximal solar mixing) Several examples of suitable non-abelian Family Symmetries: SFK, Ross; Velasco-Sevilla; Varzelias SFK, Malinsky SU(3) SO(3) A 27 4 Discrete subgroups preferred by vacuum alignment 29/05/2008 Steve King, Neutrino'08, Christchurch 22
23 Family GUT symmetry e.g. Chen and Mahanthappa T SU(5) Altarelli, Feruglio, Hagedorn A 4 SU(5) (in 5d) SFK, Malinsky A 4 Pati-Salam Varzielas, SFK, Ross 27 Pati-Salam/SO(10) t Family symmetry e.g. A 4 e d u s c b GUT symmetry e.g. SU(5) 1 29/05/2008 Steve King, Neutrino'08, Christchurch 23
24 G GUT E 6 SO(10) SU (5) U (1) SU (3) SU (3) SU (3) C L R SU (4) SU (2) SU (2) PS L R SU (5) SU (3) SU (2) SU (2) U (1) C L R B L SU (3) SU (2) U (1) C L Y 29/05/2008 Steve King, Neutrino'08, Christchurch 24
25 G Family O(3) O(3) L R SU(3) SU(2) U(1) 27 SO(3) Nothing T ' A4 12 S(3) S(3) L S(3) R 29/05/2008 Steve King, Neutrino'08, Christchurch 25
26 General Strategy Choose a GUT and family symmetry and write down the reps Asssign quarks, leptons, Higgs to reps Renormalizable Yukawas requires extended Higgs H H ij HL E H L E c ij c ij i j i j Machado,Pleitez i c H Li, E j, H 0 E i H Alternatively promote Yukawas to non-renormalizable terms involving the usual Higgs H plus SM singlet flavon fields M ij c c ijhli E j HLi E j Koide; Stech or M i j c c ijhli E j HL 2 ie j SFK,Ross 29/05/2008 Steve King, Neutrino'08, Christchurch 26
27 GUT relations.... d. 12 e Can this lead. to Quark-Lepton Complementarity (QLC)? C =45 o. Georgi-Jarlskog C Petcov,Smirnov; Raidal;Ohlsson,Seidl 29/05/2008 Steve King, Neutrino'08, Christchurch 27
28 Sum Rules U MNS Cabibbo-like Bimaximal or Tri-bimaximal E L V L V 1 o o o o Bjorken; Ferrandis, Pakvasa; SFK e 2 C 13 3, (35) o o C Antusch,SFK 45 (35) cos Sum Rule 3 2 cos Oscillation phase SFK; Antusch,SFK; Masina Bimaximal sum rule with 45 o requires 13 ¼ C and ¼ QLC is only achieved for a special phase and large 13 What about tri-bimaximal sum rule with 35 o? Antusch,SFK,Mohapatra 29/05/2008 Steve King, Neutrino'08, Christchurch 28
29 Tri-bimaximal sum rule o 35.3 cos.. Antusch, Huber, SFK, Schwetz Bands show 3 error for an optimized neutrino factory determination of 13 cos 12 =33.8 o 1.4 o (current value) Tri-bimaximal sum rule works incredibly well!! 29/05/2008 Steve King, Neutrino'08, Christchurch 29
30 RGE corrections to TBM sum rule o o o cos 35.3 ( at M ) GUT Less than 0.3 degree correction cos Boudjemma, SFK Using REAP by Antusch,Kersten,Lindner,Ratz M GUT 29/05/2008 Steve King, Neutrino'08, Christchurch 30
31 Alternative Ideas Accidental family symmetry from messenger dominance SU(8) GUTs Barr Mass matrices from shift symmetry: R R + Extremization of mass matrix Jarlskog invariants Theories of the Koide mass formula Dirac screening in the double see-saw Low energy see-saw models with gauged B-L Anarchy/Landscape (large 13 only) RH Neutrino masses in string theory Invariant classification of see-saw models Ferretti, SFK, Romanino; Barr Koide, Friedberg,Lee; Jarlskog Harrison,Scott Lindner,Smirnov,Schmidt SFK,Yanagida Hall,Murayama,Weiner Antusch,Ibanez; Nilles,Langacker SFK 29/05/2008 Steve King, Neutrino'08, Christchurch 31
32 Conclusion Neutrino mass and mixing requires new physics BSM Many roads for model building, but answers to key experimental questions will provide the signposts One key question is how accurately is TBM realised? Goal of next generation of oscillation experiments is to show that the deviations from TBM r,s,a are non-zero and measure them and If TBM is accurately realised this may imply a new symmetry of nature: family symmetry GUTs family symmetry with see-saw + CSD is very attractive framework for TBM sum rule prediction Few realistic models, complicated vacuum alignment Status quo is not an option neutrino physics demands a theory of flavour, and may provide further clues 29/05/2008 Steve King, Neutrino'08, Christchurch 32
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