Neutrinos and Fundamental Symmetries: L, CP, and CP T Outstanding issues Lepton number (L) CP violation CP T violation
Outstanding issues in neutrino intrinsic properties Scale of underlying physics? (string, GUT, TeV?) Mechanism? (seesaw, LED, HDO, stringy instanton?) Hierarchy, U e3, leptonic CP violation? (mechanism, leptogenesis) Absolute mass scale? (cosmology) Dirac or Majorana? (mechanism, scale, leptogenesis) Baryon asymmetry? (leptogenesis, electroweak baryogenesis, other?) LSND, MiniBooNE; MINOS (sterile, new interactions, CP, CP T?)
Outstanding issues in neutrino intrinsic properties Scale of underlying physics? (string, GUT, TeV?) (LHC, flavor) Mechanism? (seesaw, LED, HDO, stringy instanton?) (indirect: LHC) Hierarchy, U e3, leptonic CP violation? (mechanism, leptogenesis) (long baseline, reactor, ββ 0ν, supernova) Absolute mass scale? (cosmology) (β decay, cosmology, ββ 0ν, supernova) Dirac or Majorana? (mechanism, scale, leptogenesis) (ββ 0ν ) Baryon asymmetry? (leptogenesis, electroweak baryogenesis, other?) (indirect: LHC) LSND, MiniBooNE; MINOS (sterile, new interactions, CP, CP T?) (statistics, long baseline, cosmology, indirect)
Lepton Number (L) Many mechanisms for small neutrino mass, both Majorana and Dirac Minimal Type I seesaw Bottom-up motivation: no gauge symmetries prevent large Majorana mass for ν R Connection with leptogenesis Argument that L must be violated is misleading non-gravity: large 126 of SO(10) or HDO added by hand gravity: m ν ν 2 EW /M P 10 5 ev (unless LED); often much smaller New TeV or string scale physics/symmetries/constraints may invalidate assumptions
Bottom-up alternatives: Higgs (or fermion) triplets, extended (TeV) seesaws, loops, R p violation String-motivated alternatives: higher dimensional operators (HDO) (non-minimal seesaw, direct Majorana, Dirac); string instantons (exponential suppressions); geometric suppressions (large dimensions) Alternatives often associated with new TeV physics, electroweak baryogenesis, etc. Will explore plausible possibilities of string landscape The Type I seesaw from a string perspective Models with new TeV symmetries that forbid tree-level Dirac masses
Higher-dimensional operators The Weinberg operator (most Majorana models) l L = ( νl L φφ = C ( l L τ l ) ( R φ τ φ ) + h.c. 2M = C ( l φ) L (φ l ) R + h.c. M = C ( φ l 0 φ φ 0 φ 0 ) L l M φ φ φ φ 0 R + h.c., e L ), lr = ( e c R ν c R ), φ = ( φ + φ 0 ), φ = ( φ 0 φ ) Superpotential: W = C M LLH uh u Generate directly in string construction, or in effective 4d theory
The GUT seesaw ν L Realize Weinberg operator via heavy particle exchange in effective 4d theory ν L φ 0 φ 0 φ S ν L h T ν L Seesaw implementation Type I: heavy Majorana ν R Type II: heavy Higgs triplet ν L ν R ν R h S φ 0 φ 0 ν L φ 0 T κ φ 0 φ 0 Typeset by FoilTEX 1
Type I in SO(10): φ S 126 H (Type II also possible) W h u 16 16 10 H }{{} H +h S 16 16 126 }{{} ν L ν R φ 0 ν c L ν Rφ S Alternative (Babu,Pati,Wilczek): replace 126 H by higher-dimensional operator: W λ M 16 16 16 H 16 H Can obtain from underlying string theory or as effective operator using Majorana singlet (Kim, Raby) Need h S φ 126 H or λ M φ 16 H 2 10 14 GeV h u φ 10H 100 GeV 2
φ 126 probably unobtainable The heterotic string seesaw Heterotic E 8 E 8 (closed strings): Majorana mass for ν R from S q+1 W N c ij N c i N c S q+1 j (m νr ) ij c ij, q 0 M q s Simultaneous Dirac mass terms from ( ) S p W D LN c H u m D M s May involve multiple SM singlet fields S M q s ( ) p S H u, p 0 M s Typically, S M s = O(10 1 ) at minimum (e.g., if from FI term) Must be consistent with string constraints/symmetries; with F = D = 0 (supersymmetry); W = 0 (cosmological constant)
Difficult to satisfy all conditions No examples in Z 3 heterotic orbifold (Giedt,Kane,PL,Nelson) At least two examples in heterotic E 8 E 8 orbifold on Z 3 Z 2 (Buchmuller,Hamaguchi,Lebedev,Ramos-Sanchez,Ratz; Lebedev, Nilles,Raby,Ramos-Sanchez,Ratz,Vaudrevange,Wingerter) May be many (O(10 100)) N c ; p 0,..., 6, q 3,..., 8. Nonminimal Stringy HDO for m νr, effective FT HDO for m ν Simple SO(10) relations lost
The seesaw in intersecting brane theories Intersecting D-brane (Type IIA) Closed strings (gravitons) and open strings ending on D-branes (matter, gauge) D6-branes: fill ordinary space and 3 of the 6 extra dimensions Stringy implementation of brane world ideas U(1) W U(1) a b Gauge bosons in adj. W + Chiral matter in (N, M)
Hard to achieve Majorana or small Dirac masses perturbatively Anomalous U(1) : M Z M s, but acts like perturbative global symmetry (may forbid µ, R P violation, N c N c, LN c H u, QU c H u,... ) Field theory instantons: nonperturbative e 1/g2 effects from topologically non-trivial classical field configurations (e.g., B + L violation in SM) String instantons: nonperturbative violation of global symmetries Majorana masses from string instantons (seesaw) (also, µ, Yukawas) (Blumenhagen,Cvetič,Weigand;Ibanez,Uranga) m νr M s e S inst
Majorana masses if no ν R or no tree-level LN c H u May generate stringy Weinberg operator by underlying string dynamics (string states, KK or winding modes, moduli) (Conlon,Cremades;Antoniadis,Kiritsis,Rizos,Tomaras; Bouchard,Heckman,Seo,Vafa;Tatar,Tsuchiya,Watari) ν L ν L φ 0 φ 0 W = C M LLH uh u, with C 1, M = M s M P = M P 8π 2.4 10 18 GeV m ν 10 5 ev ( need M/C 10 14 GeV M P ) Can view as seesaw with ν R replaced by string states Can enhance by compactifying on large internal volume (M s M P, e.g., 10 11 GeV) Can enhance by infinite towers of states
Stringy instanton Weinberg operator (Cvetič,Halverson,PL,Richter) W 5 = e S inst M s LLH u H u, M s (10 3 10 14 ) GeV
Small Dirac masses Many other possibilities for small neutrino masses utilizing W or K (both Majorana and Dirac) (Cleaver,Cvetič,Espinosa,Everett,PL; PL; Arkani-Hamed,Hall,Murayama,Smith,Weiner; Borzumati,Nomura; March-Russel,West; Dvali,Nir; Frere,Libanov,Troitsky; Gogoladze, Perez-Lorenzana; Casas,Espinosa,Navarro; Chen, de Gouvea, Dobrescu; de Gouvea,Jenkins; Demir,Everett,PL; Bouchard,Heckman,Seo,Vafa;Brignole,Joaquim,Rossi) Extra symmetries (e.g., TeV-scale U(1) ) or string constraints may forbid elementary Dirac Yukawa W = LN c H u
Small Dirac from HDO in W (CCEEL): W S M LN c H u m ν S ν u M S = c 1000 TeV for M = c M P e.g. (approximately) flat breaking of U(1) (CCEEL); Z mediation (PL,Paz,Wang,Yavin),...
Small Dirac from non-holomorphic K using F X (DEL) K 1 M 2X LN c H d + h.c., with X = θθf M = SUSY mediation scale (e.g., 10 14 GeV), M SUSY = F/M W = M SUSY M LN c H d m ν M SUSY ν d M Non-holomorphic A terms (suppressed by M SUSY /M)(DEL) K 1 M 3XX LN c H d + h.c. A M 2 SUSY M Small Dirac mass from loop (need U(1) ; also forbids normal Yukawa) ~! L H d 0 ~! R ~ W ~ 3 ~ B,, Z ~ Z! L! R
Small Dirac using F Hd (BHSV) K 1 M LN c H d + h.c., with F H d = µh u Small Dirac from string instantons, e S instln c H u (natural scale, 10 3 10 1 ev) (Cvetič,PL) Large extra dimensions, with ν R propagating in bulk small Dirac masses from wave function overlap, cf., gravity (Dienes,Dudas,Gherghetta; Arkani-Hamed,Dimopoulos,Dvali,March-Russell) m ν νm F M P, M F = ( 2 ) δ+2 1 M P V δ = fundamental scale Small Dirac from wave function overlap in warped dimensions, L and ν R in bulk (Chang,Ng,Wu)
Small Dirac and Majorana Even with very small Dirac mass, there may also be HDO yielding small Majorana masses If comparable, generate ordinary-sterile mixing (LSND/MiniBooNE) m D m M pseudodirac (small mass splitting between ν L ±νc L 2 ) Acts like Dirac for most purposes But small extra m 2 could affect Solar/supernova oscillations Solar: need m M 10 9 ev (de Gouvêa,Huang,Jenkins)
An operator analysis L = 1 2 ( νl ν c L ) ( ) ( ) m T m D ν c R m D m S νr + h.c., Dirac mass by HDO, with S = new physics scale Dirac mass: m D S p ν u /M p 0.1 ev (take p = 1 0.1 TeV < S < 10 3 TeV) Majorana ν R mass (singlet): m S S q+1 /M q Majorana ν L mass (triplet Weinberg operator): m T S r 1 ν 2 u /M r
m ν (ev) 1 10 5 10 10 m M = 10 9 ev m S (q = 2) m S (q = 1) m D = 10 1 ev (p = 1) m T (r = 1) 10 15 10 20 m T (r = 2) m S (q = 3) S (TeV) 0
CP violation Quantum mechanics/field theory: most quantities intrinsically complex Key issue: are the phases observable (require interference of two contributions to an amplitude) Simple systems: can rotate phases away (e.g. two family SM, or PMNS with V 13 = 0) Can impose CP, but little motivation (domain wall problems if broken) Quark phases are large; most models should give ν phases (e.g., complex string moduli) Nevertheless, experimental question
Possible ν µ ν e vs ν µ ν e difference (LSND/MiniBooNE) could be due to CP breaking + steriles (+?) P ( ) μ e 0.020 0.015 0.010 0.005 LSND MB mode 0.000 0.005 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 L / E m / MeV ( ) 1.75 2.6
CP T violation MINOS: possible difference between ν µ ν µ vs ν µ ν µ (requires CP T violation)
Intrinsic CP T violation: CP T theorem for any local, Hermitian, Lorentz-invariant field theory (Greenberg: m m LIV even if non-local) Possible loophole: string theory (non-local) with LIV Not at perturbative level. Possibly broken by moduli VEVs (Kostelecky,Potting,Mewes,Samuel) ν sector promising for Planck-suppressed effects, but extraordinary claims Apparent/environmental CP T violation: coherent interactions with 735 km of rock FCNC ν µ ν τ (Mann et al, 1006.5270) (e.g., family-nonuniversal Z ) Z + sterile (Engelhardt et al, 1002.4452) FCNC and cosmological constraints
Conclusions Minimal seesaw is attractive possibility, but difficult to realize in string theory and/or may be excluded by new TeV symmetries Many other possibilities for small Majorana or Dirac from field theory or stringy higher dimensional operators, string instantons, large dimensions (exploration of string landscape) Alternatives often associated with new TeV physics, electroweak baryogenesis CP violation expected in field theory (LSND/MiniBooNE) CP T violation (MINOS) may be environmental (coherent interactions with rock) The best solution is not always the minimal one
Minimality