Sterile Neutrinos from the Top Down Active-sterile mixing The landscape Small Dirac/Majorana masses The mini-seesaw Light Sterile Neutrinos: A White Paper (K. Abazajian et al), 1204.5379 Neutrino Masses from the Top Down, (PL), ARNPS 62, 1112.5992 Light Sterile Neutrinos and Short Baseline Neutrino Oscillation Anomalies (JiJi Fan,PL), 1201.6662
Mixing Between Active and Sterile Neutrinos Most m ν models involve sterile neutrinos (quark-lepton symmetry) Mass anywhere from sub-ev to M P 10 19 GeV LSND/MiniBooNE: possible oscillation between active and sterile Mixing between active and sterile of same helicity Need two types of small (ev-scale) masses (usually Dirac/Majorana) Warm dark matter (e.g., kev), pulsar kicks, supernovae, collider implications
Mixed Models Can have simultaneous Majorana and Dirac mass terms L = 1 2 ( ) ( ( ) ν 0 L ν }{{ L 0c mt m D ν 0c R } m D m S νr 0 weak eigenstates ) + h.c. m T : L = 2, t 3 L = 1 (Majorana) m D : L = 0, t 3 L = 1 2 (Dirac) m S : L = 2, t 3 L = 0 (Majorana)
Active-Sterile (ν 0 L ν0c L ) Mixing (LSND/MiniBooNE) No active-sterile mixing for Majorana, Dirac, or seesaw m D and m S (and/or m T ) both small and comparable (mechanism?) (or small active-sterile and sterile-sterile Dirac) Pseudo-Dirac ( m T, m S m D ): Small mass splitting, small L violation, e.g., m T = ɛ, m S = 0 m 1,2 = m D ± ɛ/2 But small extra m 2 could affect Solar/supernova oscillations Solar: need m S,T 10 9 ev (de Gouvêa,Huang,Jenkins, 0906.1611)
The Landscape String vacuum enormously complicated Many points not consistent with what we know (but multiverse?) Goal 1: obtaining the MSSM Possibilities for SUSY breaking/mediation, µ, Bµ, R P, Goal 2: beyond (instead of) MSSM paradigm (don t prejudge TeV) (just) MSSM is not required by experimental data Many string constructions involve TeV-scale remnants or mechanisms beyond the MSSM (may be hint) Bottom-up models of new physics usually motivated by minimality and/or solving problems
Minimality
Top-down string remnants may not be minimal or motivated by SM problems Top-down may suggest new physical mechanisms (e.g., string instantons: exponentially suppressed µ, Majorana or Dirac m ν, etc) Some bottom-up ideas unlikely to emerge from simple/perturbative string constructions (e.g., high-dimensional representations) Goal 3: mapping of string-likely or unlikely classes of new physics and mechanisms (and contrast with field theory)
Allowed manifold SUSY SM msugra MSSM strong dynamics
Allowed manifold SUSY minimal MSSM SM msugra strong dynamics
Allowed manifold SUSY minimal SM msugra MSSM string strong dynamics
Unlikely to find our exact vacuum Study semi-realistic/interesting vacua for suggestive features
Very Small Masses Mechanisms for very small masses (Majorana, Dirac, or both) Very small couplings Loops Geometric suppressions Higher-dimensional operators (HDO) Focus on correlated explanations for small Majorana and Dirac Review: Neutrino Masses from the Top Down, ARNPS 62, 1112.5992
Apparent Fine-Tuning Dirac: m D h ν ν, ν = 246 GeV h ν 10 12 for m D 0.1 ev Sterile Majorana: m S Γ S M P, M P 2 10 18 GeV Γ S 10 27 for m S 1 ev May be due to geometric suppression or HDO in underlying theory No predictions without further input
Loops Would need very high order (or very small couplings), and suppression mechanism for lower-order Often combined with other mechanisms
Geometric Suppressions Wave function overlaps in large (and/or warped) extra dimensions, with ν R propagating in bulk (cf., gravity) m D νm F M P, M F = ( 2 ) δ+2 1 M P V δ = fundamental scale M F 100 TeV m D 0.01 ev Kaluza-Klein excitations (Dirac sterile) for V δ = R δ : m KK /n 1/R M F (M F /M P ) 2/δ M F 100 TeV, δ=2 Mixings too small in simplest versions 10 ev Can enhance by additional small mass terms, unequal dimensions Can add Majorana masses
Worldsheet instantons, e.g., intersecting D-brane (Type IIA) Closed strings (gravitons) and open strings ending on D-branes D6-branes: fill ordinary space and 3 of the 6 extra dimensions U(1) W + W U(1) a b Gauge bosons in adj. Chiral matter in (N, M) H Q 3 L U 3 SU(3) Q 2 L U2 Q 1 L SU(3) SU(2) U U(1) 1 SU(3) Yukawa interactions exp( A ijk ) hierarchies m D : A Lν c L Hu not large enough (at least in toroidal compactifications) m S : no Majorana masses at perturbative level
D-brane instantons Anomalous U(1) : M Z M str ; acts like perturbative global symmetry (may forbid µ, R P violation, ν c L νc L, Lνc L 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) D instantons: nonperturbative violation of global symmetries exp( S inst ) exp 2π α GUT V E2 }{{} V D6 f(winding) Examples of small Dirac, small or intermediate M S (ordinary seesaw), stringy Weinberg operator (LH u LH u /M) No known reason for correlated m D, m S
Higher-Dimensional Operators (HDO) Let O be an operator, such as Lν c L ν c L νc L (Dirac mass), (sterile ( ) Majorana), or LL (active Majorana) ν (L e, Dirac and SU(2) indices suppressed) L Lν c L and LL forbidden by SU(2); ν c L νc L by new physics (usually) L h ν LH u ν c L, h SSν c L νc L, C M LH } u {{ LH u} Weinberg op H u = Higgs doublet, S = singlet, M = new physics scale (HDO) Seesaw: h S 0 S 0 10 14 GeV ( M P ), h ν 1 (Field theory) Weinberg operator, M/C h S 0 S 0, (or h S 0 S 0 10 TeV for h ν 10 5 m e /ν) m ν 0.1 ev M may also be induced by heavy triplet, neutralinos, string excitations, KK or winding modes, moduli,
Additional symmetries (gauge, global, discrete) or string constraints (heterotic or type II) may further suppress coefficients L Sp M plh uν c L, S q+1 M q νc L νc L, S r 1 M r LH u LH u Sp M p S 1 S p M 1 Mp Similar to Froggatt-Nielsen (but for overall scales) Stringy or field-theoretic operators Wide range of S/M, M possible E.g., S/M 1/10; large p, q; M M P in heterotic seesaw (anomalous U(1) ) Many modified/extended/inverted/radiative seesaws (various symmetries, S, M TeV scale) May also be loop factors Can extend to flavor structure
Small Dirac for p > 0 m D 0.1 ev for S/M 10 12, e.g., M = M P, S 10 3 TeV (e.g., non-anomalous U(1), non-holomorphic SUSY) Majorana masses may be forbidden ( pure Dirac) Alternative: pseudo-dirac with q 2, r 2 (m S,T < 10 9 ev)
m D Sp ν 0.1 ev, M m p S Sq+1 M, m q T Sr 1 ν 2 M r 1 10-5 m S (q =1) m T (r =1) m D = 10 1 ev (p =1) m (ev) 10-10 10-15 m M = 10 9 ev m S (q =2) m T (r =2) 10-20 10-25 m S (q =3) 0.1 1 10 100 1000 hsi (TeV)
The Low-Scale Seesaw Operators PL, 9805281; Sayre,Wiesenfeldt,Willenbrock, 0504198; Chen,de Gouvêa,Dobrescu, 0612017 Motivations Foot,Volkas, 9505359; Berezhiani,Mohapatra, 9505385; Ma, 9507348; Arkani-Hamed,Grossman, 9806223; Dvali,Nir, 9810257; Borzumati,Hamaguchi,Yanagida, 0011141; Appelquist,Shrock, 0204141; Babu,Seidl, 0405197; PL, 0801.1345; McDonald, 1010.2659; Barry,Rodejohann,Zhang, 1105.3911; Zhang, 1110.6838 Analysis Casas,Ibarra, 0103065; de Gouvêa, 0501039; Smirnov,Zukanovich, 0603009; de Gouvêa,Jenkins,Vasudevan, 0608147; Donini,Hernandez,Lopez-Pavon,Maltoni, 1106.0064; Blennow,Fernandez-Martinez, 1107.3992; Xing, 1110.0083; de Gouvêa,Huang, 1110.6122; Fan,PL, 1201.6662; Donini,Hernandez,Lopez-Pavon,Maltoni,Schwetz,1205.5230
The Low-Scale Seesaw Both m S and m D suppressed by symmetries, e.g., p = q = r = 1 m D Γ D Sν u M, m S Γ S S 2 M 1 ev, m T Γ T ν 2 M Example, minimal mini-seesaw (MMS): (S ν) with Γ D = Γ S = 1, Γ T = 0 m 1 (νs/m)2 S 2 /M θ ν S m 1 m 2, = ν2 M, m 2 S2 M M 10 15 GeV m T comparable for Γ T 1
Light Active m 2 sterile 1.00 0.50 0.50 m D 0.30 m Θ Θ 0.10 0.20 0.05 m 1 active 0.15 0.5 1.0 1.5 0.10 0.5 1.0 1.5 0 M = ( 0 ΓD νs M Γ D νs M Γ S S2 M ) Γ D = Γ S = 1 M = 1.2 10 15 GeV ν = 246 GeV
Can extend to 2 + 3 [1 + 3] Inverted [normal] hierarchy favored for Γ T 0 Can incorporate flavor structures, e.g., tri-bimaximal Examples from U(1), mirror worlds, TC/ETC (including loops) Hybrids with other schemes (e.g., ordinary high-scale seesaw) possible Alternative: heavy active ( 1 ev) with Γ D = Γ T = 1, Γ S = 0, S < ν
Extension to 1 + 3 and 2 + 3 1 + 3 scheme: m 1 = m 2 = 0 U α4 = i M D α4 M 4 = ±i A }{{ να3 m3 L, } M 4 PMNS α = e, µ, τ U e4 too small for LSND/MiniBooNE anomaly U e4 M 4 = A νe3 L m 3 0.033 ev U µ4 M 4 = A νµ3 L m 3 0.16 ev No CP violation
2 + 3 scheme: m 3 = 0 (IH) or m 1 = 0 (NH) R R(z) = (Casas,Ibarra, 0103065) U αi = ia ναj 1 L mj R ji Mi ( cos z ) sin z sin z cos z (2 2 complex rotation matrix ) U αi determined up to z re iθ and one Majorana phase by masses and PMNS
Comparison of mini-seesaw with LSND and MiniBooNE Fit z re iθ, α 2 or α 3 (Majorana phase), M 4, M 5 to LSND/MiniBooNE (mock up other experiments by upper limit 0.15 on mixings) (Fan,PL, 1201.6662) Rough agreement with full analysis with general parameters by KMS (Kopp,Maltoni,Schwetz, 1103.4570), GL (Giunti,Laveder, 1107.1452) z α 2 (α 3 ) m 2 41 m 2 51 U e4 U µ4 U e5 U µ5 δ/π χ 2 /dof MMS-IH 0.38 e i0.54π 1.92 0.89 1.76 0.15 0.15 0.07 0.15 1.21 24.3/19 MMS-NH 1.22e i0.69π 1.53 0.46 1.08 0.11 0.15 0.09 0.13 1.72 27.8/19 KMS 0.47 0.87 0.128 0.165 0.138 0.148 1.64 110.1/130 GL 0.90 1.60 0.13 0.13 0.13 0.08 1.52 22.2/5
Inverted Hierarchy 0.015 Data LSND 0.015 Data MB Ν KMS KMS 0.010 GL 0.010 GL Mini seesaw Mini seesaw P ΝΜ Νe 0.005 P ΝΜ Νe 0.005 0.000 0.000 0.005 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.005 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 L E m MeV L E m MeV 0.015 Data 2011 MB Ν 1.0 KMS 0.010 GL 0.5 Mini seesaw P ΝΜ Νe 0.005 Θ Π 0.0 0.000 0.5 0.005 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 L E m MeV 1.0 0 1 2 3 4 r
Normal Hierarchy 0.015 Data LSND 0.015 Data MB Ν KMS KMS 0.010 GL 0.010 GL Mini seesaw NH Mini seesaw NH P ΝΜ Νe 0.005 P ΝΜ Νe 0.005 0.000 0.000 0.005 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.005 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 L E m MeV L E m MeV 0.015 Data 2011 MB Ν 1.0 KMS 0.010 GL 0.5 Mini seesaw NH P ΝΜ Νe 0.005 Θ Π 0.0 0.000 0.5 0.005 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 L E m MeV 1.0 0 1 2 3 4 r
Implications Parameters for tritium β decay, ββ 0ν, cosmology 3+2 (ev) 3+2 MSS-IH (ev) 3+2 MSS-NH (ev) EXP (ev) m β 0.2 0.18 0.12 (1 2) 0.2 m ββ 0 0.08 0 0 (0.2 0.7) (0.01 0.03) Σ 2 2.4 1.9 (0.5 1) (0.05 0.1) Sum rules, n 2, (de Gouvêa,Huang, 1110.6122) n+3 i=4 U αi 2 M i n=2,ih 3 j=1 0.003 0.0014 0.0014 2 A ναj L mj n=2,nh 0.001 0.02 0.02 New MiniBooNE analysis?
Conclusions Sterile neutrinos present in most theories LSND/MiniBooNE: need (small) active-sterile mixing (same helicity) Not pure Majorana or Dirac, pseudo-dirac, high-scale seesaw The three miracles! Need mechanism for two types of small masses (usually Dirac and Majorana) Small masses from HDO, string instantons, large/warped extra dimensions Low-scale seesaw: Dirac and Majorana masses both suppressed by symmetries (mass-mixing relation) (cf. Froggatt-Nielsen) consistent with data (new MiniBooNE?)
Heavy Active 1.000 0.500 m 2 active m D 0.50 0.30 m 0.100 0.050 Θ 0.20 0.15 Θ 0.010 0.005 m 1 sterile 0.10 0.05 0.10 0.15 0.05 0.10 0.15 0 M = (Γ T ν 2 M Γ D νs M Γ D νs M 0 ) Γ D = Γ T = 1 M = 6 10 13 GeV ν = 246 GeV