Sterile Neutrinos from the Top Down

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Abazajian et al), 1204.5379 Neutrino Masses from the Top Down, (PL), ARNPS 62, 1112.

1 Sterile Neutrinos from the Top Down Active-sterile mixing The landscape Small Dirac or Majorana masses (or both) The mini-seesaw Light Sterile Neutrinos: A White Paper (K. Abazajian et al), Neutrino Masses from the Top Down, (PL), ARNPS 62, Light Sterile Neutrinos and Short Baseline Neutrino Oscillation Anomalies (JiJi Fan,PL),

2 Mixing Between Active and Sterile Neutrinos Most m ν models involve sterile neutrinos (quark-lepton symmetry) Mass anywhere from sub-ev to M P 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) Reactor ( ν e ); gallium source (ν e ); ν µ (ν e ) limits; cosmology (BBN, CMB, BAO, H 0, clusters: N eff, m ν ) No coherent picture Warm dark matter (e.g., kev), pulsar kicks, supernovae, collider

3 Active and Sterile Neutrinos Active Neutrino (a.k.a. ordinary, doublet) in SU(2) doublet with charged lepton normal weak interactions ν L ν c R by CP Only three light active allowed by Γ Z Sterile Neutrino (a.k.a. singlet, right-handed) SU(2) singlet; no interactions except by mixing, Higgs, or BSM ν R ν c L by CP Almost always present: Are they light? Do they mix?

4 Neutrino Mass Terms Dirac mass term connects two distinct neutrinos: m D ( ν L ν R + ν R ν L ) (4 components) ν L h ν ν R φ 0 ν L φ S Majorana mass term connects neutrino with its CP conjugate: m T 2 ( νl ν c R + νc R ν L) (2 components) ν L m T ν L m T Also possible for sterile: ) m S The Standard Electroweak Theory 2 ( ν c L ν R + ν R ν c L ν c R ν L 409 ν L h T ν L ν ν L ν L φ 0 T φ 0 φ 0

5 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)

6 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, )

7 The String Landscape String theory very promising (finite quantum gravity and other interactions) However, enormous landscape of vacua (> ) Many contain SM or MSSM Many string constructions involve TeV-scale remnants or mechanisms beyond the MSSM (may be hint) Top-down string remnants may not be minimal or motivated by SM problems

8 Minimality

9 Some bottom-up ideas unlikely to emerge from simple/perturbative string constructions (e.g., high-dimensional representations) Top-down may suggest new physical mechanisms (e.g., string instantons: exponentially suppressed µ, Majorana or Dirac m ν, etc) Important to map string-likely or unlikely classes of new physics and mechanisms (and contrast with field theory)

10 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,

11 Apparent Fine-Tuning Dirac: m D h ν ν, ν = 246 GeV h ν for m D 0.1 ev Sterile Majorana: m S Γ S M P, M P GeV Γ S for m S 1 ev May be due to geometric suppression or HDO in underlying theory No predictions without further input

12 Loops Would need very high order (or very small couplings), and suppression mechanism for lower-order Often combined with other mechanisms

13 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

14 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

15 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

16 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 Would typically be of order M P if not suppressed However, 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) ν = 0 H u GeV

17 Seesaw: h S 0 S GeV ( M P ), h ν 1 (field theoretic) Weinberg op, M/C h S 0 S 0 for m ν 0.1 ev (or h S 0 S 0 10 TeV for h ν 10 5 m e /ν) M may also be induced by heavy triplet, neutralinos, multiple νl c, string excitations, KK or winding modes, moduli,

18 Similarly, 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

19 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)

20 m D Sp ν 0.1 ev, M m p S Sq+1 M, m q T Sr 1 ν 2 M r m S (q =1) m T (r =1) m D = 10 1 ev (p =1) m (ev) m M = 10 9 ev m S (q =2) m T (r =2) m S (q =3) hsi (TeV)

21 The Low-Scale Seesaw Operators PL, ; Sayre,Wiesenfeldt,Willenbrock, ; Chen,de Gouvêa,Dobrescu, Motivations Foot,Volkas, ; Berezhiani,Mohapatra, ; Ma, ; Arkani-Hamed,Grossman, ; Dvali,Nir, ; Borzumati,Hamaguchi,Yanagida, ; Appelquist,Shrock, ; Babu,Seidl, ; PL, ; McDonald, ; Barry,Rodejohann,Zhang, ; Zhang, Analysis Casas,Ibarra, ; de Gouvêa, ; Smirnov,Zukanovich, ; de Gouvêa,Jenkins,Vasudevan, ; Donini,Hernandez,Lopez-Pavon,Maltoni, ; Blennow,Fernandez-Martinez, ; Xing, ; de Gouvêa,Huang, ; Fan,PL, ; Donini,Hernandez,Lopez-Pavon,Maltoni,Schwetz,

22 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 GeV m T comparable for Γ T 1

23 Light Active m 2 sterile m D 0.30 m Θ Θ m 1 active M = ( 0 ΓD νs M Γ D νs M Γ S S2 M ) Γ D = Γ S = 1 M = GeV ν = 246 GeV

24 Can extend to [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

25 Extension to and 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 ev U µ4 M 4 = A νµ3 L m ev No CP violation (as suggested by MiniBooNE before 7/12)

26 2 + 3 scheme: m 3 = 0 (IH) or m 1 = 0 (NH) R R(z) = (Casas,Ibarra, ) 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 (corrections: Donini et al, )

27 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 (L/E m/mev) (mock up other experiments by upper limit 0.15 on mixings) (Fan,PL, ) Rough agreement with full analysis with general parameters by KMS (Kopp,Maltoni,Schwetz, ), GL (Giunti,Laveder, ) 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 /19 MMS-NH 1.22e i0.69π /19 KMS /130 GL /5

28 Inverted Hierarchy Data LSND Data MB Ν KMS KMS GL GL Mini seesaw Mini seesaw P ΝΜ Νe P ΝΜ Νe L E m MeV L E m MeV Data 2011 MB Ν 1.0 KMS GL 0.5 Mini seesaw P ΝΜ Νe Θ Π L E m MeV r

29 Normal Hierarchy Data LSND Data MB Ν KMS KMS GL GL Mini seesaw NH Mini seesaw NH P ΝΜ Νe P ΝΜ Νe L E m MeV L E m MeV Data 2011 MB Ν 1.0 KMS GL 0.5 Mini seesaw NH P ΝΜ Νe Θ Π L E m MeV r

30 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 (1 2) 0.2 m ββ ( ) ( ) Σ (0.5 1) ( ) Sum rules, n 2, (de Gouvêa,Huang, ) n+3 i=4 U αi 2 M i n=2,ih 3 j= A ναj L mj n=2,nh

31 New MiniBooNE Analysis Combined ν µ, ν µ analysis ( ) Full energy range ( MeV) (old: E ν > 475) Low energy excesses (drive effect) MiniBooNE ν, ν and LSND now compatible: large mixing favored Strong tension with ν µ disappearance Large L/E not fit by MMS (because of disappearance constraints)

32 ) (ev 2 m 10 1 LSND 90% CL LSND 99% CL KARMEN2 90% CL 68% 90% 95% 99% P ΝΜ Νe or P ΝΜ Νe MiniBooNEΝ e LSNDΝ e MiniBooNEΝ e Ν e orν e 3 2 best fit Ν e orν e 2Ν best fit Strong tension in global Neutrino L E Ν meters MeV 90, 99, CL, 2 dof (ev 2 ) 2 m 10 disappearan ce m appearan ce 1 10 Antineutrino sin 2θ sin 2 2Θ Μe T. Schwetz, Neutrino 2012, BeNe 2012

33 0.015 Data 2012 MB Ν Data 2012 MB Ν KMS KMS GL GL Mini seesaw fit w o low energy bins Mini seesaw fit w o low energy bins P ΝΜ Νe P ΝΜ Νe L E m MeV L E m MeV JiJi Fan

34 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 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 older data, but not new MiniBooNE

35 Neutrino Preliminaries Weyl fermion Minimal (two-component) fermionic degree of freedom ψ L ψ c R by CP (ψc R ψ L ) Active Neutrino (a.k.a. ordinary, doublet) in SU(2) doublet with charged lepton normal weak interactions ν L νr c by CP Sterile Neutrino (a.k.a. singlet, right-handed) SU(2) singlet; no interactions except by mixing, Higgs, or BSM ν R νl c by CP Almost always present: Are they light? Do they mix?

36 Fermion Mass Transition between right and left Weyl spinors: m ψ L ψ R + m ψr ψ L m ( ψl ψ R + ψ R ψ L ) ( m 0 by ψ L,R phase changes) Dirac Mass Connects two distinct Weyl spinors (usually active to sterile): m D ( ν L ν R + ν R ν L ) = m D ν D ν D ν L h ν ν R Dirac field: ν D ν L + ν R 4 components, L = 0 t 3 L = ±1 2 Higgs doublet Why small? (Large dimensions? Higherdimensional operators? String instantons?) φ 0 m D = h ν ν = 2h ν φ 0

37 Majorana Mass Connects Weyl spinor with itself: ν L ν L m T 2 ( νl ν c R + νc R ν L m S 2 ( ν c L ν R + ν R ν c L Majorana fields: ν M ν L + ν c R = νc M ) = m T 2 ν M ν M (active) ) = m S 2 ν MS ν MS (sterile) ν c R m T m T ν L The Standard Electroweak Theo ν L h T ν L ν MS ν c L + ν R = ν c M S 2 components, L = ±2, self-conjugate φ 0 T Active: t 3 L = ±1 (triplet or higher-dimensional operator) ν L ν L Sterile: t 3 L = 0 (singlet or bare mass) φ 0 φ 0 Phase of ν L or ν c L fixed by m T,S 0

38 Heavy Active m 2 active m D m Θ Θ m 1 sterile M = (Γ T ν 2 M Γ D νs M Γ D νs M 0 ) Γ D = Γ T = 1 M = GeV ν = 246 GeV

Sterile Neutrinos from the Top Down

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