Theoretical Expectations for Neutrino Parameters: Mixing Schemes, Models and Deviations. Werner Rodejohann (MPIK, Heidelberg) IPMU, 09/11/10

Transcription

1 Theoretical Expectations for Neutrino Parameters: Mixing Schemes, Models and Deviations Werner Rodejohann (MPIK, Heidelberg) IPMU, 09/11/10 1

2 Neutrino oscillations : Jose What to talk about? Neutrino models with flavor symmetry : Morimitsu try to cover the middle 2

3 Outline Current Status of PMNS Tri-bimaximal Mixing (TBM) Alternatives to TBM Importance of θ 13 Deviating Neutrino Mixing Schemes: example U e3 0.1 from zero Expectation for Non-Standard Neutrino Physics application to MINOS anomaly Importance of neutrino mass observables 3

4 Pontecorvo-Maki-Nakagawa-Sakata (PMNS) Matrix U = 0 B c 23 s 23 0 s 23 c 23 1 C C A {z } 0 B c 13 0 s 13 e iδ s 13 e iδ 0 c 13 1 C C A {z } 0 B c 12 s 12 0 s 12 c C C A {z } atmospheric and LBL SBL reactor solar and LBL reactor 0 B B q 1 2 q q 1 2 q C C C A 0 B C C A 0 B B q 2 3 q q 1 3 q C C C A (sin 2 θ 23 = 1 2 ) (sin2 θ 13 = 0) (sin 2 θ 12 = 1 3 ) = 0 B B q 2 3 q q 1 6 q 1 3 q 1 2 q 1 6 q 1 3 q C C C A Harrison,Perkins,Scott (2002) 4

5 Mixing close to TBM expand around it ( U = R 23 π ) ( R 23 (ǫ 23 ) 4 R 13 (ǫ 13 ; δ)r 12 (ǫ 12 ) R 12 sin 1 1 ) 3 Only one small ǫ ij responsible for deviation of (and only of) θ ij from θij TBM sin 2 θ 12 = 1 (cosǫ 12 + ) 2 2 sinǫ ǫ ǫ2 12 sin 2 θ 23 = sinǫ 23 cos ǫ ǫ 23 U e3 = sinǫ 13 e iδ Triminimal Parametrization Pakvasa, W.R., Weiler, PRL 100, (2008) 5

6 Mass Matrix Special case of µ τ symmetry A B B (m ν ) TBM = UTBM m diag ν U TBM = 1 2 (A + B + D) 1 2 (A + B D) 1 2 (A + B + D) where A = 1 3 ( 2 m1 + m 2 e 2iα), B = 1 3 ( m2 e 2iα m 1 ), D = m3 e 2iβ m ee + m eµ + m eτ = m µe + m µµ + m µτ = m τe + m τµ + m ττ masses independent on mixing (i.e., not V us = m d /m s ) Correlations between mass matrix elements flavor symmetries: A 4, (27), Σ(81), T, PSL 2 (7), SU(3),... 6

7 Comment on Model Zoo Example: 58 models based on A 4 leading to tri-bimaximal mixing: Barry, W.R., PRD 81, (2010) 7

8 Bari GM-I GM-II STV TBM sinθ sin 2 θ sin 2 θ all groups find deviations from one or more TBM values 8

9 = 0 U = c 23 s 23 0 s 23 c Taking Bari results as example: 1 C A 1 0 C B 0 c 13 0 s 13 e iδ s 13 e iδ 0 c e iδ C A C B c 12 s 12 0 s 12 c C A e iδ e iδ = e iδ e iδ C A e iδ e iδ C A Abbas, Smirnov, PRD 82, (2010): deviations from m TBM ν possible: TBM accidental? 9

10 Define e = (m ν) eµ (m ν ) eτ (m ν ) eµ, µ = (m ν) µµ (m ν ) ττ (m ν ) ττ, Σ 10 8 φ =0 φ =π/6 φ =π/5 φ =π/4 φ =π 6 e s 13 Abbas, Smirnov, PRD 82, (2010) 10

11 µ τ symmetry (Z 2, D 4,...): a b b m ν = d e d Alternatives to TBM U e3 = 0, θ 23 = π/4 solar neutrino mixing unconstrained (θ 12 = O(1)) 11

12 Alternatives to TBM Golden Ratio ϕ 1 (A 5 ) cotθ 12 = ϕ sin 2 θ 12 = ϕ 2 = (Datta, Ling, Ramond; Kajiyama, Raidal, Strumia; Everett, Stuart) Golden Ratio ϕ 2 (D 5 ) cos θ 12 = ϕ 2 sin 2 θ 12 = 1 4 (3 ϕ) = (W.R.; Adulpravitchai, Blum, W.R.) 12

13 Golden Ratio Prediction ϕ 1 can be generated by m ν = cotθ 12 = ϕ or: tan2θ 12 = Z 2 : S = Model based on A 5 (isomorphic to rotational icosahedral symmetry group)? Cartesian coordinates of its 12 vertices: (0, ±1, ±ϕ) (±1, ±ϕ, 0) (±ϕ, 0, ±1) 13

14 S 3 = 1 2 Golden Ratio Prediction ϕ 1 A 5 has irreps 1, 3, 3, 4, 5 e.g., generators for triplet representation 3 1 ϕ 1/ϕ ϕ 1/ϕ 1 and T 3 = 1 1 ϕ 1/ϕ 2 ϕ 1/ϕ 1 1/ϕ 1 ϕ 1/ϕ 1 ϕ Everett, Stuart, PRD 79, (2009) 14

15 Golden Ratio Prediction ϕ 2 cos θ 12 = ϕ/2 or: θ 12 = π 5 sin 2 θ 12 = sin 2 π/5 = (best-fit: 0.32) (W.R., PLB 671, 267 (2009)) AD = ϕ AB symmetry group of pentagon: D 5 15

16 Golden Ratio Prediction ϕ 2 symmetry group of decagon: D 10 16

17 Dihedral Groups Blum, Hagedorn, Lindner, Hohenegger, PRD 77, (2008): A = D n has several 2 j, generated by e2πi j n 0 and B = e 2πi j n 1 0 and Z 2 is generated by B A k = 0 e 2πi j n k e 2πi j n k 0 Thus, break D n such that m ν invariant under B A k ν and m l under B A k l : U e1 2 = cosπ j 2 n (k ν k l ) Again, D 5 or D 10 to obtain π/5 17

18 A Model based on D 10 Adulpravitchai, Blum, W.R., New J. Phys. 11, (2009) Field l 1,2 l 3 e c 1,2 e c 3 h u,d σ e χ e 1,2 ξ e 1,2 ρ e 1,2 σ ν ϕ ν 1,2 χ ν 1,2 ξ ν 1,2 D Z 5 ω ω ω 2 ω 2 1 ω 2 ω 2 ω 2 ω 2 ω 3 ω 3 ω 3 ω 3 18

19 χe 1 χ e A = v 1 e 2πik 5 1 A, A Model based on D 10 ξe 1 ξ e A = w 1 e 3πik 5 1 A, ρe 1 ρ e A = z 1 e 4πik 5 1 A ϕν 1 ϕ ν 2 = v ν 1 1 where k is an odd integer between 1 and 9, and, χν 1 = w ν 1, ξν 1 χ ν 2 1 ξ2 ν = z ν 1 1 σ e = x e, σ ν = x ν 19

20 U l = diag(e 2iΦ, 1, e i(φ+δ) ) cosθ 23 sinθ 23 0 sinθ 23 cosθ 23 U ν = where Φ = 4π P θ 12 = π/5 vanishing U e3 in general non-maximal θ 23 20

21 VEV alignment SUSY and driving fields Field ψ 0e ϕ 0e 1,2 ξ 0e 1,2 ψ 0ν χ 0ν 1,2 ξ 0ν 1,2 D Z 5 ω ω ω ω 4 ω 4 ω 4 flavon superpotential w f = w f,e + w f,ν flavor symmetry broken at high scale, thus minimize in supersymmetric limit 21

22 determine supersymmetric minimum by setting F-terms of driving fields to zero: w f,e ψ 0e = a e (χ e 1 ξ e 1 + χ e 2 ξ e 2) = 0 w f,e ϕ 0e 1 w f,e ϕ 0e 2 w f,u ξ1 0e w f,u ξ 0e 2 = b e χ e 1 ξ e 2 + c e ξ e 1 ρ e 2 = 0 = b e χ e 2 ξ e 1 + c e ξ e 2 ρ e 1 = 0 = d e ξ e 2σ e + f e ξ e 1 ρ e 1 = 0 = d e ξ e 1 σ e + f e ξ e 2 ρ e 2 = 0 solved by vev configuration given above... 22

23 Alternatives to TBM U BM = Bi-maximal S 4 : Altarelli, Feruglio, Merlo, JHEP 0905, 020 (2009) (needs large NLO corrections) CKM(-like) charged lepton corrections may also resurrect it: QLC 0 : θ 12 = π 4 θ C sin 2 θ QLC 1 : U = V U BM sin 2 θ λ/ 2 cosφ QLC 2 : U = U BM V sin 2 θ λ cos φ Quark-Lepton Complementarity 23

24 TM 2 (S 3,4, (27)) (Lam; Grimus, Lavoura) Alternatives to TBM Tri-maximal Mixing(s) U e2 2 U µ2 2 U τ2 2 = 1/3 1/3 1/3 TM 1, TM 3, TM 1, TM 2, TM 3, e.g., ( TM 1 : Ue1 2, U e2 2, U e3 2) = ( 2 3, 1 3, 0) U e1 2 2/3 TM 1 : U µ1 2 = 1/6 U τ1 2 1/6 (Lam; Albright, W.R.; Friedberg, Lee) 24

25 Alternatives to TBM tetra-maximal (Xing) U = diag(1, 1, i) R 23 (π/4; π/2) R 13 (π/4; 0) R 12 (π/4; 0) R 13 (π/4; π) symmetric mixing U = U T (Joshipura, Smirnov; Hochmuth, W.R.) U e3 = sinθ 12 sinθ 23 1 sin 2 δ cos 2 θ 12 cos 2 θ 23 + cos δ cosθ 12 cos θ 23 hexagonal mixing (D 6 ) (Albright, Dueck, W.R.; Kim, Seo) θ 12 = π/6 sin 2 θ 12 = 1 4 θ 12 = π/6, θ C = π/12: dodecal (D 12 model) 25

26 Scenario sin 2 θ 12 sin 2 θ 23 sin 2 θ 13 TBM µ τ TM ** TM ** TM TM TM 2 ** TM 3 ** T 4 M U=U T BM HM ϕ ϕ QLC QLC QLC Albright, Dueck, W.R.,

27 sin 2 θ best-fit 1σ 3σ TBM TM 1 TM 2 TM 2 TM 3 T 4 M U=U T HM QLC 1 QLC U e3 27

28 sin 2 θ best-fit 1σ 3σ TBM TM 1 TM 2 TM 2 TM 3 T 4 M U=U T HM QLC 1 QLC U e3 28

29 sin 2 θ best-fit 1σ 3σ TM 1 TM 2 TM 2 TM 3 T 4 M U=U T HM QLC 0 QLC 1 QLC sin 2 θ 12 29

30 "Typical" values for U e3 m 2 sol / m2 atm sqrt( m 2 sol / m2 atm ) m e /m µ m e /m τ U e3 0,1 0,01 0,001 0,0001 1e-05 # $ & λ ℵ m µ /m τ sqrt(m e /m µ ) sqrt(m e /m τ ) sqrt(m µ /m τ ) m d /m s m d /m b # m s /m b $ sqrt(m d /m s ) % sqrt(m d /m b ) & sqrt(m s /m b m u /m c m u /m t m c /m t sqrt(m u /m c ) sqrt(m u /m t ) sqrt(m c /m t ) λ λ λ/sqrt(2) λ/(3 sqrt(2)) λ 2 1/3 - sin 2 θ 12 sqrt( 1/3 - sin 2 θ 12 ) 1/2 - sin 2 θ 23 ℵ sqrt( 1/2 - sin 2 θ 23 ) 1/3 - sin 2 θ /2 - sin 2 θ

31 "Typical" values for U e3 normal ordering U e3 0,1 0,01 m 1 /m 2 m 1 /m 3 m 2 /m 3 sqrt(m 1 /m 2 ) sqrt(m 1 /m 3 ) sqrt(m 2 /m 3 ) (m 1 /m 2 ) 2 (m 1 /m 3 ) 2 (m 2 /m 3 ) 2 m 2 sol / m2 atm sqrt( m 2 sol / m2 atm ) 0,001 1e-05 0,0001 0,001 0,01 0,1 m 1 [ev] 31

32 "Typical" values for U e3 inverted ordering 0,1 U e3 0,01 0,001 1e-05 0,0001 0,001 0,01 0,1 m 3 [ev] m 3 /m 1 m 1 /m 2 sqrt(m 3 /m 1 ) sqrt(m 1 m 2 ) (m 3 /m 1 ) 2 (m 1 /m 2 ) 2 m 2 sol / m2 atm sqrt( m 2 sol / m2 atm ) 32

33 sin 2 θ E 6 SU(5) SO(10) lopsided SO(10) sym/antisym SRND sin 2 θ 12 Albright, Chen 33

34 Predictions of All 63 Models 12 Number of Models anarchy texture zero SO(3) A 4 S 3, S 4 L e -L µ -L τ SRND SO(10) lopsided SO(10) symmetric/asym e sin 2 θ /11/10 Albright, Chen, PRD 74, (2006) 34

35 The value U e3 0.1 seems to be interesting: little bit smaller than current limit Bari hint two numbers a, b of order one: a/b > 0.1 experimentally probed very soon Atm & LBL & CHOOZ Solar & KamLAND ALL ν oscillation data sin 2 2Θ 13 discovery reach 3Σ MINOS CNGS D CHOOZ T2K NO A Reactor II NO A FPD 2 nd GenPDExp NuFact Superbeams Reactor exps Conv. beams Superbeam upgrades Ν factories Branching point θ CHOOZ Solar excluded sin 0 Year 35

36 Log mee ev Disfavored by 0ΝΒΒ m m Disfavored by Cosmology 3.5 U e3 0.0 Best fit & 3Σ Log m ev Log mee ev Disfavored by 0ΝΒΒ m m Disfavored by Cosmology 3.5 U e Best fit & 3Σ Log m ev importance of U e3 in neutrino-less double beta decay 36

37 How to perturb a mixing scenario/model VEV misalignment, NLO terms explicit naive breaking renormalization charged leptons 37

38 naive misalignment : VEV misalignment, NLO terms if flavon = (1, 1, 1) T, perturb it to flavon = (1, 1 + ǫ 1, 1 + ǫ 2 ) T Honda, Tanimoto Barry, W.R. - typically of the same order for θ 23 and U e3 - of order flavon /Λ or flavon /M R, typically O(0.1) or O(λ C ) or O(0.01) - solar neutrino mixing angle receives larger corrections 38

39 VEV misalignment, NLO terms NLO terms, VEV misalignment due to terms allowed by the symmetry model-dependent! Altarelli, Feruglio, Merlo, JHEP 0905: δ sin 2 θ 12 δ U e3 = O(λ) and δ sin 2 θ 23 = O(λ 2 ) 39

40 Altarelli, Feruglio, Hagedorn, JHEP 0803: corrections O(λ 2 ) to all mixing angles Lin, NPB 824: δ U e3 = O(λ) and δ sin 2 θ 12 δ sin 2 θ 23 = O(λ 2 ) Hagedorn, Ziegler, : δ U e3 2 = O(λ 2 ) and δ sin 2 θ 12 = O(λ) Ishimori et al., : δ U e3 2 = O(ǫ 2 ) and δ sin 2 θ 12 = O(ǫ) and δ sin 2 θ 23 = O(ǫ 2 ) etc.: etc. 40

41 How to perturb a mixing scenario/model explicit (naive) breaking A (1 + ǫ 1 ) B (1 + ǫ 2 ) B (1 + ǫ 3 ) m ν = 1 2 (A + B + D) (1 + ǫ 1 4) 2 (A + B D) (1 + ǫ 5) 1 2 (A + B + D) (1 + ǫ 6) small complex parameters ǫ i = ǫ i e iφ 1 with ǫ i 0.2 Albright, W.R., Phys. Lett. B 665, 378 (2008) 41

42 U e U e m 1 [ev] m 3 [ev] U e requires m 1 > 0.02 ev in normal ordering ( ǫ 2 (m m 2 )/ m 2 A ) nothing in inverted ordering ( ǫ 2 ) 42

43 Normal hierarchy U e e-05 1e-06 1e-07 > + < # A AB # BB BM BO CM CY DR GK + JLM < VR > YW 1e sin 2 θ 12 sin 2 θ 12 very unstable connected to two very close eigenvalues 43

44 How to perturb a mixing scenario/model Radiative corrections θ ij θ TBM ij + k ij ǫ RG 2 m 1 + m 2 e iα 2 2 k 12 = 3 ( m 2 2 m 2 + m 3 e i(α 3 α 2 ) 2 k 23 = 3 m m 1 + m 3 e iα 3 m2 2 3 m 2 3 m2 1 ( 2 m 2 + m 3 e i(α 3 α 2 ) 2 m 1 + m 3 e iα 3 k 13 = 3 m 2 3 m2 2 m 2 3 m ) ) ǫ RG = c m 2 τ 16π 2 v 2 ln M X m Z and c = 3/2 or 1 + tan 2 β 44

45 Sign of RG correction (all best-fits have sin 2 θ ): Model mass ordering θ 12 θ 23 SM MSSM m 2 31 > 0 ց ց m 2 31 < 0 ց ր m 2 31 > 0 ր ր m 2 31 < 0 ր ց Size of RG correction (phases ignored...): Angle NH IH QD θ 12 1 m 2 A / m2 m 2 0/ m 2 θ m 2 0/ m 2 A θ m 2 0/ m 2 A 45

46 46

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48 48

49 Large U e3 and RG aim: get U e3 = 0.1 from TBM constraint: keep sin 2 θ 12 close to TBM value what is sin 2 θ 23? Goswami, Petcov, Ray, W.R., PRD 80 (2009)

50 k 12 = 2 3 m 1 + m 2 e iα 2 m 2 Effect on θ 12 2 m 2 A m 2 m 2 0 m 2 1 NH (1 + e iα 2 ) IH (1 + e iα 2 ) QD strong effect for IH and QD suppress with α 2 = π m ee m 0 1 sin 2 2θ 12 sin 2 α 2 /2 α 2=π m 0 cos2θ 12 large cancellations in 0νββ! 50

51 Renormalization and U e3 0.1 m λ (ev) Inverted tanβ = 5 m λ (ev) Inverted tanβ = m λ 0 (ev) m λ 0 (ev) m ee c 2 13 m 0 c s 2 12 e iα 2 tanβ = 5: m ee takes values between 0.26 and 0.50 ev; general upper and lower limits: 0.2 ev and 1.4 ev tanβ = 20: m ee takes values between 0.07 and 0.11 ev; general upper and lower limits: 0.05 ev and 0.34 ev 51

52 Renormalization and U e Normal Inverted sin 2 θ sin 2 θ m 0 (ev) m 0 (ev) SM: doesn t work 52

53 Renormalization and U e sin 2 θ sin 2 θ m 0 (ev) Normal tanβ = m 0 (ev) Normal tanβ = 20 MSSM: 4 < (m 0 /ev) tanβ < 7 53

54 Renormalization and U e Normal tanβ = 5, Inverted tanβ = 5, 20 sin 2 θ sin 2 θ sin 2 θ sin 2 θ 23 θ 23 π/4 = O( U e3 ) can NOT be maximal 54

55 Planck-scale? but can be zero Lower Limits on θ 13? L = 1 M Pl (L Φ) 2 U e3 < v 2 M Pl 1 m 2 A RG for m 1 = 0: U e3 > yτ 2 sin2θ 12 sin2θ 23 m 2 32 π 2 m 2 + m 2 A ln Λ λ SM (1 + tan 2 β) MSSM increases for non-zero neutrino masses with a factor 8 m 2 0 ( m 2 + ) m 2 A m ( m0 ) ev 55

56 A case without RG? θ 13 ṁ 3 m 3 inverted hierarchy with m 3 = θ 13 = 0 receives no corrections! need 2-loop RGEs, to obtain most minimal value of U e3 ṁ ν = 2 (16π 2 ) 2 Y T m ν Y with Y = diag(y 2 e, y 2 µ, y 2 τ) (Davidson, Isidori, Strumia, PLB 646 (2007) 100 have used it to get smallest neutrino mass ev) 56

57 Most minimal value of U e3 U e3 y 4 τ 2 (16π 2 ) 2 s 2 23 m 1 m 2 sin2θ 12 sin2θ 23 m 1 m 2 e i ϕ m 1 s m 2 c 2 12 e i ϕ lies between and Ray, W.R., Schmidt,

58 Most minimal value of U e3 MSSM: from SUSY breaking with sleptons in the loop, or additive terms LH u LH u U e3 MSSM U e3 SM (1 + tan 2 β) 2 / ln Λ λ Supernova physics (collective effects) rx (km) log 10 θ v Fuller et al., PRL 99, (2007) 58

59 How to perturb a mixing scenario/model Charged lepton corrections U = U l U (T)BM 1 λ λ 3 U l λ 1 λ 2 λ 3 λ 2 1 gives sin 2 θ λcosφ or sin2 θ λ cosφ U e3 1 2 λ, J CP = λ 6 sinφ sin 2 θ O(λ2 ) Direct correlation between U e3, sin 2 θ 12 and CP violation! For BM: small CP violation For TBM: large CP violation 59

60 Charged Lepton Corrections and U e sin 2 θ J CP U e U e3 CP violation maximal! θ 23 π/4 = O( U e3 2 ) θ 23 can be maximal Goswami, Petcov, Ray, W.R., PRD 80, (2009) 60

61 sin 2 θ charged leptons renormalization (MSSM) explicit breaking U e3 λ 2 m2 0 m 2 A ( m 2 A > 0) ( m 2 A < 0) (1 + tan 2 β) ǫ q ǫ m 1 / m 2 A mass QD: m 0 tan β (4 7) ev IH, PD, QD m ee m 0 c 2 13 cos 2θ 12 CP oscillations: almost maximal CP violation α 2 π m 0 c 2 13 cos 2θ 12 q m 2 A c2 13 cos 2θ 12 large U e3 requires (IH) (PD/QD) suppressed m ee only when initially α 2 π (QD) (IH) U e

62 Summary so far Corrections to U e3 and θ 23 similar do we need precision experiments for θ 12? could distinguish very different approaches sin 2 θ 12 = 1 2 λ/ vs. sin 2 θ 12 = 1 3 BUT: Corrections to θ 12 tend to be largest... where else is θ 12 important? 62

63 63

64 Testing Inverted Ordering Nature gives us a scale: m ee IH min = ( 1 U e3 2) m 2 A ( 1 2 sin 2 θ 12 ) = ( ) ev 1σ ( ) ev 3σ Desiderata: small U e3 large m 2 A small sin 2 θ 12 Recall: a limit m ee lim scales with Talk by Kishimoto ( E B M t )1 4 64

65 Testing Inverted Ordering Nature gives us another scale: m ee IH max = ( 1 U e3 2) m 2 A = ( ) ev 1σ ( ) ev 3σ small U e3 large m 2 A Desiderata: 65

66 m ee [ev] m 0 = ev m A 2 [10-3 ev 2 ] IH, 3σ IH, BF T 0ν 1/2 [10 28 y] m ee [ev] m 0 = ev sin 2 (θ 12 ) IH, 3σ IH, BF T 0ν 1/2 [10 28 y] m ee [ev] m 0 = ev sin 2 (θ 13 ) IH, 3σ IH, BF T 0ν 1/2 [10 28 y] m ee vs. m 2 A m ee vs. sin 2 θ 12 m ee vs. U e3 2 sin 2 θ 12 gives strongest dependence! 66

67 m 0 = ev m ee IH min, bf m ee IH max, bf 0.1 m ee [ev] sin (θ 12 ) m 2 A [10-3 ev 2 m ee vs. sin 2 θ 12 and U e3 2 67

68 sterile neutrinos Non-Standard Neutrino Physics LSND/MiniBooNE, return of the 3+1 scenarios cosmology: N eff 4 phenomenology: mass-related observables expected from theory? Non-Standard Interactions effective approach: L = ǫ αβ G F (ν α γ µ ν β ) (fγ µ f) ( ) 2 m expectation ǫ αβ = O W m NP flavorαβ gauge invariance reduces neutrino limits... 68

69 Unitarity violation U U 1, or N = (1 + η)u 0 sub-percent bounds already there (Antusch et al.) expected from type I and III seesaw, but tiny unless mild hierarchy in M ν and/or extended see-saws, e.g. inverse see-saw (Mohapatra, Valle) 0 m T D 0 M = m D 0 m T RS M S m D m RS 0 m RS M S m ν ( m D ) ( ) 2 2 ( TeV MS 10 2 GeV m RS 0.1keV) ev η 1 2 m D (m RS ) 1 (m T RS ) 1 m D equivalent: NLO term m 1 ν = O(m 4 D m 4 RS M S) at percent level natural also in E 6 models with < TeV exotic new leptons (Stech) 69

70 Non-Standard Neutrino Physics new U(1) generating interactions/potential for neutrinos ( leptonic forces, Z, etc.) no real expectation on scale neutrinos can give best limits on such forces (better than equivalence principle) exotic exotics Lorentz invariance violation CPT violation for mass scale m expect it to be order m/m Pl see-saw: M R /M Pl permille? Fermi-Dirac statistics violation... 70

71 Example MINOS anomaly m 2 = ( ) 10 3 ev 2, sin 2 2θ > 0.91 m 2 = ( ) 10 3 ev 2, sin 2 2θ = 0.86 ±

72 Is this......non-standard Interaction (Mann, Cherdack, Musial, Kafka, ; Kopp, Machado, Parke, )?...sterile neutrino (plus gauged Z from U(1) according to B L) (Engelhardt, Nelson, Walsh, )?...gauged ultra-light Z from U(1) according to L µ L τ (Heeck, W.R., )?...CPT violation? (Barenboim, Lykken, ; Choudhury, Datta, Kundu, )?...nothing and will go away (common sense)? 72

73 Gauged L α L β L e L µ or L e L τ or L µ L τ can be gauged without anomaly in SM (Foot, 1991) 73

74 SM: Y i = 0 in each family extra U(1): anomalies cancel among different (lepton) generations example L e L µ : ν e, L e have Q = 1, ν µ, L µ have Q = 1 there is an extra Z which couples to ν e, L e and ν µ, L µ with coupling g no expectation for mass scale... 74

75 if Z from L e L α is ultra-light: particles in Sun (or Earth) create potential for terrestrial neutrinos (Joshipura, Mohanty, PLB 584, 103 (2004)) V = g 2 4π Scale: m Z 1/A.U ev... V must be added to Hamiltonian: H eµ = m2 cos2θ 4 E sin2θ N e R αn e R sin2θ cos2θ + V 0 0 V looks like NSI, but does not depend on matter density! also works for vacuum oscillations! V changes sign for anti-neutrinos! P(ν α ν α ) P( ν α ν α ) without CPT violation 75

76 V = α N e = α R A.U ev α ev atmospheric neutrinos m 2 ( ) A GeV 4E ev E Limits α eµ and α eτ (Joshipura, Mohanty, PLB 584, 103 (2004)) solar neutrinos m 2 4E ( ) MeV ev E Limits (θ 13 = 0) α eµ and α eτ (Bandyopadhyay, Dighe, Joshipura, PRD 75, (2007)) stronger than limits from equivalence principle! 76

77 Gauged L µ L τ never considered for oscillation physics, but very interesting because 0 0 a L e L τ : m ν = b 0 not successful 0 but L µ L τ has zeroth order mass matrix a 0 0 L µ L τ : m ν = 0 b 0 masses a, ±b and U e3 = 0, θ 23 = π/4 automatically µ τ symmetric! flavor gauge 77

78 Gauged L µ L τ L = 1 4 Z µν Z µν M 2 Z Z µ Z µ g j µ Z µ sinχ 2 with new current j µ = µ γ µ µ + ν µ γ µ P L ν µ τ γ µ τ ν τ γ µ P L ν τ Diagonalizing kinetic and mass terms gives Z µν B µν + δm 2 Z µ Z µ L A = e (j EM ) µ A µ ( ) e ( L Z1 = (j3 ) µ s 2 ) W (j EM ) µ + g ξ (j ) µ Z µ 1 s W c W ( L Z2 = g (j ) µ e (ξ s W χ) ( ) (j 3 ) µ s 2 ) W (j EM ) µ e cw χ (j EM ) µ s W c W Z-Z mixing Z µ 2 78

79 Potential through Z-Z mixing (Heeck, W.R., ): V = g (ξ s W χ) e 4 s W c W N n 4πR A.U. α e 4 s W c W N n 4πR A.U. sin 2 2θ V = With η = 2 E V / m 2 : sin 2 2θ 1 4 η cos2θ + 4 η 2 m 2 V = m η cos2θ + 4 η 2 Recall: V changes sign for anti-neutrinos!! 79

80 sin 2 2θ V = sin 2 2θ 1 4 η cos2θ + 4 η 2 m 2 V = m η cos2θ + 4 η 2 m 2 V m 2 V = m2 1 4 η cos2θ + 4 η 2 m η cos2θ + 4 η 2 4 η m 2 cos 2θ works only with non-maximal θ 80

81 Gauged L µ L τ m 2 V m 2 V 4 η m2 cos2θ goes only with non-maximal θ sin 2 2θ = 0.83±0.08, m 2 = ( 2.48±0.19) 10 3 ev 2, α = ( ) with χ 2 min /N dof = 47.77/50, (without α: χ 2 min /N dof = 49.43/51) Heeck, W.R.,

82 60 Χ 2 with 1, 2 and 3Σ ranges Χ sin 2 2Θ 82

83 looks in H like NSI, hence apply NSI limits α = ǫ µµ 0.25 current limit ǫ µµ < α flavor effects...? 83

84 GLoBES Experiment Sensitivity to α/10 50 at 99.73% CL T2K (ν-run) 11.8 T2K 4.3 T2HK 1.7 SPL 7.5 NOνA 1.9 Combined Superbeams 1.4 Nufact

85 a µ = g 2 /(8π 2 ) Other aspects/limits of L µ L τ BBN: Γ(Z Z ν µ,τ ν µ,τ ) g 2 T g < 10 5 other EW precision: there are only 10 8 Z... 85

86 Other aspects/limits of L µ L τ coupling of Z with electromagnetic current gives modified charge Q(µ + ( ) Q(e + ) 1 + g (ξ s W χ)( 1 ) e 4 s2 W)/(s W c W ) + c W χ measured to be 1 ±

87 H = 1 2E Non-Standard Interactions L eff = G F 2 ǫ f αβ (ν αγ µ ν β ) (fγ µ f) and ǫ αβ ǫ αβ for anti-neutrinos U 0 0 U + A 0 m 2 32 ǫ µµ ǫ µτ ǫ µτ ǫ ττ Kopp, Machado, Parke, (only ǫ µτ: Mann et al., ) 87

88 H = 1 2E U NSIs 0 0 U + A ǫ µµ ǫ µτ 0 m 2 32 ǫ µτ ǫ ττ 88

89 Charged Current NSIs L NSI 2 2 G F ǫ d τµ V ud [ūγ µ d] [ µγ µ P L ν τ ] leads to interference of ν µ ν τ + N X + µ and ν µ + N X + µ Kopp, Machado, Parke,

90 Gauge Invariance strikes back! L NSI 2 2 G F ǫ d τµ V ud [ūγ µ d] [ µγ µ P L ν τ ] gives 1-loop diagram for τ µ π 0 : ǫ d τµ 0.2 BUT: gauge invariant term L NSI 2 2 G F ǫ d τµ V ud [Ūγ µ U] [ L µ γ µ L τ ] gives tree-level diagram for τ µ π 0 : ǫ d τµ 10 4 Gavela, Talk@NOW2010 this argument does not apply to gauged U(1)! 90

91 Mass Observables Example: 58 models based on A 4 leading to tri-bimaximal mixing: Barry, W.R., PRD 81, (2010) 91

92 How to distinguish? LFV low scale scalars: Higgs, LFV compatible with GUTs? leptogenesis possible? neutrino mass sum-rules! 92

93 0-nu DBD & FLAVOR PRL 99 (2007) PRD78: (2008) A4 PRD72, (2005) 12 Valle 93

94 Sum-rules in Models and 0νββ Normal Inverted <m ee > (ev) σ 30% error 3σ exact TBM exact 2m 2 + m 3 = m 1 m 1 + m 2 = m m β (ev) Barry, W.R., NPB 842, 33 (2011) 94

95 Sum-rules in Models and 0νββ Normal Inverted <m ee > (ev) σ 30% error 3σ exact TBM exact 2/m 2 + 1/m 3 = 1/m 1 1/m 1 + 1/m 2 = 1/m m β (ev) Barry, W.R., NPB 842, 33 (2011) 95

96 Mass Observables and New Physics LSND/MiniBooNE/cosmology are compatible with a sterile neutrino having ev mass and 0.1 mixing m ee st (0.1) ev m st β (0.1) ev is of order of inverted hierarchy contribution 96

97 Suppose there are 2 sterile neutrinos 8 Orderings 4 phenomenologies 4 cases to the right usually NOT considered in fits... 97

98 scheme KATRIN 0νββ feature SSN maybe maybe NH plus ν s1, ν s2 SSI maybe maybe IH plus ν s1, ν s2 NSS, ISS, SNSb, SISb yes yes QD with m 2 s1 SNSa, SISa yes yes QD with m 2 s2 Goswami, W.R., JHEP 0710, 073 (2007) 98

99 Summary Corrections/Predictions for θ 13 and θ 23 π/4 are typically similar to test them on a level of 0.1 is a good idea... once θ 13 will be determined, deviation from maximal θ 23 will become crucial interesting theoretical speculations on θ 12, but receives typically large corrections (of phenomenological interest for 0νββ) Non-standard neutrino physics: various speculations and hints, with different theoretical expectation/motivation not really comparable to SUSY in quark flavor physics but: neutrino mass generation different: keep on looking! 99

100 Go seisho arigato gozaimashita 100