What is the impact of the observation of θ 13 on neutrino flavor structure?

Transcription

1 What is the impact of the observation of θ 13 on neutrino flavor structure? 第 25 回宇宙ニュートリノ研究会 宇宙線研究所 March 29, 2012, Kashiwa Morimitsu Tanimoto (Niigata University) 1

2 Plan of my talk 1 Introduction Toward observation for θ 13 2 Tri-bimaximal mixing Paradigm and Discrete Flavor Symmetry 3 Breaking with Tri-bimaximal mixing 4 Large θ 13 and the neutrino masses 5 Summary 2

3 1 Introduction Discovery of the Lepton Mixing Angles Evidence of neutrino oscillation in 1998 Atmospheric Neutrinos Talk at Takayama 1998 by Kajita Large Mixing Angle, almost maximal mixing! Theorists could not predict such large one. 3

4 Solar Neutrinos SuperK Ⅰ combined

5 Kamaland 2003 Evidence for Reactor anti-neutrino disappearence

6 There are three mixing angles for leptons. Two large mixing angles How large is the last mixing angle? Lepton Mixing Pattern Bi-maximal mixing Tri-bi maximal mixing However, there is no reason why θ 13 =0 exactly. Mission : Observe θ 13! Predict θ 13! 6

7 Toward observation for θ 13 Neutrino Mixing Matrix (MNS Matrix) Including Majorana Phases

8

9

10 Global Fit of Neutrino Parameters ( including T2K, MINOS before Daya Bay) Daya Bay Upper (Lower) : Normal (Inverted) Mass Hierarchy Schwetz, Tortola, Valle, New J, Phys.13:109401, 2011

11 2 Tri-bimaximal mixing Paradigm and Discrete Flavor Symmetry (Before T2K, DChooz and Daya Bay) Neutrino Data suggested Tri-bimaximal Mixing of Neutrinos Harrison, Perkins, Scott (2002) 11

12 Consider the structure of Neutrino Mass Matrix, which gives Tri-bi maximal mixing Mixing angles are independent of mass eigenvalues Different from quark mixing angles 12

13 For example, consider A 4 group Four irreducible representations in A 4 symmetry Consider A 4 triplet, 3 ( l e, l μ, l τ ) L l l h h/λ ( ) gives (le le + l μ l τ + l μ l τ ) v 2 /Λ A 4 symmetric

14 The third matrix is A 4 symmetric! The first and second matrices are well known to be of S 3 symmetric. In order to get the first and second matrix in A 4 model, non-trivial flavons are required.

15 Typical Non-Abelian Discrete Groups S 3 S 4 A 4 T D 4 Δ(27) Δ(54) Singlet Doublet families Triplets 3. 3 families : includes both 2 and 3 Remark: S 3 and A 4 are sub-groups of S 4. Text book to be published at Springer for Physicist (2012)

16 Stringy origin of non-abelian discrete flavor symmetries T. Kobayashi, H. Niles, F. PloegerS, S. Raby, M. Ratz, hep-ph/ Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models H. Abe, K-S. Choi, T. Kobayashi, H. Ohki,

17 Remark: Tri-bimaximal Mixing realized in Additional Matrices break Tri-bimaximal mixing which could appear in A 4, S 4, Δ(27) flavor symmetries.

18 Famous Model of Tri-bimaximal Mixing A 4 Symmetry Tetrahedral Symmetry Four irreducible representations in A 4 symmetry E. Ma and G. Rajasekaran, PRD64(2001)

19 At first let us understand how to get the tri-bimaximal mixing in the example of A 4 flavor model. A 4 Flavor model ω 3 =1 19

20 L 3 flavon 1 3 L 3 flavon 1 3 L 3 flavon 1 3 L 3 L 1 flavon 1 3 L 3 L 3 flavon 1 20

21 The mass matrices do not yet predict tri-bimaximal mixing! Can one get Desired Vacuum in Spontaneous Symmetry Breaking? We need Scalar Potential Analysis. 21

22 L 3 L 3 flavon 3 L 3 L 1 flavon 22

23 In order to get Tri-bimaximal Mixing, one needs Non-trivial Flavons 3 Additional U(1) or Zn VEV Alignment (1,0,0), (1,1,1) 23

24 3 Breaking with tri-bimaximal mixing T2K, DChooz, Daya Bay suggest us the breaking with tri-bimaximal paradigm! Let us show how to go beyond the tri-bi maximal mixing.

25 Consider Modified A 4 Model to get non-zero θ Y. Simizu, M. Tanimoto, A. Watanabe, PTP 126, 81(2011)

26 There is one relation

27 Normal Inverted

28 4 Large θ 13 and the neutrino masses A 4 model could give non-zero θ 13 by adding a new flavon A4, 1 and/or 1. However, mass dependence of θ 13 is not clear. Daya Bay results (3σ) = Order of Cabbibo angle!? What does this value of θ 13 indicate? Θ 13 could be related to neutrino masses clearly! 28

29 Ratio of Neutrino Mass Squared differences λ=0.2 29

30 W.Rodejohann, M.Tanimoto, A.Watanabe, arxiv: σ 30

31 The relation of masses and mixing angles is given by the texture zeros! Well known Simple approach: Texture one zero or two zeros! Example 31

32 Suppose normal mass hierachy and neglect smallest m 1, then we have m 1 =0 32

33 In the case of In the case of U e3 is given by the fourth root!! In the case of U e3 is given by the square root!! 33

34 W.Rodejohann, M.Tanimoto, A.Watanabe, arxiv: σ m 1 =0 limit 34

35 Model Neutrino Masses S 3 (m ν ) ee =0!! Charged Lepton Masses 35

36 Deviation from the maximal θ 23 3σ =sinθ 13

37 Suppose inverted mass hierachy and neglect smallest m 3, then we have 37

38 Simple Model to get Large θ 13 Fukugita, Tanimoto, Yanagida, PLB 562(2003) 273 [arxiv:hep-ph/ ]. Fritzsch texture failed in Quark sector! 38

39 Lepton Mixing Matrix Before Daya Bay 39

40 sinθ 13 : input maximal θ 23 is excluded Normal Mass Hierarchy Fukugita, Shimizu, Tanimoto, Yanagida (2012) 40

41 Neutrinoless Double Beta Decay mev 41

42 CP Violation Non-Zero Jcp! Unitarity Triangle 42

43 5 Summary Large θ suggests breaking with tri-bimaximal mixing. θ 13 probably depends on neutrino masses! More Precise determination of θ 13 is required in order to clarify the mass dependence. Specific textures will be tested clearly. 43