What is the impact of the observationof θ13 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Plan of my talk1 Introduction
Toward observation for θ13
2 Tri-bimaximal mixing Paradigm
and Discrete Flavor Symmetry
3 Breaking with Tri-bimaximal mixing
4 Large θ13 and the neutrino masses
5 Summary2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.

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Solar Neutrinos
SuperK Ⅰcombined

Kamaland 2003

Evidence for Reactor anti-neutrino disappearence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 θ13=0 exactly.

Mission : Observe θ13 !

Predict θ13 !
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Toward observation for θ13
Neutrino Mixing Matrix(MNS Matrix)

Including Majorana Phases

Global Fit of Neutrino Parameters( including T2K, MINOS before Daya Bay)Daya Bay 0.012-0.038

Upper (Lower) : Normal (Inverted) Mass Hierarchy
Schwetz, Tortola, Valle, New J, Phys.13:109401, 2011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)

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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
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For example, consider A 4 group
Four irreducible representations in A4 symmetry

1 1’ 1” 3Consider A4 triplet, 3 ( le, lμ, lτ)Ll l h h/Λ （3×３×１×１） gives(le le + lμlτ+ lμlτ) v2/ΛA4 symmetric○The third matrix is A4 symmetric !
The first and second matrices arewell known to be of S3 symmetric.

In order to get the first and second matrix
in A4 model, non-trivial flavons are required.

Typical Non-Abelian Discrete Groups

S3 S4○A4T’ D4 Δ(27) Δ(54) ……
○○ : includes both 2 and 3
Singlet 1 1’ 1’’ …..
Doublet 2 ….. 2 families
Triplets 3 …. 3 families

Remark: S3 and A4 are sub-groups of S4 .

Text book to be published at Springer for Physicist (2012)

Stringy origin of non-Abelian discrete flavor symmetries
T. Kobayashi, H. Niles, F. PloegerS, S. Raby, M. Ratz, hep-ph/0611020
Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
H. Abe, K-S. Choi, T. Kobayashi, H. Ohki, 0904.2631

Remark:Tri-bimaximal Mixing realized in

Additional Matrices break Tri-bimaximal mixing

which could appear in A4, S4, Δ(27) flavor symmetries.

Famous Model of Tri-bimaximal Mixing
A4 Symmetry
Tetrahedral Symmetry
Four irreducible representationsin A4 symmetry

1 1’ 1” 3E. Ma and G. Rajasekaran, PRD64(2001)113012

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At first
let us understand how to get the tri-bimaximal
mixing in the example of A4 flavor model.

A4 Flavor model

ω3=1
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1’ × 1” → 1
3L × 3flavon → 1
3L × 3flavon → 1”

3L × 3flavon → 1’3L × 3L × 1flavon → 1
3L × 3L × 3flavon → 120

○○○The mass matrices do not yet predict tri-bimaximal mixing !

Can one get Desired Vacuumin Spontaneous Symmetry Breaking ?
We need Scalar Potential Analysis.

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----------- -------------

3L × 3L × 3flavon

3L × 3L × 1flavon

22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) ……

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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.

Consider Modified A4 Model to get non-zero θ13

○○

○

○

1’ ×

Y. Simizu, M. Tanimoto, A. Watanabe, PTP 126, 81(2011)1”

There is one relation

NormalInverted

4 Large θ13 and the neutrino masses
A4 model could give non-zero θ13
by adding a new flavon A4 , 1’ and/or 1” .
However, mass dependence of θ13 is not clear.
Daya Bay results (3σ)=Order of Cabbibo angle !?

What does this value of θ 13 indicate ?
Θ13 could be related to neutrino masses clearly!

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Ratio of Neutrino Mass Squared differences

λ=0.2
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W.Rodejohann, M.Tanimoto, A.Watanabe, arXiv:1201.4936

3σ30

The relation of masses and mixing angles
is given by the texture zeros !

ExampleWell known Simple approach:Texture one zero or two zeros!

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Suppose normal mass hierachy andneglect smallest m1 , then we have

m1=032

In the case of

Ue3 is given by the fourth root !!

In the case of

Ue3 is given by the square root !!

In the case of33

W.Rodejohann, M.Tanimoto, A.Watanabe, arXiv:1201.4936

3σm1=0 limit

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ModelS3Neutrino Masses(mν)ee=0 !!
Charged Lepton Masses

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Deviation from the maximal θ23

3σ=sinθ13

Suppose inverted mass hierachy andneglect smallest m3 , then we have37

Simple Model to get Large θ13
Fukugita, Tanimoto, Yanagida,
PLB 562(2003) 273 [arXiv:hep-ph/0303177].

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Fritzsch texture failed in Quark sector!

Lepton Mixing Matrix
Before Daya Bay39

sinθ13 : inputmaximal θ23 is excluded
Normal Mass Hierarchy

Fukugita, Shimizu, Tanimoto, Yanagida (2012)40

Neutrinoless Double Beta Decay

4 - 5.5 meV
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CP Violation
Non-Zero Jcp !

Unitarity Triangle

425SummaryLarge θ13 ≒ 0.15 suggests☆breaking with tri-bimaximal mixing.

θ13 probably depends on neutrino masses !
More Precise determination of θ 13 is requiredin order to clarify the mass dependence.
Specific textures will be tested clearly.
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