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フレーバーの離散対称性と ニュートリノフレーバー混合 22 February 2008 仙台市 作並温泉 谷本盛光 ( 新潟大学 )

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Presentation on theme: "フレーバーの離散対称性と ニュートリノフレーバー混合 22 February 2008 仙台市 作並温泉 谷本盛光 ( 新潟大学 )"— Presentation transcript:

1 フレーバーの離散対称性と ニュートリノフレーバー混合 22 February 2008 仙台市 作並温泉 谷本盛光 ( 新潟大学 )

2 1Introduction Neutrinos: Windows to New Physics ● Tiny Neutrino Masses ● Large Neutrino Flavor Mixings Flavor Symmetry Neutrino Oscillations provided information

3 Global fit for 3 flavors Maltoni et al : hep-ph/ ver.6 (Sep 2007)

4 Two Large Mixings Tri-bi maximal (Δm sol / |Δm atm | ) 1/2 = ≒ λ 22

5 Tri-Bi-Maximal Harrison, Perkins, Scott (2002) sin 2 θ 12 =1/3, sin 2 θ 23 = 1/2

6 Neutrino Mixing closes to Tri-bi maximal mixing ! Tri-bi maximal mixing provides good theoretical motivation to search flavor symmetry. A key to looking for “ hidden ” flavor symmetry.

7 Mixing angles are independent of mass eigenvalues Different from quark mixing angles

8 Non-Abelian Flavor Symmetry is appropriate for lepton flavor physics. 2 Discrete Flavor Symmetry

9 Quark Sector

10 order SN : permutation groupsS3... DN : dihedral groupsD3D4D5D6D7... QN : quaternion groupsQ4Q6... T : tetrahedral groupsT(A4)... Discrete Symmetry Non-Abelian discrete groups have non-singlet irreducible representations which can be assigned to interrelate families. Pakvasa and Sugawara (’78) : S 3 Frampton and Rasin (’99) : D 4, Q 4 Frigerio, S.K., Ma and Tanimoto (’04) : Q 4 Babu and Kubo (’04) : Q 6 Frampton and Kephart (’94), Frampton and Kong (’95) Chang, Keung and Senjanovic, (’90) Kubo et al. (’03,’04,’05) : S Grimus and Lavoura (’03) : D 4 Discrete symmetric models have long history...

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13 Need some ideas to realize Tri-bi maximal mixing by S3 flavor symmetry

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15 by E. Ma 1 1’ 1” 3 3 A4 Model

16 by E. Ma

17 Diagonal terms come from 3 × 3 → (1, 1’,1”) 1’ × 1” → 1 Off Diagonal terms come from 3 × 3 ×3 → 1

18 h i are yukawa couplings; v i are VEV

19 Move to diagonal basis of the charged lepton mass matrix

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21 What is the origin of b=c and e=f=0 ? Can one predict the deviation from Tri-bi maximal mixing ? In order to answer this question, we should discuss the model: Altarelli, Feruglio, Nucl.Phys.B720:64-88,2005 Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions

22 h d (1), h u (1) : gauge doublets gauge singlets b=c and e=f=0 is required for Tri-bi maximal.

23 4Deviations from Tri-bi maximal mixing M.Honda and M. Tanimoto, arXiv:

24 Deviations in Charged Lepton Sector

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26 CP violating phases

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28 Deviations in Charged Lepton Sector b=c=0 e=f=0

29 5 Discussions Experiments indicate Tri-bi maximal mixing for Leptons, which is easily realized in A4 flavor symmetry. does not deviate from 1 largely due to A4 phase. can deviate from 0.5 largely. can be as large as 0.2. Deviation from Tri-bi maximal mixing is important to test A4 flavor symmetry. Desired vacuum

30 Can we predict CKM Quark Mixing angles in A4 flavor symmetry ? Quark mass matrices are given as There is no Quark mixing while tri-bi maximal mixing for Leptons. Deviation is a clue to deeper understanding of flavor symmetry !

31 What is the origin of the Discrete Symmetry ? Stringy origin of non-Abelian discrete flavor symmetries: Tatsuo KobayashiTatsuo Kobayashi, Hans Peter Nilles, Felix Ploger, Stuart Raby, Michael RatzHans Peter NillesFelix PlogerStuart RabyMichael Ratz Nucl.Phys.B768: ,2007.

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34 arXiv: Hajime Iashimori, Tatsuo Kobayashi, Ohki Hiroshi Yuji Omura, Ryo Takahashi, Morimitsu Tanimoto

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38 SUSY 化が 容易にできる D4 モデルが構成できる。 ・ FCNC の抑制の大きさが予言できる。 ・ Slepton の質量行列の構造が予言できる。 LHC でのテスト可能 再び クォークセクターは?

39 Hirsch, Ma, Moral, Valle: Phys. Rev. D72(2005)091301(R) L l c Φi 3 ×3× (1,1’,1”) ← Diagonal matrix LL η i 3 ×3 × (1,1’,1”) LL ξ 3 ×3 × 3 = v 1, v 2, v 3

40 Bi - Maximal θ 12 = θ 23 =π/4, θ 13 =0 Tri - Bi-maximal θ 12 ≒ 35°, θ 23 =π/4, θ 13 =0

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42 A4 flavor symmetry can easily realize (approximate or exact) Tri-Bi-maximal Mixing A4 symmetry (Tetrahedral Symmetry)

43 Landau and Lifschitz (理論物理学教程 量子力学12章対称性の理論 点群) 群 T (正四面体群):正4面体の対称軸系 立方体の向かい合った面の中心を通る3っの2回対称軸と この立方体の空間対角線である4っの3回対称軸 (二面的ではない) 二つの同じ角度の回転は、もしも群の元の中に、一方の回転軸を 他の回転軸に重ねるような変換があれば、同じ類に属する。 定義: ある物体がある軸のまわりを角度 2π/n 回転するとき自分自身に 重なり合うとすれば、このような軸はn回対称軸と呼ばれる。 同じ軸の周りの、同じ角度の、反対方向の回転が共役ならば、 この軸を二面的と呼ぶ。 従って、 群 T の12の元(回転)は4っの類に分類される。 E (単位元) C 2(4っの回転) C 3(4っの回転) C 4(3っの回転)

44 Tri - Bi-maximal θ 12 ≒ 35°, θ 23 =π/4, θ 13 =0 A, B, C are independent complex parameters

45 S-Kam Atmospheric Neutrino Data

46 MINOS Experiment SK atmospheric neutrinos

47 KamLand

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49 Numerical Results: Deviations from Tri-bi maximal mixing.


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