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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

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 ). Introduction Neutrinos: Windows to New Physics. Neutrino Oscillations provided information. ● Tiny Neutrino Masses ● Large Neutrino Flavor Mixings. Flavor Symmetry. Global fit for 3 flavors

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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

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  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 February2008 仙台市 作並温泉 谷本盛光 (新潟大学 )

  2. IntroductionNeutrinos: Windows to New Physics Neutrino Oscillations provided information ●Tiny Neutrino Masses ●Large Neutrino Flavor Mixings Flavor Symmetry

  3. Global fit for 3 flavors Maltoni et al : hep-ph/0405172 ver.6 (Sep 2007)

  4. Two Large Mixings Tri-bi maximal 2 2 (Δmsol / |Δmatm| )1/2 = 0.16 - 0.20 ≒λ

  5. Tri-Bi-Maximal Harrison, Perkins, Scott (2002) sin2θ12=1/3 , sin2θ23 =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. 2Discrete Flavor Symmetry Non-Abelian Flavor Symmetry is appropriate for lepton flavor physics.

  9. Quark Sector

  10. Discrete symmetric models have long history . . . Pakvasa and Sugawara (’78): S3 Chang, Keung and Senjanovic, (’90) Frampton and Kephart (’94), Frampton and Kong (’95) Grimus and Lavoura (’03): D4 Frampton and Rasin (’99): D4, Q4 Frigerio, S.K., Ma and Tanimoto (’04): Q4 Kubo et al. (’03,’04,’05): S3 Babu and Kubo (’04): Q6 . . . . . . . . . . . Discrete Symmetry Non-Abelian discrete groups have non-singlet irreducible representations which can be assigned to interrelate families.

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

  12. 3A4Model 1 1’ 1” 3 by E. Ma

  13. by E. Ma

  14. Diagonal terms come from3 × 3 → (1, 1’,1”) 1’ ×1” → 1 Off Diagonal terms come from3 × 3×3→ 1

  15. hiare yukawa couplings; vi are VEV

  16. Move to diagonal basis of the charged lepton mass matrix

  17. 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

  18. hd (1) , hu (1) : gauge doublets gauge singlets b=c and e=f=0 is requiredfor Tri-bi maximal.

  19. Deviations from Tri-bi maximal mixing • M.Honda and M. Tanimoto, arXiv:0801.0181

  20. Deviations in Charged Lepton Sector

  21. CP violating phases

  22. Deviations in Charged Lepton Sector b=c=0 e=f=0

  23. 5Discussions Experiments indicate Tri-bi maximal mixingfor Leptons, which is easily realized inA4flavor symmetry. Desired vacuum Deviation from Tri-bi maximal mixing is important to test 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.

  24. 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 !

  25. What is the origin of the Discrete Symmetry ? Stringy origin of non-Abelian discrete flavor symmetries: Tatsuo Kobayashi, Hans Peter Nilles, Felix Ploger , Stuart Raby , Michael Ratz Nucl.Phys.B768:135-156,2007.

  26. arXiv:0802.2310 Hajime Iashimori, Tatsuo Kobayashi, Ohki Hiroshi Yuji Omura, Ryo Takahashi, Morimitsu Tanimoto

  27. SUSY化が　容易にできる　D4モデルが構成できる。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？

  28. Hirsch, Ma, Moral, Valle: Phys. Rev. D72(2005)091301(R) LlcΦi 3 ×3×(1,1’,1”)←Diagonal matrix LLηi3 ×3 ×(1,1’,1”) LLξ3 ×3 × 3 < Φi >=v1, v2, v3

  29. Bi - Maximalθ12=θ23 =π/4 , θ13 =0 Tri - Bi-maximal θ12≒35°,θ23 =π/4 , θ13 =0

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

  31. 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）　 C２（４っの回転） 　C３（４っの回転）　 C４（３っの回転）

  32. Tri - Bi-maximal θ12≒35°,θ23 =π/4 , θ13 =0 A, B, C are independent complex parameters

  33. S-Kam Atmospheric Neutrino Data

  34. MINOS Experiment SK atmospheric neutrinos

  35. KamLand

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

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