Transcript ppt

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 )

1 Introduction Neutrinos: Windows to New Physics

Neutrino Oscillations provided information ● ● Tiny Large

Neutrino Masses Neutrino Flavor Mixings

Flavor Symmetry

Global fit for 3 flavors

Maltoni et al : hep-ph/0405172 ver.6 (Sep 2007)

Two Large Mixings Tri-bi maximal (Δm 2 2 sol / |Δmatm| ) 1/2 = 0.16 - 0.20 ≒ λ

Tri-Bi-Maximal

Harrison, Perkins, Scott (2002)

sin

2

θ

12

=1/3

,

sin

2

θ

23 =

1/2

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

symmetry.

flavor

Mixing angles are independent of mass eigenvalues

Different from quark mixing angles

2 Discrete Flavor Symmetry

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

Quark Sector

Discrete Symmetry

Non-Abelian discrete groups have non-singlet irreducible representations which can be assigned to interrelate families. order

SN

: permutation groups

DN

: dihedral groups 6

S3 D3

8

D4

10

D5

12

D6

14

D7 QN

: quaternion groups

T

: tetrahedral groups

Q4 Q6 T(A4)

...

...

...

...

...

Discrete symmetric models have long history . . .

Pakvasa and Sugawara (’78) : S 3 Chang, Keung and Senjanovic, (’90) Frampton and Kephart (’94), Frampton and Kong (’95) Frampton and Rasin (’99) : D 4 , Q 4 Grimus and Lavoura (’03) : D 4 Kubo et al. (’03,’04,’05) : S 3 Frigerio, S.K., Ma and Tanimoto (’04) : Q 4 Babu and Kubo (’04) : Q 6 . . . . . . . . . . .

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

3 A4 Model

1 1

1

3

by E. Ma

by E. Ma

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

h i

are yukawa couplings;

v i

are VEV

Move to diagonal basis of the charged lepton mass matrix

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

h d (1) , h u (1) : gauge doublets

gauge singlets b=c and e=f=0 is required for Tri-bi maximal.

4 Deviations from Tri-bi maximal mixing

M.Honda and M. Tanimoto, arXiv:0801.0181

Deviations in Charged Lepton Sector

CP violating phases

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

5

Discussions

Experiments indicate Tri-bi maximal mixing for Leptons, which is easily realized in A4 flavor 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.

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 !

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 Nucl.Phys.B768:135-156,2007. , Michael Ratz

arXiv:0802.2310

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

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?

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

Bi - Maximal

θ 12 = θ 23 =π/4 , θ 13 =0 θ 12

Tri - Bi-maximal

≒35°, θ 23 =π /4 , θ 13 = 0

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

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)

θ 12

Tri - Bi-maximal

≒35°, θ 23 =π /4 , θ 13 = 0 A, B, C are independent complex parameters

S-Kam Atmospheric Neutrino Data

MINOS Experiment

SK atmospheric neutrinos

KamLand

Numerical Results: Deviations from Tri-bi maximal mixing.