Presentation on theme: "Quark and Lepton Mixing in S 4 Flavor Model September 28, 2010 Max-Planck-Institut für Kernphysik Heidelberg, Germany Morimitsu Tanimoto (Niigata University)"— Presentation transcript:
Quark and Lepton Mixing in S 4 Flavor Model September 28, 2010 Max-Planck-Institut für Kernphysik Heidelberg, Germany Morimitsu Tanimoto (Niigata University) with H. Ishimori and Y. Shimizu 1
Niigata University Niigata City Population: 811,996 Niigata City is an urban center developed by its port. Even though it is located on a substantial expansion of agricultural landscapes, it has also easy accesses to major cities by airplanes, express omnibuses, and bullet trains. Also from its international airport, there are regular flights to Harbin, Shanghai, Seoul, Vladivostok, Khabarovsk, Guam. Niigata aspires to be a gateway to the East Asia.
1 Tri-bi maximal mixing and Flavor Symmetry 2 S 4 Flavor Model in Quarks and Leptons 3 S 4 Flavor Model in Sleptons 4 Summary Plan of my talk 4
Three Flavor analysis strongly suggests Tri-bimaximal Mixing of Neutrinos 5 Harrison, Perkins, Scott (2002) 1 Tri-bimaximal mixing and Flavor symmetry Recent experiments of the neutrino oscillations go into a new phase of precise determination of mixing angles and mass squared differences. indicates Non-Abelian Flavor Symmetry ?
Mixing angles are independent of mass eigenvalues Different from quark mixing angles Consider the structure of Neutrino Mass Matrix, which gives Tri-bi maximal mixing 6
Stringy origin of non-Abelian discrete flavor symmetries T. Kobayashi, H. Niles, F. Ploeger, S. Raby, M. Ratz, NPB768,135(2007) hep-ph/0611020 Non-Abelian Discrete Flavor Symmetry from T 2 /Z N Orbifolds A.Adulpravitchai, A. Blum, M. Lindner, JHEP0907, 053 (2009), 0906.0468 Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models H. Abe, K-S. Choi, T. Kobayashi, H. Ohki, NPB820, 317 (2009) 0904.2631 H. Abe, K-S. Choi, T. Kobayashi, H. Ohki, NPB820, 317 (2009), 0904.2631 Origin of the non-Abelian Flavor symmetry ? Tri-bimaximal neutrino mixing from orbifolding, G.Altarelli, F.Feruglio, Y.Lin, NPB775, 31 (2007) hep-ph/0610165 Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries A.Adulpravitchai, A. Blum, M. Lindner, JHEP0909, 018 (2009), 0907.2332 A.Adulpravitchai, A. Blum, M. Lindner, JHEP0909, 018 (2009), 0907.2332
Non-Abelian Discrete Symmetries in Particle Physics Hajime IshimoriHajime Ishimori, Tatsuo Kobayashi, Hiroshi Ohki,Tatsuo KobayashiHiroshi Ohki Hiroshi OkadaHiroshi Okada, Yusuke Shimizu, Morimitsu Tanimoto,Yusuke ShimizuMorimitsu Tanimoto e-Print: arXiv:1003.3552 [hep-th] Prog.Theor.Phys.Suppl.183:1-163,2010 We review pedagogically non-Abelian discrete groups and show some applications for physical aspects. This article includes a brief view on general aspects of group theory, i.e. something basic and useful theorems. Reference 13
● CKM mixing in Quarks ? Cabibbo angle? We need Quark-lepton unification in a GUT. We need Quark-lepton unification in a GUT. ● Ue3=0 in Tri-bimaximal mixing! There are hints Non-zero U e3 in experiments. How can one predict U e3 ? Flavor Symmetry of Neutrinos is related with Physical Phenomena. ● SUSY Flavor Sector, SUSY FCNC, EDM We discuss the case of S 4 symmetry.
11’1”311’1”3 Four irreducible representations in A 4 symmetry Before discussing S 4 model, let us understand how to get the tri-bimaximal mixing in the example of A 4 flavor model. E. Ma and G. Rajasekaran, PRD64(2001)113012 15
As seen in this A 4 model, in order to reproduce the tri-bi maximal mixing, we need Non-Abelian Discrete Symmetry (A 4, T ’, S 4 … ) and Symmetry Breaking Vacuum Alignment of flavons. 20 Spontaneous Breaking ? ( Scalar potential ) Explicit Breaking ? (Boundary condition in extra-dim.)
H. Ishimori, K. Saga, Y. Shimizu, M. Tanimoto, arXiv:1004.5004 2 S 4 Flavor Model in Quarks and Leptons S 4 ×Z 4 with SUSY SU(5) GUT ⇒ Tri-bimaximal, Cabibbo angle C.Hagedorn, M.Lindner, R.N.Mohapatra, JHEP 0606, 042 (2006) SO(10) B.Dutta, Y. Mimura, R.N. Mohapatra, arXiv:0911.2242 SO(10) C.Hagedorn, S. F. King, C. Luhn, arXiv:1003.4249 SU(5) R.d.A. Toorop, F. Bazzocchi, L. Merlo, arXiv: 1003.4502 Pati-Salam
Up quarks MRMR Dirac Neutrinos Charged leptons Down quarks We take l =m=1, n=2. S 4 ×Z 4 ×U(1) FN with SUSY SU(5) GUT
S 4 invariant superpotential for leptons 23 3 L ×2 R ×3 flavon 3 L ×1 R ×3 flavon 2 R ×2 R ×2 flavon 3 L ×1 R ×3 flavon 2 R ×2 R 1 R ×1 R 3 L ×2 R ×3 flavon
We take VEV ’ s We get Lepton Mass Matrices Due to m-n<0 ○ ○ ○ ○ 24
No mixing in the left-hand ! Θ 12 =60°in the right-hand ! Vacuum alignment
After seesaw, we get the tri-bimaximal mixing 26
Deviation from the Tri-bimaximal mixing due to Higher dimensional mass operators Superpotential of next-to-leading order 27
The charged lepton mass matrix including the next-to-leading terms Since the lepton mixing is given as we have non-zero U e3 0.003
Up Quark Sector We add the next-to-leading mass matrix 34 Direct Yukawa coupling
We take alignment, we get After rotating it by the orthogonal matrix, We obtain Up Quarks
We obtain CKM matrix elements In the leading order, we predict 36
Including next-to-leading order corrections, we get The parameter set reproduces observed values very well. Values of parameters are consistent with our mass matrices. 37 CP violation can be discussed !
Flavor symmetry constrains not only quark/lepton mass matrices, but also mass matrices of their superpartner, i.e. squark/slepton Specific patterns of squark/slepton mass matrices could be tested in future experiments. In this talk, we concentrate on lepton FCNC. 3. S 4 Flavor Symmetry in Sleptons Consider Soft SUSY Breaking Term in Supergravity.
Second order Slepton mass matrices are derived from 39
For the left-handed sector, higher dimensional terms are given as Left-handed Slepton mass matri ｘ is 40
Move to Super-CKM basis ( Diagonal Basis of Charged Lepton) in order to estimate magnitudes of FCNC. Mass Insertion Parameters F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, Nucl. Phys. B477(1996) 321 Experimental Constraint from μ→eγ Numerical analyses are required. where ○ Dominant term
A terms are obtained as Experimental Constraint We need numerical analyses of μ→eγ. Dangerous !
4 Summary ☆ S 4 Flavor Symmetry in SU(5) can give realistic quark and lepton mixing matrices. Tri-bimaximal mixing, Cabibbo angle ☆ S 4 discrete symmetries work to suppress FCNC in the framework of gravity mediation in SUSY breaking. ★ Squark sectors in S 4 Symmetry ? ★ Origin of S 4 Symmetry ? 50 ★ Mass Spectrum ?
One of Future Problems One of Future Problems Can we predict Neutrino Masses? Symmetry cannot predict mass spectrum. Symmetry breaking gives mass spectrum. Normal mass hierarchy Inverted mass hierarchy T2K and NOν Ａ ! T2K and NOν Ａ ! 51
We know Koide formula ! Can we predict neutrino spectrum consistent with Tri-bimaximal Mixing ？ We need more studies of Symmetry Breakings ! Accuracy 10 -5 for neutrinos 52