1 / 25

Prediction of U e3 and cosθ ２３ from Discrete symmetry

Prediction of U e3 and cosθ ２３ from Discrete symmetry. Morimitsu TANIMOTO Niigata University, Japan. XXXXth RENCONTRES DE MORIOND March ６ , 2005 @ La Thuile, Aosta Valley, Italy. Based on the work by W.Grimus, A.Joshipura, S.Kaneko, L.Lavoura, H.Sawanaka and M.Tanimoto,

king
Download Presentation

Prediction of U e3 and cosθ ２３ from Discrete symmetry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Prediction of Ue3 and cosθ２３from Discrete symmetry • MorimitsuTANIMOTO • Niigata University, Japan XXXXth RENCONTRES DE MORIOND March ６, 2005 @La Thuile, Aosta Valley, Italy Based on the work by W.Grimus, A.Joshipura, S.Kaneko, L.Lavoura, H.Sawanaka and M.Tanimoto, Nucl. Phys. B, 2005 (hep-ph/0408123)

  2. sin2θatm > 0.92 (90% C.L.) 2 θ23 = 45° ±8° tanθsol = 0.33 - 0.49 (90% C.L.) 2 θ12 = 33° ± 4° sinθchooz < 0.057 (3σ) 2 θ13 < 12° I. Introduction NeutrinoMixingsare near Bi-Maximal

  3. Questions: ★Why are θ23and θ12 so large ? ★Why does sinθ12deviate from maximal although sinθ23 is almost maximal ? ★Why is θ13small ? How small isθ13 ? Expectation: ★Flavor Symmetry prevents non-zero θ13

  4. Plan of the talk 1. Introduction 2. Vanishing Ue3 and Discrete Symmetry 3. Symmetry Breaking and Neutrino Mixing Angles Grimus, Joshipura, Kaneko, Lavoura, Sawanaka and Tanimoto Nucl. Phys. B(2005) hep-ph/0408123 4. Summary and Discussions

  5. 2. Vanishing Ue3 and Discrete Symmetry • Basic Idea : Naturalness of Theory • Suppose a dimensionless small parameter a.If a 0, the Symmetry is enhanced. Neutrino Mass Matrix is constructed in terms of neutrino masses and mixings m1, m2, m3

  6. which has Z2 Symmetry

  7. 2 2 2 2 2 2 Normal : m1 < m2 < m3 (Δmsol = m2ーm１, Δmatm = m３ーm１) Inverted : m3 < m1 < m2 (Δmsol = m2ーm１, Δmatm = m１ーm３) Quasi-Degenerate : m1 ~ m2 ~ m3 2 2 2 2 2 2

  8. In the limitγ=2θ23 =π/2, θ13 =0 μ-τ(Z2) Interchange Symmetry Remark: θ12 is arbitrary !

  9. W.Grimus and L.Lavoura(2003) Neutrino mass matrix Assumption : θ23= 45°, θ13= 0° Framework : SM + 3νR(seesaw model) θ12 = arbitrary, no Dirac phase, two Majorana phases

  10. Charge assignment of D4 : SM + 3νR+ 3φ + 2χ D4 × Z2 model W.Grimus and L.Lavoura (2003) φ : gauge doublet Higgs χ : gauge singlet Higgs

  11. D4 × Z2model origin of lepton mixings

  12. 3. Symmetry breaking and neutrino mixing angles Two Independent Symmetry Breakings Terms should be considered. |ε|,|ε’| are constrained by experiments. Small perturbations ε,ε’ give non-zero Ue3 and cos 2θ23 W.Grimus, A.S.Joshipura, S.Kaneko., L.Lavoura H.Sawanaka and M.T (’0５　N.P.B)

  13. In the hierarchical case (m3 >> m2 > m1)with Majorana phases ρ=σ=0

  14. Normal hierarcy of ν mass CHOOZ |ε|,|ε’| < 0.3 |Ue3| < 0.2 |cos2θ23| < 0.28 ρ＝0, σ=0 atm. symmetric ρ＝π/4, σ=0 ρ＝π/2, σ=0

  15. Inverted hierarcy of ν mass CHOOZ ρ＝0, σ=0 atm. ρ＝π/4, σ=0 ρ＝π/2, σ=0

  16. Quasi-degenerate of ν mass |ε| < 0.3, |ε’| < 0.03, m = 0.3 eV CHOOZ ρ＝π/4, σ=0 ρ＝0, σ=0 atm. ρ＝π/2, σ=0 ρ＝0, σ=π/2

  17. 1. Normal ν mass hierarchy : small deviation of |Ue3| large deviation of |cos2θ23| 2. Inverted ν mass hierarchy : small / large deviation of |Ue3| (depend on Majorana phases) large deviation of |cos2θ23| 3. Quasi-Degenerate ν mass hierarchy : small / large deviation of |Ue3| (depend on Majorana phases) small deviation of |cos2θ23|

  18. Model of Symmetry Breaking: Radiatively generated Ue3 and cos2θatm Assumption : ε,ε’ are generated due to radiative corrections. MEW MX SM MSSM GUT Ue3 = ０ cos2θ23 = 0 Ue3 = non-zero cos2θ23 =non- zero

  19. tanβ is constrained : tanβ< 23 ~ Effect of Radiative correction is significant in Qusi-Degenerate case m = 0.3 eV, ρ＝0, σ=π/2

  20. 4. Summary and Discussions We easily find the Neutrino Models based on Discrete Symmetry which predictsθ13 = 0°, θ23 = 45°in the symmetric limit. |Ue3| and |cos2θ23| are deviated from zero by small symmetry breaking (ex. Ｒadiative correction) These deviations depend on Majorana phases ρ, σ. Discrete Symmetry: S3 , D4, Q4, Q6 Q4(8) Model (Talk of M. Frigerio)

  21. Models based on non-Abelian discrete groups S3 S.Pakvasa and H.Sugawara, PLB 73(1978)61. J.Kubo, A.Modragon, M.Mondragon and E.Rodrigues-Jauregui, Prog.Theor.Phys.109(2003)795. D4 W.Grimus and L.Lavoura, PLB 572 (2003) 189. Grimus, Joshipura, Kaneko, Lavoura, Sawanaka and M.T hep-ph/0408123 Q8(Q4) M. Frigerio, S. Kaneko., E. Ma and M. T, hep-ph/0409187. A4 E.Ma and G.Rajasekaran, PRD 64 (2001) 113012. K.S.Babu, E.Ma and J.W.F.Valle, PLB 552 (2003) 207. Q12(Q6) K.S.Babu and J.Kubo, hep-ph/0411226.

  22. Future Unify the lepton and quark sectors S-quark and S-lepton sector in SUSY Higgs potential

  23. 2×２ Decompositions of D4 Mass matrix in D4 doublet basis lepton : (lL1, lL2), (lR1, lR2) Higgs : H1, H2

  24. Non-Abelian discrete groups order : number of elements Geometrical object : D3(=S3) : rotations and reflections of △ D4 : rotations and reflections of □ A4 : rotations and reflections of tetrahedron

  25. Group D4 2 1 1 4 C3 3 2 4 3 Σ(dim. of reps.)^2 = # of elements # of reps. = # of classes n : # of elements h : order of any elements in that class(gh=1)

More Related