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Masses and Mixings of Quark-Lepton in the non-Abelian Discrete Symmetry

Masses and Mixings of Quark-Lepton in the non-Abelian Discrete Symmetry. VI th Rencontres du Vietnam August 9 , 2006. Morimitsu Tanimoto Niigata University. This talk is based on collaborated work with E.Ma and H. Sawanaka. Plan of the talk. 1 Introduction : Motivations

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Masses and Mixings of Quark-Lepton in the non-Abelian Discrete Symmetry

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  1. Masses and Mixings of Quark-Leptonin the non-Abelian Discrete Symmetry VIthRencontres du Vietnam August 9 , 2006 • Morimitsu Tanimoto • Niigata University This talk is based on collaborated work with E.Maand H. Sawanaka

  2. Plan of the talk • 1Introduction : Motivations • 2 A4 Symmetry • 3 A4 Model for Leptons • 4 A4 Model for Quarks • 5 Summary

  3. 1 Introduction : Motivations Neutrino Oscillation Experiments already taught us θsol ~ 33°, θatm ~ 45°, θCHOOZ < 12° 2 2 Δmatm ~ 2×10-3 eV2, Δmsol ~ 8×10-5 eV2, δ :unknown Two Large Mixing AnglesandOne Small MixingAngle (Δmsol / Δmatm )1/2 = 0.2 ≒　λ Ideas 2 2 ？ structure of mass matrix flavor symmetry observed values texture zeros, flavor democracy, μ-τ symmetry, ... Discrete Symmetry S3, D4, Q4, A4... Θij , mi

  4. Quark/Lepton mixing Lepton : θ12 = 30〜35°, θ23 = 38〜52°, θ13 < 12° Quark : θ12 ~ 13°, θ23 ~ 2.3°, θ13 ~ 0.2° (90% C.L.) by M.Frigerio ●Comparable in 1-2 and 1-3 mixing. ● Large hierarchy in 2-3 mixing. (Maximal 2-3 mixing in Lepton sector ?) Tri-Bi maximal mixing ? Quark ⇔ Lepton :

  5. Bi-Maximal Barger,Pakvasa, Weiler,Whisnant (1998) Tri-Bi-Maximal Harrison, Perkins, Scott (2002) θ12≒35°

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

  7. What is Origin of the maximal 2-3 mixing ? Discrete Symmetries are nice candidate. Flavor Symmetry S3, D4, Q4, A4... Tri-Bi-Maximal mixing is easily realized inA4 .

  8. 2 A4 Symmetry Non-Abelian discrete groups have non-singlet irreducible representations which can be assigned to interrelate families.

  9. 1 1’ 1” 3 by E. Ma

  10. by E. Ma

  11. 3 A4 Model for Leptons E.Ma L=(νi,li )～3li～1, 1’, 1” （Φi, Φi）～3< Φi, >=v1, v2, v3 c － 0 0 MνLL3 ×3 L lcΦ 3 ×(1,1’,1”)× 3

  12. Taking b=c ,e=f=0 , v1=v2=v3=v

  13. Seesaw Realization He, Keum, Volkas hep-ph/0601001 L=(νi,li )～3li～1, 1’, 1” （Φi, Φi）～3< Φi, >=v1, v2, v3 c － 0 0 νRi ～3 － χi ～3 0 （Φ, Φ ）～1 LνR Φ +νRiνRj χk +M0νRiνRj 0 Another assignment: Altarelli, Feruglio, hep-ph/0512103

  14. Quark Sector ? If the A4 assignments are Q=(ui , di )～3di , ui～1, 1’, 1” （Φi, Φi）～3 <Φi> = v1, v2, v3 c c - 0 0 withv1=v2=v3=v VCKM= UU† UD = I CKM mixings come from higher operators!

  15. 4 A4 Model for Quarks Ma, Sawanaka, Tanimoto, hep-ph/0606103 Quark-Lepton Unification in SU(5) 5*i(νi , li, dic ) ～3 c c c 10i ( li , uic , uic, dic)～1, 1’, 1” 0 － 0 （Φi, Φi）D～3 <Φi>D = v1D, v2D, v3D － 0 （Φi, Φi）E～3 <Φi>E = v1E, v2E, v3E 0 Withv1E=v2E=v3E 0 － （Φ1,Φ1）U～1’ <Φ1>U = v1U 0 0 － （Φ2,Φ2）U～1” <Φ2>U = v2U 0

  16. v1D<< v2D << v3D in order to get quark mass hierarchy v1E=v2E=v3E in order to get Tri-Bi-maximal mixing 11’1” 11’1” 1’1’1’ 1”1”1” D Parameters in Quarks: hi , viD , μ2 , μ3 , m2 , m3

  17. Taking account in phase ω and Im(μ3) CP violation is predicted. ↑ O(λ) comes from A4 phaseω How to test the quark mass matrices : SinceVub depends on the phase ofμ3 , We expect the correlation between Vub and sin2β.

  18. 5 Summary A4Flavor Symmetry gives us Tri-Bi-maximal neutrino mixing and CKM Quark Mixings in the SU(5) unification of quarks/leptons. （Φi, Φi）E～3 <Φi>E = v1E, v2E, v3E v1E=v2E=v3E （Φi, Φi）D～3 <Φi>D = v1D, v2D, v3D v1D<< v2D<<v3D （Φ1,Φ1）U ～1’（Φ2,Φ2）U ～1” ★JCP comes from mainly A4 phaseω. ★Strong correlation betweenVubandsin2β. 0 - 0 0 - 0 - - 0 0

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