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Fermion Masses

Fermion Masses. G.G.Ross, Corfu, September 2005. The Standard Model. Masses. 1. GeV. DATA :. ?. Mixing. Masses. 1. GeV. Mixing. 10 -1. 10 -2. 10 -3. 10 -4. eV. DATA :. ?. Bi-Tri Maximal Mixing … Non Abelian Structure?. Perturbative analysis (hierarchical basis).

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Fermion Masses

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  1. Fermion Masses G.G.Ross, Corfu, September 2005 The Standard Model

  2. Masses 1 GeV DATA : ? Mixing

  3. Masses 1 GeV Mixing 10-1 10-2 10-3 10-4 eV DATA : ? Bi-Tri Maximal Mixing … Non Abelian Structure?

  4. Perturbative analysis (hierarchical basis) (small) off diagonal Diagonal Off diagonal

  5. Quark Textures Hierarchical :

  6. Quark Textures Hierarchical :

  7. Symmetric fit Asymmetric fit Roberts Romanino GGR Velasco Sevilla

  8. GATTO, SARTORI, TONIN symmetric / CP SM phase Texture zero Fritzsch, Weinberg Roberts, Romanino, GGR,Velasco

  9. Symmetric fit Asymmetric fit Roberts Romanino GGR Velasco Sevilla

  10. Infra red fixed point Pendleton, Ross Hill Kobayashi, Kubo, Mondragon, Zoupanos

  11. … dimension of operator … order of radiative corrections

  12. Textures and flavour models Symmetries Coherent picture of quark and lepton masses and mixing? Family? Family?

  13. FAMILY SYMMETRY? MESSENGER SECTOR? Symmetries and textures Hierarchical structure strongly suggests a broken symmetry Froggatt, Nielsen

  14. Abelian Family symmetry  -3 2 1 -3 2 1  1 -1 Ibanez GGR

  15. Symmetric fit Asymmetric fit Is one favoured?

  16. Probes RH angles Cannot align Yukawa and A terms Vives, GGR Favours near symmetric structure With similar structure for charged leptons Neutrino mixing not related to large RH mixing

  17. Quark masses and mixing angles Lepton masses and mixing angles

  18. Extension to charged leptons – GUT? ?

  19. Extension to charged leptons – GUT? Georgi Jarlskog

  20. 10 100 10-1 10-2 10-3 10-4 eV Extension to neutrinos??? Possible with “see-saw” Dirac Mass Majorana Mass King, GGR

  21. CP violation SUSY CP problem - In string theory CP is a discrete gauge symmetry : Dine, Leigh, MacIntyre Vives, GGR Cannot align Yukawa and A terms OK with suitable family symmetry

  22. Masses 1 GeV Mixing 10-1 10-2 10-3 10-4 eV Fermion Masses II ? Bi-Tri Maximal Mixing … Non Abelian Structure?

  23. Textures and flavour models Symmetries Coherent picture of quark and lepton masses and mixing?

  24. Abelian Family symmetry  -3 2 1 -3 2 1  1 -1

  25. Probes RH angles D-term problems for FCNC Family dependent soft mass Murayama Discrete family symmetry Gauge mediated breaking Gravity mediation

  26. Abelian Family symmetry  -3 2 1 -3 2 1  1 -1 Ibanez GGR

  27. Abelian Family symmetry  -3 2 1 -3 2 1  Need special choice of O(1) coefficients 1 -1 Ibanez GGR

  28. Masses 1 GeV Mixing 10-1 10-2 10-3 10-4 eV DATA : ? Bi-Tri Maximal Mixing … Non Abelian Structure?

  29. Non-Abelian family symmetry Symmetries Coherent picture of quark and lepton masses and mixing? Simple(?) flavour Group restricting Yukawa couplings

  30. I de Medeiros, GGR King, Vives, Velasco Sevilla… Spontaneous symmetry breaking c.f. Georgi-Jarskog only terms allowed by G

  31. Dirac mass structure

  32. Dirac mass structure

  33. Dirac mass structure

  34. Structure determinedfrom symmetries too Neutrino masses Actually cancelled by small off diagonal Majorana terms Bi-Tri Maximal Mixing

  35. Bi-maximal Vacuum alignment Discrete (Non Abelian) family symmetry?

  36. Vacuum alignment Altarelli, Feruglio

  37. Ma; Altarelli, Feruglio  Bi-Tri-maximal mixing X Grand Unified King,GGR Allows symmetric invariant - vacuum alignment  since only small high dimension corrections  Bi-Tri-maximal mixing Grand Unified 

  38. Summary Texture and texture zero hints at underlying structure Family symmetry ? GUT symmetry? Due to the see-saw mechanism, the quark, charged lepton and neutrino masses and mixing angles can be consistent with a similar structure for their Dirac mass matrices. Hints at an underlying (spontaneously broken) family symmetry? SO(10)XSU(3)? Extraction of Yukawa couplings crucial to understanding fermion structure Bounded off diagonal terms (anti)symmetric, hermitian SUSY data

  39. Summary Texture and texture zero hints at underlying structure Family symmetry ? GUT symmetry? Due to the see-saw mechanism, the quark, charged lepton and neutrino masses and mixing angles can be consistent with a similar structure for their Dirac mass matrices. Hints at an underlying (spontaneously broken) family symmetry? SO(10)XSU(3)? gives a new solution to the SUSY FCNC and CP problems Extraction of Yukawa couplings crucial to understanding fermion structure Bounded off diagonal terms (anti)symmetric, hermitian SUSY data A discrete non-Abelian subgroup can give vacuum alignment needed For bi-tri-maximal mixing

  40. Ramage,GGR

  41. Majorana Mass Matrix

  42. Ramage,GGR

  43. Ma; Altarelli, Feruglio Neutrinos Charged leptons 3

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