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

2. DATA : ? 1 GeV Masses Mixing

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

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

6. Quark Textures Hierarchical :

7. Quark Textures Hierarchical :

8. Symmetric fit Asymmetric fit Roberts Romanino GGR Velasco Sevilla

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

12. Symmetric fit Asymmetric fit Roberts Romanino GGR Velasco Sevilla

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

15. … dimension of operator … order of radiative corrections

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

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

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

19. Symmetric fit Asymmetric fit Is one favoured?

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

21. Quark masses and mixing angles Lepton masses and mixing angles

22. Extension to charged leptons – GUT? ?

23. Georgi Jarlskog Extension to charged leptons – GUT?

24. Possible with “ see-saw ” Extension to neutrinos??? Majorana Mass Dirac Mass 10 0 10 -1 10 10 -2 10 -3 10 -4 eV King, GGR

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

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

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

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

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

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

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

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

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

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

36. Dirac mass structure

39. Neutrino masses Structure determined from symmetries too Actually cancelled by small off diagonal Majorana terms Bi-Tri Maximal Mixing

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

41. Vacuum alignment Altarelli, Feruglio

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

43. Summary 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  Texture and texture zero hints at underlying structure Family symmetry ? GUT symmetry?

44. Summary 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  Texture and texture zero hints at underlying structure Family symmetry ? GUT symmetry? A discrete non-Abelian subgroup can give vacuum alignment needed For bi-tri-maximal mixing

46. Ramage,GGR

48. Majorana Mass Matrix

49. Ramage,GGR

50. Charged leptons Neutrinos Ma; Altarelli, Feruglio 3

51. Bi-tri maximal Harrison, Scott -Ma Charged leptons Neutrinos Ma; Altarelli, Feruglio 3

52. Phenomenological implications : 10 0 10 -1 10 10 -2 10 -3 10 -4 eV DegenerateNormalInverted Degenerate, normal and inverted spectra possible No connection between quark, charged lepton and neutrino masses