Flavor Mixing, Neutrino Masses, and Neutrino Oscillations

1. Flavor Mixing, Neutrino Masses, and Neutrino Oscillations H. Fritzsch CERN

2. Standard Model 28 fundamental constants

3. 4 G

4. 14 G

5. 28 G (22 related to fermion masses)

6. Masses of W-Bosons: ? Higgs Mechanism ?

7. Mass and Symmetry Breaking Brout-Englert, Higgs, Kibble... Higgs particle Fermi constant

8. Fermion Masses: Arbitrary R 246 GeV g L

9. Masses: Charged leptons and quarks: (MeV) tau: 1 777 muon: 105.7 electron: 0.51 - t: 174 000 c: 1 100 u: 5.3 ? b: 4 500 s: 170 d: 7.8 (quark masses at 1 GeV)

10. Quark Masses: • Observed: m(c) : m(t) = m(u):m(c) 1/207 1/207 m(s):m(b) = m(d):m(s) 1/23 1/23

11. ln m b c s d ? u

12. ln m b c s d ? u

13. ln m t b c s d ? u predicting t-mass (1987)

14. ln m tau mu e? e

15. - - III 2 families flavor mixing II I

16. Mass Matrices u,c - d,s Fritzsch, Weinberg

17. texture zero: Reflection symmetries (~parity) ===> Grand Unification

18. Relations between masses and mixing angles Quarks: Cabibbo angle: Exp.: angle 90 degrees ( symmetry ! )

19. Cabibbo angle ====> data require rectangular triangle

20. 0.0506 0.0452 + 0.0053 = 0.0505 Origin: both for up-type and down type quarks

21. - 3 families III flavor mixing II I

22. Mixing for three families unitary 3x3 matrix (CKM) Three angles + 1 phase

23. Theory: 3 texture zeros agrees well with experiment F., Z. Z. Xing

24. Flavor-Symmetries, Flavor-Mixing, Neutrino Masses and Neutrino Mixing H. Fritzsch LMU / MPI Munich (rectangular triangle)

25. Cabibbo angle ====> Unitarity triangle data require rectangular triangle

26. - - - 0 0 alpha: 86 ... 95

27. Neutrinos Thus far neutrinos have been used as tools, like electrons, to study nuclear matter (quark distributions etc.) New focus now: What type of mass? How big or small are masses? How big are the mixing angles? Relations among angles and masses?

28. Kamiokande, SNO

29. Kamioka Ewigkeit ist lang, speziell gegen dem Ende zu. W.A. neutrinos from upper atmosphere

30. SNO Sudbury Neutrino Observatory Canada

31. Neutrino masses:A: masses about 1 eV m(1) = 0.94 eV m(2) = 0.95 eV m(3) = 1 eV (nearly degenerate)

32. Neutrino masses: B: masses much smaller than 1 eV m(1) = 0 eV m(2) = 0.009 eV m(3) = 0.06 eV (strong hierarchy)

33. Neutrino masses: C: neither hierarchy nor degeneracy m(1) = 0.10 eV m(2) = 0.14 eV m(3) = 0.29 eV

34. See-saw mechanism: m: Dirac mass M: Majorana mass ==>

35. Ex.: tau-neutrino mass at about 1 eV: new intermediate energy scale M

36. Grand Unification SU(3)xSU(2)xU(1)<<SU(5) (Glashow, Georgi - 1974) Now excluded by experiment.

37. SU(5) theory with supersymmetry ok

38. without supersymmetry SU(5) with supersymmetry ======energy======

39. SU(3)xSU(2)xU(1) <<SO(10) ( Fritzsch, Minkowski - 1975 )

40. In SO(10): lefthanded and righthanded neutrinos Electroweak theory:SU(2) x SU(2) x U(1)U(1): (B-L) L R

41. In SO(10): lefthanded and righthanded neutrinos Electroweak theory:SU(2) x SU(2) x U(1)U(1): (B-L) L R New energy scale for righthanded SU(2) ( related to neutrino masses? )

42. SO(10) Fermions in 16-plet (incl. righthanded neutrinos)

43. SO(10) leptons and quarks in one multiplet O(10) Neutrinos are massive

44. 1/coupling constant Grand Unification ======energy ======= =================

45. Neutrino Masses: Mass terms for charged leptons and neutrinos are not parallel  Neutrino Mixing ( Pontecorvo ... ==>)

46. like the quarks

47. Neutrino Mixing Matrix: (like CKM Matrix)

49. Neutrino mixing V=UxP (not measured)

50. Kamiokande, SNO Mean values: