1. Neutrino Oscillations
Flavor Mixing -
Neutrino Masses -
Neutrino Oscillations
Harald Fritzsch
IAS Princeton -
LMU-MPI Munich

2. The Standard Model - - I II
III I II
III
3 families - 3 colors

3. 1. SU(3) : c
exact gauge symmetry
2. SU(2) x U(1):
broken gauge symmetry

4. Further symmetries,
beyond the SM ?
(grand unfication?
supersymmetry?...)

5. problem
===> 28
fundamental
constants

6. 4 fundamental constantsG

7. 14 fundamental constantsG
quarks
leptons 4 4
flavor mixing

8. fermion masses 28
constants G

9. ==> six fundamental constants
m(fermions) ==>0
proton mass G
==> six fundamental constants

10. proton mass

11. dimensional transmutation
Mass from no-mass
1 /
QCD
dimensional transmutation

12. ( Brout - Englert - Higgs )
Masses of W-Bosons are
generated by
S.S.B.
(B-E-H Mechanism)
( Brout - Englert - Higgs )

13. Mass and Symmetry Breaking
Higgs particle
Fermi constant

14. ==========>>> Z + Z
LHC
muon
Higgs particle
==========>>> Z + Z

15. The Dark Corner of HEP Fermion Masses: Arbitrary
???Higgs mech.??? R
246 GeV g L

16. Some constants
might vary in time,
e.g. the finestructure
constant

17. Charged leptons and quarks (MeV)
Masses -
Charged leptons and quarks (MeV)
tau:
muon:
electron: - t:
c: 1 100
u: 5.3 b: s:
d: 7.8
(u, d, c, s - quark masses at 1 GeV)

18. relations between quark masses?
Observed:
m(c) : m(t) = m(u):m(c)
1/ /207
m(s):m(b) = m(d):m(s)
1/ /23

19. ln m b s d

20. ln m b s d

21. ln m t b c s d ? u

22. 175 GeV
ln m t b c s d ? u
FNAL: 1995
predicting t-mass (1987)

23. ln m
22 GeV
tau
muon - -
5 MeV e -

24. quark masses
flavor mixing angles

25. - -
III
2 families
flavor
mixing II I

26. mixing of mass eigenstates
by weak interaction

28. (beyond Standard Model)
Mass Matrices
u,c - d,s
texture zero
Fritzsch,
Weinberg
(beyond Standard Model)

29. Reflection symmetries (~parity)
texture zero:
SU(2) x SU(2) L R
Reflection symmetries
(~parity)
===> Grand Unification -SO(10)

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

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

32. both for up-type and down type quarks
0.049
= 0.049
Origin:
both for up-type and down type quarks

33. -
3 families
III
flavor
mixing II I

35. Mixing for three families
CKM matrix
(Fritzsch, Xing)
Three angles + 1 phase

36. The angles
and
can be measured
separately.

37. Theory:
3 texture zeros

38. agrees perfectly with experiment
SLAC - DESY - CERN - KEK

39. -

40. unitarity triangle

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

42. - - -
alpha:

43. Cabibbo
angle
====>
Unitarity triangle
==> CP violation

44. CKM matrix -i
phase 90 degrees
Maximal CP violation

45. Neutrinos

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

47. SNO
Sudbury
Canada
1000 t
heavy
water

48. SNO
charged current
and
neutral current

49. neutrino mass differences
Kamiokande, SNO
neutrino mass differences

50. Neutrinos
What type of mass?
How big or small are masses?
How big are the mixing angles?
Relations among angles and masses?

51. nearly degenerate neutrino masses. masses about 1 eV m(1) = 0
nearly degenerate neutrino masses? masses about 1 eV m(1) = 0.94 eV m(2) = 0.95 eV m(3) = eV eV 1

52. hierarchical neutrino masses
hierarchical neutrino masses? much smaller than 1 eV m(1) = 0 eV m(2) = eV m(3) = eV

53. reality
0.05 eV - - -

54. Gell-Mann, Ramond, Slansky
See-saw mechanism:
m: Dirac mass
M: Majorana mass
Minkowski
Yanagida,
Gell-Mann, Ramond, Slansky
==>

55. Ex.: tau-neutrino mass at about 1 eV:
Dirac mass: t-quark
new intermediate energy scale M

56. ===> Grand Unification

57. ( F., Minkowski; Georgi - 1975 )
SU(3)xSU(2)xU(1)
==>SO(10)
( F., Minkowski; Georgi )

58. Neutrino Mixing Matrix:
(like CKM Matrix)

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

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

61. Electroweak theory: SU(2) x SU(2) x U(1)
In SO(10):
lefthanded and
righthanded neutrinos
Electroweak theory: SU(2) x SU(2) x U(1) L R
New energy scale for righthanded SU(2)
related to neutrino masses? - consistent with LEP unlike SU(5)

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

65. Neutrino mixing
V=UxP
(not measured)

66. Kamiokande, SNO

67. Chooz

68. CHOOZ reactor

69. Mean values of angles

70. same pattern as for quarks:

71. Observation:
weak mass hierarchy
for neutrinos

72. ==> neutrino masses fixed

73. relations between
angles and masses

74. neutrino masses very smalleV eV -
0.051 eV
0.01 eV - -
neutrino masses very small

75. m(1) = 0.0036 … 0.0059 eV m(2) = 0.0085 … 0.0140 eV m(3) = 0.044 … 0.058 eV

76. Masses
(relative)

77. Neutrino masses less hierarchical than the masses of the charged leptons

78. Reflection symmetry in
mass matrices
Leptons:
Reflection symmetry in
SO(10) theory

79. What is atm. angle?
(ok with exp.)

80. The atm. angle is the sum of the two large angles (14 and 26 degrees).
The atm. angle is large,
but not precisely 45 degrees
The atm. angle is the sum of the two large angles (14 and 26 degrees).

81. limit:
==>

82. A mass matrix of this type
does not work for the quarks.
m(top) < 90 GeV

83. quarks c

84. Neutrino Mixing Matrix:
<=====
not 0

85. Prediction for mixing of
reactor neutrinos:

86. Present limit:
CHOOZ
V(e3) < 0.1
New experiments:
Double CHOOZ: =>0.01
Daya Bay (China) =>0.03
T 2 K: ==> (J-PARC)
(soon observed?)

87. neutrino = antineutrino
Majorana masses:
no fermion number
neutrino = antineutrino

89. 76
Ge ==>

90. Neutrinoless Double Beta Decay
Present limit about 0.23 ev
Cuoricino Exp.: Te (130)
Gran Sasso Lab.

91. Improvement by about 100 necessary!
expected:
Improvement by about 100 necessary!

92. Neutrino mixing -
Maximal CP-violation
for leptons ?

93. Conclude: Fermion masses remain a mystery
Conclude: Fermion masses remain a mystery. Neutrino masses might be Dirac masses or Majorana masses. Mixing angles for quarks are fixed by ratios of quark masses. Very good agreement with experiment.

94. quarks _
leptons

95. This works also well for leptons
This works also well for leptons. One finds, using the observed mass differences:
m(1)/m(2)=0.42, m(2)/m(3)=0.19.
m(1): eV
m(2): eV
m(3): eV

96. Neutrino
masses

97. Atmospheric angle about 40 degrees
Neutrinoless double beta decay: difficult
Reactor neutrinos: V (3e) ~ 0.052
(Daya Bay exp. ==> 0.03)