1. Neutrino Masses
and
Flavor Mixing
H. Fritzsch

2. momentum - energy
not conserved!

3. W. Pauli
1930
„Neutron“

5. electron

6. Savannah river reactor
1956: discovery of the neutrino
Savannah river reactor

7. (Fred Reines – Clyde Cowan)

8. n-capture by cadmium

9. Standard Model I

10. Standard Model
neutrinos
massless
no mixing of neutrinos

11. electroweak gauge group SU(2,L) x SU(2,R) x U(1)
neutrino masses

13. ===>
Grand Unification
SU(2,L) x SU(2,R)

14. SU(3) x SU(2) x U(1)
SU(4) x SU(2) x SU(2)
~ SO(6) x SO(4)
=>SO(10)
Fritzsch / Minkowski

15. Bruno
Pontecorvo

16. neutrino mixing

17. (1957) (1976) Physics Letters 62B, 76 B. Pontecorvo Phys. JETP 6, 429
H. Fritzsch - P. Minkowski
Physics Letters 62B, 76
(1976)

18. neutrino oscillations
A neutrino is produced with a
certain momentum. The different mass eigenstates propagate with different velocities, less than the speed of light.
neutrino
neutrino oscillations

21. neutrino oscillation

23. only mass differences enter

24. Sun

26. 1963
Calculation of
solar flux
John
Bahcall

27. 1965 => Homestake Goldmine
SouthDakota

29. solar neutrino deficit observed: 0.5 neutrinos / day
expected: 1.5 neutrinos / day
observed: 0.5 neutrinos / day
solar neutrino
deficit

30. Kamioka

31. speziell gegen dem Ende zu.
Kamiokande
Kamioka Nucleon Decay Experiment
Ewigkeit ist lang,
speziell gegen dem Ende zu.
W.A.

32. 40 m

33. 2001 =>
Kanada
Sudbury
Neutrino
Obervatory
SNO

34. SNO: neutral current
( no oscillations )

35. flavor mixing - quarks
CKM - matrix

36. observed CKM - matrix

37. weak transitions and weak mixing

38. :H. Fritzsch – Z. Xing

40. flavor mixing angles -
fermion masses

41. - -
III
2 families
flavor
mixing II I

42. mass matrices:
texture 0
u,c - d,s
H. Fritzsch
S. Weinberg
1978

43. mixing angles <=> masses-
mixing angles <=> masses

44. Cabibbo angle

45. Cabibbo
angle ==>

46. -
3 families
III
flavor
mixing II I

47. -
texture zeros

48. -

49. -

50. -

51. -
unitarity triangle

53. Cabibbo angle
 unitarity triangle
(rectangular)

54. -

55. -
LHCb:

56. -
Maximal
CP-violation

57. 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

58. ln m

59. QED-corrections

60. neutrino mixing matrix
(==> CKM Matrix)

61. V = U P
Fritzsch - Xing

62. n
Kamiokande - SNO

63. 3 texture zeros

64. Observed ==>

65. observation
weak mass hierarchy

66. ==> neutrino masses

67. 0.05 eV -
0.01 eV
0.01 eV -
0.004 eV -

68. m(1) = ( 0.0040 +/- 0.001 ) eV m(2) = ( 0.0096 +/- 0.002 )eV m(3) = ( 0.049 eV +/- 0-007 ) eV
normal mass hierarchy

69. masses
(relative)

70. normal
spectrum
inverted spectrum

71. weak mass hierarchy
for neutrinos 
large mixing angles

72. Neutrino Mixing Matrix
???

73. ln m

74. ln m ?

75. radiative corrections

76. ln m

77. -muon and tauon mass-
only small changes by radiative corrections

79. ln m

80. -

82. Daya Bay

83. Daya Bay

84. Daya Bay

85. Daya Bay

86. observed CKM - matrix

87. mixing of leptons

88. ???????? ???????
neutrino masses
very small

89. Dirac mass ?
Majorana mass ?

91. Dirac mass
Majorana mass

92. Superposition of Dirac mass and Majorana mass:
See-Saw Mechanism
D: Dirac mass
M: Majorana mass

93. History Seesaw T. Yanagida 1979
Footnote:
H. Fritzsch,
M. Gell-Mann,
P. Minkowski,
PLB 59 (1975) 256
T. Yanagida
M. Gell-Mann, P. Ramond, R. Slansky

94. neutrino = antineutrino
Majorana masses
no fermion number
neutrino = antineutrino

95. decay ~
Majorana
mass term

97. Gran Sasso Laboratory

100. Cuoricino
130Te

101. Majorana
neutrino mass
< ev

102. relevant mass term:
expected:
factor 15 improvement !?

103. maximal
CP-violation

104. ===> reactor neutrinos
maximal CP – violation
(leptons)
===> reactor neutrinos

105. Conclusions neutrinos:
m very small: m<0.1 eV

106. neutrino oscillations
le lepton flavor mixing
neutrino oscillations
(large mixing angles)

107. 3 texture zeros

108. m(1): ~ eV
m(2): ~ 0.01 eV
m(3): ~ 0.05 eV

109. Dirac mass ?
Majorana mass ?

110. double beta decay
Cuoricino
Experiment
m< 0.23 eV
expected: eV