Neutrino Masses and Flavor Mixing H. Fritzsch

momentum - energy not conserved!

W. Pauli 1930 „Neutron“

electron

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

(Fred Reines – Clyde Cowan)

n-capture by cadmium

Standard Model I

Standard Model neutrinos massless no mixing of neutrinos

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

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

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 - 1975

Bruno Pontecorvo 1913 - 1993

neutrino mixing

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

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

neutrino oscillation

only mass differences enter

Sun

1963 Calculation of solar flux John Bahcall

1965 => Homestake Goldmine SouthDakota

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

Kamioka

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

40 m

2001 => Kanada Sudbury Neutrino Obervatory SNO

SNO: neutral current ( no oscillations )

flavor mixing - quarks CKM - matrix

observed CKM - matrix

weak transitions and weak mixing

:H. Fritzsch – Z. Xing

flavor mixing angles - fermion masses

- - III 2 families flavor mixing II I

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

mixing angles <=> masses - mixing angles <=> masses

Cabibbo angle

Cabibbo angle ==>

- 3 families III flavor mixing II I

- texture zeros

-

-

-

- unitarity triangle

Cabibbo angle  unitarity triangle (rectangular)

-

- LHCb:

- Maximal CP-violation

relations between 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

ln m

QED-corrections

neutrino mixing matrix (==> CKM Matrix)

V = U P Fritzsch - Xing

n Kamiokande - SNO

3 texture zeros

Observed ==>

observation weak mass hierarchy

==> neutrino masses

0.05 eV - 0.01 eV 0.01 eV - 0.004 eV -

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

masses (relative)

normal spectrum inverted spectrum

weak mass hierarchy for neutrinos  large mixing angles

Neutrino Mixing Matrix ???

ln m

ln m ?

radiative corrections

ln m

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

ln m

-

Daya Bay

Daya Bay

Daya Bay

Daya Bay

observed CKM - matrix

mixing of leptons

???????? ??????? neutrino masses very small

Dirac mass ? Majorana mass ?

Dirac mass Majorana mass

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

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

neutrino = antineutrino Majorana masses no fermion number neutrino = antineutrino

decay ~ Majorana mass term

Gran Sasso Laboratory

Cuoricino 130Te

Majorana neutrino mass < 0.23 ev

relevant mass term: expected: factor 15 improvement !?

maximal CP-violation

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

Conclusions neutrinos: m very small: m<0.1 eV

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

3 texture zeros

m(1): ~ 0.004 eV m(2): ~ 0.01 eV m(3): ~ 0.05 eV

Dirac mass ? Majorana mass ?

double beta decay Cuoricino Experiment m< 0.23 eV expected: 0.02 eV