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Neutrino Masses and Flavor Mixing. H. Fritzsch LMU Munich. (Erice - 2009). Neutrino Oscillations. at least 2 neutrinos have a mass. ( masses unknown ). theory:. flavor mixing angles. fermion masses. -. -. III. 2 families. flavor mixing. II. I. mixing of mass eigenstates
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Neutrino Masses and Flavor Mixing H. Fritzsch LMU Munich (Erice - 2009)
Neutrino Oscillations at least 2 neutrinos have a mass ( masses unknown )
theory: flavor mixing angles fermion masses
- - III 2 families flavor mixing II I
mixing of mass eigenstates by weak interaction (Cabibbo angle)
mass matrices: texture 0 u,c - d,s F., Weinberg 1978 (beyond Standard Model)
texture zero: SU(2) x SU(2) L R Reflection symmetries (~parity) ===> Grand Unification -SO(10)
Cabibbo angle: Exp.: phase 90 degrees ( symmetry ! )
Cabibbo angle \
- 3 families III flavor mixing II I
Mixing for three families CKM matrix: 3 angles, 1 phase F. and Xing
The angles and can be measured separately.
Theory: 3 texture zeros
theory: -
theory: -
Flavor-Symmetries, Flavor-Mixing, Neutrino Masses and Neutrino Mixing H. Fritzsch LMU / MPI Munich (~rectangular triangle)
- - - 0 0 alpha: 86 ... 95
Cabibbo angle Unitarity triangle (rectangular)
Kamioka Ewigkeit ist lang, speziell gegen dem Ende zu. W.A.
- - Yoji Totsuka
SNO Sudbury Neutrino Observatory Canada
S N O charged current and neutral current
Kamiokande, SNO neutrino mass differences ( absolute masses unknown)
neutrino masses What type of mass term? How big or small are masses? How big are the mixing angles? Relations among angles and masses?
Neutrino Masses: Mass terms for charged leptons and neutrinos are not parallel Neutrino Mixing ( Pontecorvo ,1957... ==>)
B. Pontecorvo (1913 - 1993)
neutrino mixing matrix: (like CKM Matrix)
Theory: 3 texture zeros ( charged leptons and neutrinos)
Observation: weak mass hierarchy for neutrinos
result: 0.05 eV - 0.01 eV 0.01 eV 0.005 eV - -
m(1) = 0.0036 … 0.0059 eVm(2) = 0.0085 … 0.0140 eVm(3) = 0.044 … 0.058 eV normal hierarchy (not inverted)
Masses (relative)
Neutrino masses less hierarchical than the masses of the charged leptons
Neutrino Mixing Matrix: <===== not 0
Chooz Maas
present limit from CHOOZ: V(e3) < 0.1
prediction: - - - -