G

G

G

Fermion Masses: Arbitrary L R

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

III II I

Relations between masses and mixing angles

III II I

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?

Ewigkeit ist lang, speziell gegen dem Ende zu.W.A.Ewigkeit ist lang, speziell gegen dem Ende zu.W.A.

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

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

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

See-saw mechanism:

Ex.: tau-neutrino mass at about 1 eV:

SU(5) theory with supersymmetry ok

Electroweak theory: SU(2) x SU(2) x U(1) U(1): (B-L)

O(10)

Neutrino Masses: Mass terms for charged leptons and neutrinos are not parallel  Mass terms for charged leptons and neutrinos are not parallel  Neutrino Mixing

Neutrino mixing V=UxP

Observation:

Neutrino masses fixed, since the mass differences are given by the experiment, and the angles are fixed by the mass matrix

Neutrino masses less hierarchical than the masses of the charged leptons

Double Beta Decay

The atm. angle is the sum of the two large angles (14 and 26 degrees). The atm. angle is the sum of the two large angles (14 and 26 degrees).

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. 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.

This works also well for leptons. One finds, using the observed mass differences: 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(1): eV m(2): eV m(2): eV m(3): eV m(3): eV Atmospheric angle about 40 degrees Neutrinoless double beta decay: difficult Reactor neutrinos: V (3e) ~ 0.052