On Non-Unitary Lepton Mixing and Neutrino Mass Observables
  There are three observables related to neutrino mass, namely the kinematic
mass in direct searches, the effective mass in neutrino-less double beta decay,
and the sum of neutrino masses in cosmology. In the limit of exactly degenerate
neutrinos there are very simple relations between those observables, and we
calculate corrections due to non-zero mass splitting. We discuss how the
possible non-unitarity of the lepton mixing matrix may modify these relations
and find in particular that corrections due to non-unitarity can exceed the
corrections due to mass splitting. We furthermore investigate constraints from
neutrino-less double beta decay on mass and mixing parameters of heavy
neutrinos in the type I see-saw mechanism. There are constraints from assuming
that heavy neutrinos are exchanged, and constraints from assuming light
neutrino exchange, which arise from an exact see-saw relation. The latter has
its origin in the unitarity violation arising in see-saw scenarios. We
illustrate that the limits from the latter approach are much stronger. The
drastic impact on inverse neutrino-less double beta decay (e e -> W W) is
studied. We furthermore discuss neutrino mixing in case there is one or more
light sterile neutrino. Neutrino oscillation probabilities for long baseline
neutrino oscillation experiments are considered, and the analogy to general
non-unitarity phenomenology, such as zero-distance effects, is pointed out.
