At the previous Venice meeting NO-VE 2008, we discussed possible hints in favor of a nonzero value for the unknown neutrino mixing angle theta(13), emerging from the combination of solar and long-baseline reactor data, as well as from the combination
of atmospheric, CHOOZ and long-baseline accelerator nu_mu->nu_mu data. Recent MINOS 2009 results in the nu_mu->nu_e appearance channel also seem to support such hints. A combination of all current oscillation data provides, as preferred range, sin^2 theta(13) = 0.02 +- 0.01 (1sigma). We review several issues raised by such hints in the last year, and comment on their possible near-future improvements and tests.
The variances and covariances associated to the nuclear matrix elements (NME) of neutrinoless double beta decay are estimated within the quasiparticle random phase approximation (QRPA). It is shown that correlated NME uncertainties play an important
role in the comparison of neutrinoless double beta decay rates for different nuclei, and that they are degenerate with the uncertainty in the reconstructed Majorana neutrino mass.
In core-collapse supernovae, neutrinos and antineutrinos are initially subject to significant self-interactions induced by weak neutral currents, which may induce strong-coupling effects on the flavor evolution (collective transitions). The interpret
ation of the effects is simplified when self-induced collective transitions are decoupled from ordinary matter oscillations, as for the matter density profile that we discuss. In this case, approximate analytical tools can be used (pendulum analogy, swap of energy spectra). For inverted neutrino mass hierarchy, the sequence of effects involves: synchronization, bipolar oscillations, and spectral split. Our simulations shows that the main features of these regimes are not altered when passing from simplified (angle-averaged) treatments to full, multi-angle numerical experiments.
We present updated values for the mass-mixing parameters relevant to neutrino oscillations, with particular attention to emerging hints in favor of theta_13>0. We also discuss the status of absolute neutrino mass observables, and a possible approach
to constrain theoretical uncertainties in neutrinoless double beta decay. Desiderata for all these issues are also briefly mentioned.
