Observables sensitive to absolute neutrino masses: A reappraisal after WMAP-3y and first MINOS results

In the light of recent neutrino oscillation and non-oscillation data, we revisit the phenomenological constraints applicable to three observables sensitive to absolute neutrino masses: The effective neutrino mass in single beta decay (m_beta); the effective Majorana neutrino mass in neutrinoless double beta decay (m_2beta); and the sum of neutrino masses in cosmology (Sigma). In particular, we include the constraints coming from the first Main Injector Neutrino Oscillation Search (MINOS) data and from the Wilkinson Microwave Anisotropy Probe (WMAP) three-year (3y) data, as well as other relevant cosmological data and priors. We find that the largest neutrino squared mass difference is determined with a 15% accuracy (at 2-sigma) after adding MINOS to world data. We also find upper bounds on the sum of neutrino masses Sigma ranging from ~2 eV (WMAP-3y data only) to ~0.2 eV (all cosmological data) at 2-sigma, in agreement with previous studies. In addition, we discuss the connection of such bounds with those placed on the matter power spectrum normalization parameter sigma_8. We show how the partial degeneracy between Sigma and sigma_8 in WMAP-3y data is broken by adding further cosmological data, and how the overall preference of such data for relatively high values of sigma_8 pushes the upper bound of Sigma in the sub-eV range. Finally, for various combination of data sets, we revisit the (in)compatibility between current Sigma and m_2beta constraints (and claims), and derive quantitative predictions for future single and double beta decay experiments.