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

In the light of recent neutrino oscillation and nonoscillation 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 $(m_{\beta \beta })$; 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 $\sim 2\mathrm{eV}$ (WMAP-3y data only) to $\sim 0.2\mathrm{eV}$ (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 $m_{\beta \beta }$ constraints (and claims), and derive quantitative predictions for future single and double beta decay experiments.