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

Abstract

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 $({m}_{\ensuremath{\beta}})$; the effective Majorana neutrino mass in neutrinoless double beta decay $({m}_{\ensuremath{\beta}\ensuremath{\beta}})$; and the sum of neutrino masses in cosmology $(\ensuremath{\Sigma})$. 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 $2\ensuremath{\sigma}$) after adding MINOS to world data. We also find upper bounds on the sum of neutrino masses $\ensuremath{\Sigma}$ ranging from $\ensuremath{\sim}2\text{ }\text{ }\mathrm{eV}$ (WMAP-3y data only) to $\ensuremath{\sim}0.2\text{ }\text{ }\mathrm{eV}$ (all cosmological data) at $2\ensuremath{\sigma}$, in agreement with previous studies. In addition, we discuss the connection of such bounds with those placed on the matter power spectrum normalization parameter ${\ensuremath{\sigma}}_{8}$. We show how the partial degeneracy between $\ensuremath{\Sigma}$ and ${\ensuremath{\sigma}}_{8}$ in WMAP-3y data is broken by adding further cosmological data, and how the overall preference of such data for relatively high values of ${\ensuremath{\sigma}}_{8}$ pushes the upper bound of $\ensuremath{\Sigma}$ in the sub-eV range. Finally, for various combination of data sets, we revisit the (in)compatibility between current $\ensuremath{\Sigma}$ and ${m}_{\ensuremath{\beta}\ensuremath{\beta}}$ constraints (and claims), and derive quantitative predictions for future single and double beta decay experiments.