Observables sensitive to absolute neutrino masses: Constraints and correlations from world neutrino data

In the context of three-flavor neutrino mixing, we present a thorough study of the phenomenological constraints applicable to three observables sensitive to absolute neutrino masses: The effective neutrino mass in Tritium 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 $(\Sigma )$. We discuss the correlations among these variables which arise from the combination of all the available neutrino oscillation data, in both normal and inverse neutrino mass hierarchy. We set upper limits on $m_{\beta }$ by combining updated results from the Mainz and Troitsk experiments. We also consider the latest results on $m_{\beta \beta }$ from the Heidelberg-Moscow experiment, both with and without the lower bound claimed by such experiment. We derive upper limits on $\Sigma$ from an updated combination of data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite and the two degrees Fields (2dF) Galaxy Redshifts Survey, with and without Lyman-$\alpha$ forest data from the Sloan Digital Sky Survey (SDSS), in models with a nonzero running of the spectral index of primordial inflationary perturbations. The results are discussed in terms of two-dimensional projections of the globally allowed region in the $(m_{\beta },m_{\beta \beta },\Sigma )$ parameter space, which neatly show the relative impact of each data set. In particular, the (in)compatibility between $\Sigma$ and $m_{\beta \beta }$ constraints is highlighted for various combinations of data. We also briefly discuss how future neutrino data (both oscillatory and nonoscillatory) can further probe the currently allowed regions.