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_2beta); 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_2beta 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 2 degrees Fields (2dF) Galaxy Redshifts Survey, with and without Lyman-alpha forest data from the Sloan Digital Sky Survey (SDSS), in models with a non-zero 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_2beta,Sigma) parameter space, which neatly show the relative impact of each data set. In particular, the (in)compatibility between Sigma and m_2beta constraints is highlighted for various combinations of data. We also briefly discuss how future neutrino data (both oscillatory and non-oscillatory) can further probe the currently allowed regions.
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