Neutrino mass variables in 3 active and 2 sterile neutrino scenario

The three-flavor framework of neutrino oscillations successfully explains most experimental results, but persistent anomalies at short- and long-baseline experiments hint at the existence of additional light sterile states. In particular, eV-scale sterile neutrinos are motivated by LSND and MiniBooNE results, while sub-eV sterile states with mass-squared differences at the $10^{-2}$ and $10^{-5}$~eV$^2$ scales have been proposed to address the T2K--NO$\nu$A tension and the absence of the expected upturn in the solar neutrino energy spectrum, respectively. Such sterile states are singlets under the Standard Model gauge group and mix only through their admixture with active neutrinos. In this work, we investigate the phenomenology of the $3+2$ scenario, incorporating one eV-scale sterile neutrino together with a sub-eV state, and analyze their impact on absolute-mass related observables: the sum of neutrino masses $\Sigma$ constrained by cosmology, the effective electron neutrino mass $m_\beta$ from beta decay, and the effective Majorana mass $m_{\beta\beta}$ probed in neutrinoless double beta decay. We demonstrate that the presence of two sterile states can significantly modify the allowed parameter space compared to the three-flavor and $3+1$ frameworks, with some mass-ordering schemes already disfavored by current cosmological and laboratory limits. Finally, we assess the implications of upcoming sensitivities from KATRIN, Project~8, and LEGEND-1000, highlighting the complementary role of sub-eV sterile neutrinos in probing physics beyond the minimal three-flavor paradigm.