Unfinished fabric of the three neutrino paradigm

In the current 3 ν paradigm, neutrino flavor oscillations probe three mixing angles (θ12, θ23, θ13), one C P-violating phase δ, and two independent differences between the squared masses ..., that can be chosen as ... and ..., where sign (Δm2) = +(−) for normal (inverted) mass ordering. Absolute ν masses can be probed by the effective mass m β in beta decay, by the total mass Σ in cosmology and-if neutrinos are Majorana-by another effective mass m β β in neutrinoless double beta decay. Within an updated global analysis of oscillation and nonoscillation data, we constrain these 3 ν parameters, both separately and in selected pairs, and highlight the concordance or discordance among different constraints. Five oscillation parameters (δm2, |Δm2|, θ12, θ23, θ13) are consistently measured, with an overall accuracy ranging from ~ 1 % for |Δm2| to ~ 6 % for sin 2θ23 (due to its persisting octant ambiguity). We find overall hints for normal ordering (at ~ 2.5σ), as well as for θ23 < π / 4 and for sin δ < 0 (both at 90% C.L.), and discuss some tensions among different datasets. Concerning nonoscillation data, we include the recent KATRIN constraints on m β, and we combine the latest 76Ge , 130Te and 136Xe bounds on mββ, accounting for nuclear matrix element covariances. We also discuss some variants related to cosmic microwave background (CMB) anisotropy and lensing data, which may affect cosmological constraints on Σ and hints on sign (Δm2). The default option, including all Planck results, irrespective of the so-called lensing anomaly, sets upper bounds on Σ at the level of ~ 10−1 eV , and further favors normal ordering up to ~ 3σ. An alternative option, that includes recent ACT results plus other independent results (from WMAP and selected Planck data) globally consistent with standard lensing, is insensitive to the ordering but prefers Σ ~ few × 10−1 eV, with different implications for mβ and mββ searches. In general, the unfinished fabric of the 3ν paradigm appears to be at the junction of diverse searches in particle and nuclear physics, astrophysics and cosmology, whose convergence will be crucial to achieve a convincing completion.