The unfinished fabric of the three neutrino paradigm

Abstract: In the current 3nu paradigm, flavor oscillations probe 3 mixing angles (theta_12, theta_23, theta_13), one CP phase delta, and two squared mass differences delta m^2>0 and Delta m^2, where sign(Delta m^2)=+ (-) for normal (inverted) ordering. Absolute nu masses can be probed by the effective m_beta in beta decay, by the total mass Sigma in cosmology and, if neutrinos are Majorana, by another effective m_{beta beta} in 0nu2beta decay. Within an updated global analysis of (non)oscillation data, we constrain these 3nu parameters, both separately and in selected pairs, and highlight the concordance or discordance among different constraints. Five oscillation parameters (delta m^2, Delta m^2, theta_12, theta_23, theta_13) are consistently measured, with an overall accuracy ranging from ~1% for Delta m^2 to ~6% for sin^2(theta_23) (due to its octant ambiguity). We find overall hints for normal ordering (at 2.5 sigma), as well as for theta_23<pi/4 and for sin(delta)<0 (both at 90% C.L.), and discuss some tensions among datasets. Concerning nonoscillation data, we include the recent KATRIN constraints on m_beta, and we combine the latest 76-Ge, 130-Te and 136-Xe bounds on m_{beta beta}, accounting for NME covariances. We also discuss some variants related to CMB anisotropy and lensing data, which may affect cosmological constraints on Sigma and hints on sign(Delta m^2). The default option, including all Planck results, irrespective of the lensing anomaly, sets upper bounds on Sigma at the level of ~10^-1 eV, and further favors normal ordering up to ~3 sigma. An alternative option, that includes recent ACT results + other independent results (from WMAP and selected Planck data) globally consistent with standard lensing, is insensitive to the ordering but prefers Sigma ~(few) x 10^-1 eV, with different implications for m_beta and m_{beta beta} searches. (Abridged)