The standard three-neutrino ($3$\nu${}$) oscillation framework is being increasingly refined by results coming from different sets of experiments, using neutrinos from solar, atmospheric, accelerator and reactor sources. At present, each of the known oscillation parameters [the two squared mass gaps $($\delta${}{m}^{2},\mathrm{$\Delta${}}{m}^{2})$ and the three mixing angles $({$\theta${}}_{12},{$\theta${}}_{13},{$\theta${}}_{23})$] is dominantly determined by a single class of experiments. Conversely, the unknown parameters (the mass hierarchy, the ${$\theta${}}_{23}$ octant and the CP-violating phase $$\delta${}$) can currently be constrained only through a combined analysis of various (eventually all) classes of experiments. In the light of recent new results coming from reactor and accelerator experiments, and of their interplay with solar and atmospheric data, we update the estimated $N$\sigma${}$ ranges of the known $3$\nu${}$ parameters and revisit the status of the unknown ones. Concerning the hierarchy, no significant difference emerges between normal and inverted mass ordering. A slight overall preference is found for ${$\theta${}}_{23}$ in the first octant and for nonzero CP violation with $\mathrm{sin}$\delta${}<0$; however, for both parameters, such preference exceeds $1$\sigma${}$ only for normal hierarchy. We also discuss the correlations and stability of the oscillation parameters within different combinations of data sets.

Within the standard three-neutrino framework, the absolute neutrino masses and their ordering (either normal, NO, or inverted, IO) are currently unknown. However, the combination of current data coming from oscillation experiments, neutrinoless double beta ($0\nu \beta \beta$) decay searches, and cosmological surveys, can provide interesting constraints for such unknowns in the sub-eV mass range, down to $O({10}^{-1})\mathrm{eV}$ in some cases. We discuss current limits on absolute neutrino mass observables by performing a global data analysis that includes the latest results from oscillation experiments, $0\nu \beta \beta$ decay bounds from the KamLAND-Zen experiment, and constraints from representative combinations of Planck measurements and other cosmological data sets. In general, NO appears to be somewhat favored with respect to IO at the level of $\sim 2\sigma$, mainly by neutrino oscillation data (especially atmospheric), corroborated by cosmological data in some cases. Detailed constraints are obtained via the ${\chi }^2$ method, by expanding the parameter space either around separate minima in NO and IO or around the absolute minimum in any ordering. Implications for upcoming oscillation and nonoscillation neutrino experiments, including $\beta$-decay searches, are also discussed.

Within the standard 3ν mass–mixing framework, we present an up-to-date global analysis of neutrino oscillation data (as of January 2016), including the latest available results from experiments with atmospheric neutrinos (Super-Kamiokande and IceCube DeepCore), at accelerators (first T2K ν‾ and NOνA ν runs in both appearance and disappearance modes), and at short-baseline reactors (Daya Bay and RENO far/near spectral ratios), as well as a reanalysis of older KamLAND data in the light of the “bump” feature recently observed in reactor spectra. We discuss improved constraints on the five known oscillation parameters (δm2, |Δm2|, sin2⁡θ12, sin2⁡θ13, sin2⁡θ23), and the status of the three remaining unknown parameters: the mass hierarchy [sign(±Δm2)], the θ23 octant [sign(sin2⁡θ23−1/2)], and the possible CP-violating phase δ. With respect to previous global fits, we find that the reanalysis of KamLAND data induces a slight decrease of both δm2 and sin2⁡θ12, while the latest accelerator and atmospheric data induce a slight increase of |Δm2|. Concerning the unknown parameters, we confirm the previous intriguing preference for negative values of sin⁡δ (with best-fit values around sin⁡δ≃−0.9), but we find no statistically significant indication about the θ23 octant or the mass hierarchy (normal or inverted). Assuming an alternative (so-called LEM) analysis of NOνA data, some δ ranges can be excluded at >3σ, and the normal mass hierarchy appears to be slightly favored at ∼90% C.L. We also describe in detail the covariances of selected pairs of oscillation parameters. Finally, we briefly discuss the implications of the above results on the three non-oscillation observables sensitive to the (unknown) absolute ν mass scale: the sum of ν masses Σ (in cosmology), the effective νe mass mβ (in beta decay), and the effective Majorana mass mββ (in neutrinoless double beta decay)

In the current $3\nu$ paradigm, neutrino flavor oscillations probe three mixing angles $({\theta }_{12},{\theta }_{23},{\theta }_{13})$, one $CP$-violating phase $\delta$, and two independent differences between the squared masses $m_i^2$, that can be chosen as $\delta m^2=m_2^2-m_1^2>0$ and $\mathrm{\Delta }{m}^2=m_3^2-(m_1^2+m_2^2)/2$, where $\mathrm{sign}(\mathrm{\Delta }{m}^2)=+(-)$ for normal (inverted) mass ordering. Absolute $\nu$ masses can be probed by the effective mass $m_{\beta }$ in beta decay, by the total mass $\mathrm{\Sigma }$ in cosmology and—if neutrinos are Majorana—by another effective mass $m_{\beta \beta }$ in neutrinoless double beta decay. Within an updated global analysis of oscillation and nonoscillation data, we constrain these $3\nu$ parameters, both separately and in selected pairs, and highlight the concordance or discordance among different constraints. Five oscillation parameters $(\delta m^2,|\mathrm{\Delta }{m}^2|,{\theta }_{12},{\theta }_{23},{\theta }_{13})$ are consistently measured, with an overall accuracy ranging from $\sim 1\%$ for $|\mathrm{\Delta }{m}^2|$ to $\sim 6\%$ for ${\sin }^2{\theta }_{23}$ (due to its persisting octant ambiguity). We find overall hints for normal ordering (at $\sim 2.5\sigma$), as well as for ${\theta }_{23}<\pi /4$ and for $\sin \delta <0$ (both at 90% C.L.), and discuss some tensions among different datasets. Concerning nonoscillation data, we include the recent KATRIN constraints on $m_{\beta }$, and we combine the latest ${}^{76}\mathrm{Ge}$, ${}^{130}\mathrm{Te}$ and ${}^{136}\mathrm{Xe}$ bounds on $m_{\beta \beta }$, 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 $\mathrm{\Sigma }$ and hints on $\mathrm{sign}(\mathrm{\Delta }{m}^2)$. The default option, including all Planck results, irrespective of the so-called lensing anomaly, sets upper bounds on $\mathrm{\Sigma }$ at the level of $\sim {10}^{-1}\mathrm{eV}$, and further favors normal ordering up to $\sim 3\sigma$. 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 $\mathrm{\Sigma }\sim \mathrm{few}\times {10}^{-1}\mathrm{eV}$, with different implications for $m_{\beta }$ and $m_{\beta \beta }$ searches. In general, the unfinished fabric of the $3\nu$ 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.

The brightness of the tip of the red-giant branch (TRGB) allows one to constrain novel energy losses that would lead to a larger core mass at helium ignition and, thus, to a brighter TRGB than expected by standard stellar models. The required absolute TRGB calibrations strongly improve with reliable geometric distances that have become available for the galaxy NGC 4258 that hosts a water megamaser and to the Large Magellanic Cloud based on 20 detached eclipsing binaries. Moreover, we revise a previous TRGB calibration in the globular cluster $\omega$ Centauri with a recent kinematical distance determination based on Gaia data release 2. All of these calibrations have similar uncertainties, and they agree with each other and with recent dedicated stellar models. Using NGC 4258 as the cleanest extragalactic case, we thus find an updated constraint on the axion-electron coupling of $g_{ae}<1.6\times {10}^{-13}$ and ${\mu }_{\nu }<1.5\times {10}^{-12}{\mu }_{\mathrm{B}}$ (95% C.L.) on a possible neutrino dipole moment, whereas $\omega$ Centauri as the best galactic target provides instead $g_{ae}<1.3\times {10}^{-13}$ and ${\mu }_{\nu }<1.2\times {10}^{-12}{\mu }_{\mathrm{B}}$. The reduced observational errors imply that stellar evolution theory and bolometric corrections begin to dominate the overall uncertainties.