We perform a global analysis of neutrino oscillation data, including high-precision measurements of the neutrino mixing angle $\theta${}13 at reactor experiments, which have confirmed previous indications in favor of $\theta${}13>0. Recent data presented at the Neutrino 2012 conference are also included. We focus on the correlations between $\theta${}13 and the mixing angle $\theta${}23, as well as between $\theta${}13 and the neutrino CP-violation phase $\delta${}. We find interesting indications for $\theta${}23<$\pi${}/4 and possible hints for $\delta${}$\sim${}$\pi${}, with no significant difference between normal and inverted mass hierarchy.

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.

We present a thorough analysis of the current solar neutrino data, in the context of two-flavor active neutrino oscillations. We aim at performing an accurate and exhaustive statistical treatment of both the input and the output information. Concerning the input information, we analyze 81 observables, including the total event rate from the chlorine experiment, the total gallium event rate and its winter-summer difference, the 44 bins of the Super-Kamiokande (SK) energy-nadir electron spectrum, and the 34 day-night energy spectrum bins from the Sudbury Neutrino Observatory (SNO) experiment. We carefully evaluate and propagate the effects of 31 sources of correlated systematic uncertainties, including 12 standard solar model (SSM) input errors, the ${}^8\mathrm{B}$ neutrino energy spectrum uncertainty, as well as 11 and 7 systematics in SK and SNO, respectively. Concerning the output information, we express the ${\chi }^2$ analysis results in terms of “pulls,” embedding the single contributions to the total ${\chi }^2$ coming from both the observables and the systematics. It is shown that the pull method, as compared to the (numerically equivalent) covariance matrix approach, is not only simpler and more advantageous, but also includes useful indications about the preferred variations of the neutrino fluxes with respect to their SSM predictions. Our final results confirm the current best-fit solution at large mixing angle (LMA), but also allow, with acceptable statistical significance, other solutions in the low-mass (LOW) or in the quasivacuum oscillation (QVO) regime. Concerning the LMA solution, our analysis provides conservative bounds on the oscillation parameters, and shows that the contribution of correlated systematics to the total ${\chi }^2$ is rather modest. In addition, within the LMA solution, the allowed variations from SSM neutrino fluxes are presented in detail. Concerning the LOW and QVO solutions, the analysis of the pull distributions clearly shows that they are still statistically acceptable, while the small mixing angle (SMA) solution could be recovered only by ad hoc “recalibrations” of several SSM and experimental systematics. A series of Appendixes elucidate various topics related to the ${\chi }^2$ statistics, the winter-summer difference in GALLEX-GNO, the treatment of the SK and SNO spectra, and a quasi-model-independent comparison of the SK and SNO total rates.

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)