We present an updated global fit of neutrino oscillation data in the simplest three-neutrino framework. In the present study we include up-to-date analyses from a number of experiments. Concerning the atmospheric and solar sectors, besides the data considered previously, we give updated analyses of IceCube DeepCore and Sudbury Neutrino Observatory data, respectively. We have also included the latest electron antineutrino data collected by the Daya Bay and RENO reactor experiments, and the long-baseline T2K and NOνA measurements, as reported in the Neutrino 2020 conference. All in all, these new analyses result in more accurate measurements of θ₁₃, θ₁₂, $$ \Delta {m}_{21}^2 $$Δ m 21 2 and $$ \left|\Delta {m}_{31}^2\right| $$Δ m 31 2 . The best fit value for the atmospheric angle θ₂₃ lies in the second octant, but first octant solutions remain allowed at ∼ 2.4σ. Regarding CP violation measurements, the preferred value of δ we obtain is 1.08π (1.58π) for normal (inverted) neutrino mass ordering. The global analysis still prefers normal neutrino mass ordering with 2.5σ statistical significance. This preference is milder than the one found in previous global analyses. These new results should be regarded as robust due to the agreement found between our Bayesian and frequentist approaches. Taking into account only oscillation data, there is a weak/moderate preference for the normal neutrino mass ordering of 2.00σ. While adding neutrinoless double beta decay from the latest Gerda, CUORE and KamLAND-Zen results barely modifies this picture, cosmological measurements raise the preference to 2.68σ within a conservative approach. A more aggressive data set combination of cosmological observations leads to a similar preference for normal with respect to inverted mass ordering, namely 2.70σ. This very same cosmological data set provides 2σ upper limits on the total neutrino mass corresponding to Σm_ν< 0.12 (0.15) eV in the normal (inverted) neutrino mass ordering scenario. The bounds on the neutrino mixing parameters and masses presented in this up-to-date global fit analysis include all currently available neutrino physics inputs.

We present the results of an updated fit of short-baseline neutrino oscillation data in the framework of 3+1 active-sterile neutrino mixing. We first consider ν _e and \( {\overline{\nu}}_e \) disappearance in the light of the Gallium and reactor anomalies. We discuss the implications of the recent measurement of the reactor \( {\overline{\nu}}_e \) spectrum in the NEOS experiment, which shifts the allowed regions of the parameter space towards smaller values of |U _e4|². The β-decay constraints of the Mainz and Troitsk experiments allow us to limit the oscillation length between about 2 cm and 7 m at 3σ for neutrinos with an energy of 1 MeV. The corresponding oscillations can be discovered in a model-independent way in ongoing reactor and source experiments by measuring ν _e and \( {\overline{\nu}}_e \) disappearance as a function of distance. We then consider the global fit of the data on short-baseline \( {}_{\nu_{\mu}}^{\left(-\right)}{\to}_{\nu_e}^{\left(-\right)} \) transitions in the light of the LSND anomaly, taking into account the constraints from \( {}_{\nu_e}^{\left(-\right)} \) and \( {}_{\nu_{\mu}}^{\left(-\right)} \) disappearance experiments, including the recent data of the MINOS and IceCube experiments. The combination of the NEOS constraints on |U _e4|² and the MINOS and IceCube constraints on |U _μ4|² lead to an unacceptable appearance-disappearance tension which becomes tolerable only in a pragmatic fit which neglects the MiniBooNE low-energy anomaly. The minimization of the global χ ² in the space of the four mixing parameters Δm ₄₁ ² , |U _e4|², |U _μ4|², and |U _τ4|² leads to three allowed regions with narrow Δm ₄₁ ² widths at Δm ₄₁ ² ≈ 1.7 (best-fit), 1.3 (at 2σ), 2.4 (at 3σ) eV². The effective amplitude of short-baseline \( {}_{\nu_{\mu}}^{\left(-\right)}{\to}_{\nu_e}^{\left(-\right)} \) oscillations is limited by 0.00048 ≲ sin² 2ϑ _eμ ≲ 0.0020 at 3σ. The restrictions of the allowed regions of the mixing parameters with respect to our previous global fits are mainly due to the NEOS constraints. We present a comparison of the allowed regions of the mixing parameters with the sensitivities of ongoing experiments, which show that it is likely that these experiments will determine in a definitive way if the reactor, Gallium and LSND anomalies are due to active-sterile neutrino oscillations or not.

The ordering of the neutrino masses is a crucial input for a deep understanding of flavor physics, and its determination may provide the key to establish the relationship among the lepton masses and mixings and their analogous properties in the quark sector. The extraction of the neutrino mass ordering is a data-driven field expected to evolve very rapidly in the next decade. In this review, we both analyse the present status and describe the physics of subsequent prospects. Firstly, the different current available tools to measure the neutrino mass ordering are described. Namely, reactor, long-baseline (accelerator and atmospheric) neutrino beams, laboratory searches for beta and neutrinoless double beta decays and observations of the cosmic background radiation and the large scale structure of the universe are carefully reviewed. Secondly, the results from an up-to-date comprehensive global fit are reported: the Bayesian analysis to the 2018 publicly available oscillation and cosmological data sets provides strong evidence for the normal neutrino mass ordering vs. the inverted scenario, with a significance of 3.5 standard deviations. This preference for the normal neutrino mass ordering is mostly due to neutrino oscillation measurements. Finally, we shall also emphasize the future perspectives for unveiling the neutrinomass ordering. In this regard, apart from describing the expectations from the aforementioned probes, we also focus on those arising from alternative and novel methods, as 21 cm cosmology, core-collapse supernova neutrinos and the direct detection of relic neutrinos.