We review the present status of global analyses of neutrino oscillations, taking into account the most recent neutrino data including the latest KamLAND and K2K updates presented at Neutrino2004, as well as state-of-the-art solar and atmospheric neutrino flux calculations. We give the two-neutrino solar + KamLAND results, and the two-neutrino atmospheric + K2K oscillation regions, discussing in each case the robustness of the oscillation interpretation against departures from the Standard Solar Model and the possible existence of non-standard neutrino physics. Furthermore, we give the best fit values and allowed ranges of the three-flavour oscillation parameters from the current worlds' global neutrino data sample and discuss in detail the status of the small parameters α ≡ ∆m 2 sol /∆m 2 atm as well as sin 2 θ 13 , which characterize the strength of CP violating effects in neutrino oscillations. We also update the degree of rejection of four-neutrino interpretations of the LSND evidence in view of the most recent developments.PACS numbers: 26.65.+t, 13.15.+g, 14.60.Pq, 95.55.Vj

We present the results of a global analysis of the neutrino oscillation data available as of fall 2018 in the framework of three massive mixed neutrinos with the goal at determining the ranges of allowed values for the six relevant parameters. We describe the complementarity and quantify the tensions among the results of the different data samples contributing to the determination of each parameter. We also show how those vary when combining our global likelihood with the χ 2 map provided by Super-Kamiokande for their atmospheric neutrino data analysis in the same framework. The best fit of the analysis is for the normal mass ordering with inverted ordering being disfavoured with a ∆χ 2 = 4.7 (9.3) without (with) SK-atm. We find a preference for the second octant of θ 23 , disfavouring the first octant with ∆χ 2 = 4.4 (6.0) without (with) SK-atm. The best fit for the complex phase is δ CP = 215 • with CP conservation being allowed at ∆χ 2 = 1.5 (1.8). As a byproduct we quantify the correlated ranges for the laboratory observables sensitive to the absolute neutrino mass scale in beta decay, m νe , and neutrino-less double beta decay, m ee , and the total mass of the neutrinos, Σ, which is most relevant in Cosmology.

Our herein described combined analysis of the latest neutrino oscillation data presented at the Neutrino2020 conference shows that previous hints for the neutrino mass ordering have significantly decreased, and normal ordering (NO) is favored only at the 1.6σ level. Combined with the χ2 map provided by Super-Kamiokande for their atmospheric neutrino data analysis the hint for NO is at 2.7σ. The CP conserving value δCP = 180° is within 0.6σ of the global best fit point. Only if we restrict to inverted mass ordering, CP violation is favored at the ∼ 3σ level. We discuss the origin of these results — which are driven by the new data from the T2K and NOvA long-baseline experiments —, and the relevance of the LBL-reactor oscillation frequency complementarity. The previous 2.2σ tension in ∆m221 preferred by KamLAND and solar experiments is also reduced to the 1.1σ level after the inclusion of the latest Super-Kamiokande solar neutrino results. Finally we present updated allowed ranges for the oscillation parameters and for the leptonic Jarlskog determinant from the global analysis.

We perform a combined fit to global neutrino oscillation data available as of fall 2016 in the scenario of three-neutrino oscillations and present updated allowed ranges of the six oscillation parameters. We discuss the differences arising between the consistent combination of the data samples from accelerator and reactor experiments compared to partial combinations. We quantify the confidence in the determination of the less precisely known parameters θ 23 , δ CP , and the neutrino mass ordering by performing a Monte Carlo study of the long baseline accelerator and reactor data. We find that the sensitivity to the mass ordering and the θ 23 octant is below 1σ. Maximal θ 23 mixing is allowed at slightly more than 90% CL. The best fit for the CP violating phase is around 270 • , CP conservation is allowed at slightly above 1σ, and values of δ CP 90 • are disfavored at around 99% CL for normal ordering and higher CL for inverted ordering.

We present a global analysis of solar, atmospheric, reactor and accelerator neutrino data in the framework of three-neutrino oscillations based on data available in summer 2014. We provide the allowed ranges of the six oscillation parameters and show that their determination is stable with respect to uncertainties related to reactor neutrino and solar neutrino flux predictions. We find that the maximal possible value of the Jarlskog invariant in the lepton sector is $0.0329 \pm 0.0009$ ($\pm 0.0027$) at the $1\sigma$ ($3\sigma$) level and we use leptonic unitarity triangles to illustrate the ability of global oscillation data to obtain information on CP violation. We discuss "tendencies and tensions" of the global fit related to the octant of $\theta_{23}$ as well as the CP violating phase $\delta_\mathrm{CP}$. The favored values of $\delta_\mathrm{CP}$ are around $3\pi/2$ while values around $\pi/2$ are disfavored at about $\Delta\chi^2 \simeq 6$. We comment on the non-trivial task to assign a confidence level to this $\Delta\chi^2$ value by performing a Monte Carlo study of T2K data.Comment: 28 pages, 10 figures, 1 table. Typos corrected. Updated results of the global fit will be available at http://www.nu-fit.org