v4.1: Threeneutrino fit based on data available in July 2019
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 Summary of data included
 Parameter ranges
 Leptonic mixing matrix
 Twodimensional allowed regions
 Onedimensional χ^{2} projections
 CPviolation: Jarlskog invariant
 CPviolation: unitarity triangle
 Synergies: atmospheric masssquared splitting
 Synergies: disappearance data and θ_{23}
 Synergies: determination of θ_{23}
 Synergies: determination of δ_{CP}
 Synergies: determination of Δm^{2}_{3ℓ}
 Synergies: DeepCore data and Δm^{2}_{3ℓ}
 Correlation between δ_{CP} and other parameters
 Neutrino mass scale observables
 Available data files
If you are using these results please refer to JHEP 01 (2019) 106 [arXiv:1811.05487] as well as NuFIT 4.1 (2019), www.nufit.org.

Threeflavor oscillation parameters from our fit to global data as of November 2018. The results shown in the upper (lower) section are obtained without (with) the inclusion of the tabulated χ^{2} data on atmospheric neutrinos provided by the SuperKamiokande collaboration (SKatm). The numbers in the 1st (2nd) column are obtained assuming NO (IO), i.e., relative to the respective local minimum. Minimization with respect to the ordering provides the same results as Normal Ordering, except for the 3σ range of Δm^{2}_{3ℓ} in the analysis without SKatm. Note that Δm^{2}_{3ℓ} = Δm^{2}_{31} > 0 for NO and Δm^{2}_{3ℓ} = Δm^{2}_{32} < 0 for IO. 

3σ CL ranges of the magnitude of the elements of the threeflavor leptonic mixing matrix under the assumption that the matrix U is unitary. The ranges in the different entries of the matrix are correlated due to the fact that, in general, the result of a given experiment restricts a combination of several entries of the matrix, as well as to the constraints imposed by unitarity. As a consequence choosing a specific value for one element further restricts the range of the others. The upper (lower) limits are obtained without (with) the inclusion of the tabulated SKatm χ^{2} data. 
Twodimensional allowed regions
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Global 3ν oscillation analysis. Each panel shows the twodimensional projection of the allowed sixdimensional region after marginalization with respect to the undisplayed parameters. Colored regions (black contour curves) are obtained without (with) the inclusion of the tabulated SKatm χ^{2} data. The different contours correspond to the twodimensional allowed regions at 1σ, 90%, 2σ, 99%, 3σ CL (2 dof). Note that as atmospheric masssquared splitting we use Δm^{2}_{31} for NO and Δm^{2}_{32} for IO. The regions in the lower 4 panels are based on a Δχ^{2} minimized with respect to the mass ordering. 
Onedimensional χ^{2} projections
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Global 3ν oscillation analysis. The red (blue) curves are for Normal (Inverted) Ordering. The solid (dashed) lines are obtained without (with) the inclusion of SKatm χ^{2} data. As atmospheric masssquared splitting we use Δm^{2}_{31} for NO and Δm^{2}_{32} for IO. 
CPviolation: Jarlskog invariant
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Dependence of Δχ^{2} on the Jarlskog invariant (right) and its δ_{CP}independent modulus (left). The red (blue) curves are for Normal (Inverted) Ordering. The solid (dashed) lines are obtained without (with) the inclusion of the tabulated SKatm χ^{2} data. 
CPviolation: unitarity triangle
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Leptonic unitarity triangle for the first and third columns of the mixing matrix. After scaling and rotating each triangle so that two of its vertices always coincide with (0,0) and (1,0), we plot the 1σ, 90%, 2σ, 99%, 3σ CL (2 dof) allowed regions of the third vertex. Colored regions (black contour curves) are obtained without (with) the inclusion of the tabulated SKatm χ^{2} data. The contours for Normal (right) and Inverted (left) ordering are defined with respect to the common global minimum. Note that in the construction of the triangles the unitarity of the U matrix is always explicitly imposed. 
Synergies: atmospheric masssquared splitting
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Determination of Δm^{2}_{3ℓ} at the 2σ confidence level (2 dof), where ℓ = 1 for NO (upper panels) and ℓ = 2 for IO (lower panels). The left panels show regions in the (sin^{2}θ_{23}, Δm^{2}_{3ℓ}) plane using both appearance and disappearance data from MINOS (green), NOνA (darkredwood) and T2K (red), as well as atmospheric data from DeepCore (orange) and SuperKamiokande (lightbrown), and a combination of all of the above (darkgrey region). Here a prior on θ_{13} is included to account for reactor bounds. The right panels show regions in the (sin^{2}θ_{13}, Δm^{2}_{3ℓ}) plane using data from DayaBay (pink), DoubleChooz (magenta), RENO (violet), and their combination (black regions). In all panels solar and KamLAND data are included to constrain Δm^{2}_{21} and θ_{12}. Contours are defined with respect to the global minimum of the two orderings. 
Synergies: disappearance data and θ_{23}
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Bounds on θ_{23} (upper panels) and 2σ allowed regions in the (sin^{2}θ_{23}, Δm^{2}_{31}) plane (lower panels) from the analysis of MINOS (green), NOνA (darkredwood) and T2K (red) disappearance data assuming Normal Ordering. The dotted (dashed) lines correspond to neutrino (antineutrino) data. In the left panels a prior on θ_{13} has been imposed to account for reactor bounds, while in the right panels LBL and reactor data are consistently combined together. In all panels solar and KamLAND data are included to constrain Δm^{2}_{21} and θ_{12}. 
Synergies: determination of θ_{23}
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Bounds on θ_{23} from MINOS (green), NOνA (darkredwood), T2K (red) and their combination (blue). Left (right) panels are for IO (NO); for each experiment Δχ^{2} is defined with respect to the global minimum of the two orderings. The upper panels show the 1dimensional Δχ^{2} from LBL accelerator experiments after imposing a prior on θ_{13} to account for reactor bounds. The lower panels show the corresponding determination when the full information of LBL and reactor experiments is used in the combination. In all panels solar and KamLAND data are included to constrain Δm^{2}_{21} and θ_{12}. 
Synergies: determination of δ_{CP}
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Bounds on δ_{CP} from MINOS (green), NOνA (darkredwood), T2K (red) and their combination (blue). Left (right) panels are for IO (NO); for each experiment Δχ^{2} is defined with respect to the global minimum of the two orderings. For NOνA we also show as dotted (dashed) lines the results obtained using only neutrino (antineutrino) data. The upper panels show the 1dimensional Δχ^{2} from LBL accelerator experiments after imposing a prior on θ_{13} to account for reactor bounds. The lower panels show the corresponding determination when the full information of LBL and reactor experiments is used in the combination. In all panels solar and KamLAND data are included to constrain Δm^{2}_{21} and θ_{12}. 
Synergies: determination of Δm^{2}_{3ℓ}
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Bounds on Δm^{2}_{3ℓ} from reactor experiments (black) as well as MINOS (green), NOνA (darkredwood), T2K (red) and all LBL data (blue). Left (right) panels are for IO (NO); for each experiment Δχ^{2} is defined with respect to the global minimum of the two orderings. The upper panels show the 1dimensional Δχ^{2} from LBL accelerator experiments after imposing a prior on θ_{13} to account for reactor bounds. The lower panels show the corresponding determination when the full information of LBL and reactor experiments is used in the combination. In all panels solar and KamLAND data are included to constrain Δm^{2}_{21} and θ_{12}. 
Synergies: DeepCore data and Δm^{2}_{3ℓ}
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Bounds on Δm^{2}_{3ℓ} from DeepCore data (orange), reactor and LBL data (black), and their combinations (red & blue). Solid lines are based on our own impementation of the 2016 DeepCore data release (DC16), whereas dotdashed lines correspond to the new analysis presented in 2017 and released in the form of a χ^{2} table (DC17). As atmospheric masssquared splitting we use Δm^{2}_{31} for NO and Δm^{2}_{32} for IO. In all panels solar and KamLAND data are included to constrain Δm^{2}_{21} and θ_{12}. 
Correlation between δ_{CP} and other parameters
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Allowed regions from the global analysis after minimizing with respect to all undisplayed parameters. The upper (lower) panel corresponds to IO (NO). Colored regions (black contour curves) are obtained without (with) the inclusion of the tabulated SKatm χ^{2} data. The different contours correspond to the twodimensional allowed regions at 1σ, 90%, 2σ, 99%, 3σ CL (2 dof). Note that as atmospheric masssquared splitting we use Δm^{2}_{31} for NO and Δm^{2}_{32} for IO. 
Neutrino mass scale observables
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Allowed regions at 2σ (2 dof) obtained by projecting the results of the global analysis of oscillation data (w/o SKatm) over the planes (Σm_{ν}, m_{νe}) and (Σm_{ν}, m_{ee}). The region for each ordering is defined with respect to its local minimum. 
We provide one and twodimensional Δχ^{2} projections for both the analysis without (Normal and Inverted Ordering) and including (Normal and Inverted Ordering) SuperKamiokande atmospheric data. A description of the content of these files and a summary of the data included in our analysis can be found here. 
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