Joint neutrino oscillation analysis from the T2K and NOvA experiments

Abstract

The landmark discovery that neutrinos have mass and can change type (or flavour) as they propagate-a process called neutrino oscillation^1-6-has opened up a rich array of theoretical and experimental questions being actively pursued today. Neutrino oscillation remains the most powerful experimental tool for addressing many of these questions, including whether neutrinos violate charge-parity (CP) symmetry, which has possible connections to the unexplained preponderance of matter over antimatter in the Universe^7-11. Oscillation measurements also probe the mass-squared differences between the different neutrino mass states (Δm²), whether there are two light states and a heavier one (normal ordering) or vice versa (inverted ordering), and the structure of neutrino mass and flavour mixing¹². Here we carry out the first joint analysis of datasets from NOvA¹³ and T2K¹⁴, the two currently operating long-baseline neutrino oscillation experiments (hundreds of kilometres of neutrino travel distance), taking advantage of our complementary experimental designs and setting new constraints on several neutrino sector parameters. This analysis provides new precision on the $\Delta m_{32}^2$ mass difference, finding $2.43_{-0.03}^{+0.04}\times 10^{-3}{\mathrm{eV}}^2$ in the normal ordering and $-2.48_{-0.04}^{+0.03}\times 10^{-3}{\mathrm{eV}}^2$ in the inverted ordering, as well as a 3σ interval on δ_CP of [-1.38π, 0.30π] in the normal ordering and [-0.92π, -0.04π] in the inverted ordering. The data show no strong preference for either mass ordering, but notably, if inverted ordering were assumed true within the three-flavour mixing model, then our results would provide evidence of CP symmetry violation in the lepton sector.

Fig. 1. The impact of mass ordering and δ_CP on event rates.

a,b, A bi-event plot that shows experimental sensitivity to neutrino mass ordering and δ_CP, with panels representing the NOvA (a) and T2K (b) cases. Black points with 1σ Poisson statistical error bars show the total number of ν_e and ${\overline{\nu }}_{\mathrm{e}}$ candidates selected in the far detectors. The oval parametric curves trace out predicted numbers of events under the normal (blue) or inverted (orange) mass ordering assumption as the parameter δ_CP varies from −π to π. Four specific δ_CP values are labelled for reference. All other oscillation parameters are kept fixed in this graphic, set to their most probable values from the joint analysis (Extended Data Table 3).

Fig. 2. Experimental measurements of ∣Δm322∣.

The measurements assume the inverted ordering preferred by this analysis. Sources for the results from top to bottom, starting with the second line, are as follows: refs. ^,,–. The normal ordering case is available in Extended Data Fig. 9.

Fig. 3. Constraints on sin2θ23 and δ_CP.

Marginalized posterior probabilities and 1D or 2D Bayesian credible regions of ${\sin }^2{\theta }_{23}$ and δ_CP in the case of the normal (blue, left side) and inverted (orange, right side) neutrino mass ordering with the reactor constraint applied. Shaded areas correspond to 1σ, 2σ and 3σ credible regions. a,b, The 2D panels of ${\sin }^2{\theta }_{23}$ vs δ_CP (a,b) are overlaid with 1σ credible regions from the T2K-only (dark red) and NOvA-only (dark blue) data fits assuming normal (a) and inverted ordering (b). c–f, The 1D panels show the posterior probabilities of ${\sin }^2{\theta }_{23}$ (c) and δ_CP (d) in the normal ordering, and δ_CP (e) and ${\sin }^2{\theta }_{23}$ (f) in the inverted ordering.

Fig. 4. Constraints on the Jarlskog invariant.

a–d, Marginalized posterior probabilities of the Jarlskog invariant, J_CP, in the case of the normal (blue; a,b) and inverted (orange; c,d) neutrino mass ordering with the reactor constraint applied. The posterior distributions use prior distributions either flat in δ_CP (a,c) or sin δ_CP (b,d). Shaded areas show the 1σ, 2σ and 3σ Bayesian credible intervals.

Extended Data Fig. 1. Correlation study comparison plots.

Posterior probability distributions of δ_CP (a), ${\sin }^2{\theta }_{23}$ (b), and $\mathrm{\Delta }{m}_{32}^2$ (c) and 1σ credible regions in $\mathrm{\Delta }{m}_{32}^2-{\sin }^2{\theta }_{23}$ (d), marginalized over both neutrino mass ordering hypotheses (‘Both MO’) from fits to pseudo-data simulated with the NuFit-like oscillation parameter values. The fits were run in three configurations while treating the systematic uncertainties with the largest impact on ${\sin }^2{\theta }_{23}$ (visible neutron energy and 2p2h C/O scale) as either 100% correlated (gray), uncorrelated (teal), or 100% anticorrelated (magenta). Overlaid with the corresponding 1σ (dark shaded areas, dashed) and 2σ (light shaded areas, dash-dotted) credible intervals.

Extended Data Fig. 2. ‘Nightmare’ study comparisons.

1σ credible regions in $\mathrm{\Delta }{m}_{32}^2-{\sin }^2{\theta }_{23}$ posterior probability distributions marginalized over both neutrino mass ordering hypotheses (‘Both MO’) from fits to pseudo-data simulated with the NuFit-like oscillation parameter values and a fully symmetric systematic bias to affect (a) $\mathrm{\Delta }{m}_{32}^2$ (‘Δm² nightmare’) and (b) ${\sin }^2{\theta }_{23}$ (‘θ₂₃ nightmare’). The fits were run while treating the NOvA and T2K nightmare parameters as either 100% correlated (gray), uncorrelated (teal), or 100% anticorrelated (magenta).

Extended Data Fig. 3. Out-of-model study spectra and comparison plots in 1D.

NOvA+T2K out-of-model study with suppressed pion production at low Q² (‘MINERvA 1π’ case). The change on the FD pseudo-data and prediction with systematic uncertainties after incorporating the alternate data at the ND is shown for T2K (a) and NOvA (b). Central value of the nominal model is shown for comparison. 1D posterior probability distributions from a fit to pseudo-data generated at the NuFit-like oscillation parameter values are shown for $\mathrm{\Delta }{m}_{32}^2$ marginalized separately over the normal (c) and inverted (d) mass orderings, and for δ_CP (e), ${\sin }^{2}2{\theta }_{13}$ (f), and ${\sin }^2{\theta }_{23}$ (g) marginalized over both mass orderings. The in-model (blue shaded) and out-of-model (red curve) scenarios are displayed.

Extended Data Fig. 4. Out-of-model study comparison plots in 2D.

NOvA+T2K out-of-model study with suppressed pion production at low Q² (‘MINERvA 1π’ case). 68% and 90% contours are shown on the ${\sin }^2{\theta }_{23}$ − $\mathrm{\Delta }{m}_{32}^2$ surface marginalized separately over the normal (a) and inverted (b) mass orderings, and on the surfaces of ${\delta }_{\mathrm{CP}}-{\sin }^{2}2{\theta }_{13}$ (c) and ${\delta }_{\mathrm{CP}}-{\sin }^2{\theta }_{23}$ (d) parameters, marginalized over both mass orderings, from a fit to pseudo-data generated at the NuFit-like oscillation parameter values. The in-model (blue shaded) and out-of-model (red curve) scenarios are shown.

Extended Data Fig. 5. NOvA and T2K post-fit spectra.

NOvA (a, b) and T2K (c, d) posterior spectra compared to observed data for the largest ν_e-like (a, c) and ν_μ-like (b, d) event samples with the beam running enriched in ν_μ (as opposed to ${\overline{\mathrm{\nu }}}_{\mathrm{\mu }}$) extracted from a fit with reactor constraint, marginalized over both mass orderings. The NOvA ν_e-like sample (a) is divided into three subsets as shown here: events with a lower (I) or higher (II) event classification score and events lying near the periphery of the detector (III). Note that T2K also has a ν_e-like sample targeting events with single π not shown here.

Extended Data Fig. 6. Constraints on PMNS oscillation parameters in 1D and 2D for both orderings.

The 1D posterior probability distributions of ${\sin }^{2}2{\theta }_{13}$ (a), ${\sin }^2{\theta }_{23}$ (b), $\mid \mathrm{\Delta }{m}_{32}^2\mid$ (c), δ_CP (d), and corresponding 1σ, 2σ, 3σ 2D contours ${\sin }^2{\theta }_{23}-{\sin }^{2}2{\theta }_{13}$ (e), $\mathrm{\Delta }{m}_{32}^2-{\sin }^2{\theta }_{23}$ (f), ${\delta }_{\mathrm{CP}}-\mathrm{\Delta }{m}_{32}^2$ (g), $\mathrm{\Delta }{m}_{32}^2-{\sin }^{2}2{\theta }_{13}$ (h), ${\delta }_{\mathrm{CP}}-{\sin }^2{\theta }_{23}$ (i), and ${\delta }_{\mathrm{CP}}-{\sin }^{2}2{\theta }_{13}$ (j) from the joint fit with reactor constraints marginalized over both mass orderings.

Extended Data Fig. 7. Constraints on PMNS oscillation parameters in 1D and 2D for normal ordering.

As in Extended Data Fig. 6, but conditional on the assumption of normal ordering.

Extended Data Fig. 8. Constraints on PMNS oscillation parameters in 1D and 2D for inverted ordering.

As in Extended Data Fig. 6, but conditional on the assumption of inverted ordering.

Extended Data Fig. 9. Experimental measurements of oscillation parameters.

$\mid \mathrm{\Delta }{m}_{32}^2\mid$ assuming normal ordering (a), with sources for the results from top to bottom starting with the second line as follows:^,,–. ${\sin }^{2}2{\theta }_{13}$ assuming normal (b) and inverted (c) ordering, with sources for the results from top to bottom starting with the second line as follows:^,,–,. NOvA+T2K measurement here does not use the reactor constraint. ${\sin }^2{\theta }_{23}$ assuming normal (d) and inverted (e) ordering, with sources for the results from top to bottom starting with the second line as follows:^,,–. Open circles denote a local minima position in lower octant. δ_CP assuming normal (f) and inverted (g) ordering, with sources for the results from top to bottom starting with the second line as follows:^,,,.