Atmospheric neutrino oscillation analysis with neutron tagging and an expanded fiducial volume in Super-Kamiokande I–V

We present a measurement of neutrino oscillation parameters with the Super-Kamiokande detector using atmospheric neutrinos from the complete pure-water SK I–V (April 1996–July 2020) dataset, including events from an expanded fiducial volume. The dataset corresponds to 6511.3 live days and an exposure of 484.2 kiloton-years. Measurements of the neutrino oscillation parameters $\mathrm{\Delta }{m}_{32}^2$, ${\sin }^2{\theta }_{23}$, ${\sin }^2{\theta }_{13}$, ${\delta }_{\mathrm{CP}}$, and the preference for the neutrino mass ordering are presented with atmospheric neutrino data alone, and with constraints on ${\sin }^2{\theta }_{13}$ from reactor neutrino experiments. Our analysis including constraints on ${\sin }^2{\theta }_{13}$ favors the normal mass ordering at the 92.3% level.

Figure 1

Electron-to-muon flavor oscillation probabilities of atmospheric neutrinos as a function of cosine zenith angle and neutrino energy. The top row shows the probabilities for neutrinos and antineutrinos in the normal mass-ordering scenario, and the bottom row shows the same probabilities for the inverted mass-ordering scenario. The probabilities are calculated assuming ${\sin }^2{\theta }_{23}=0.5$, ${\sin }^2{\theta }_{13}=0.022$, ${\sin }^2{\theta }_{12}=0.307$, $|\mathrm{\Delta }{m}_{32,31}^2|=2.4\times {10}^{-3}{\mathrm{eV}}^2$, $\mathrm{\Delta }{m}_{21}^2=7.53\times {10}^{-5}{\mathrm{eV}}^2$, and ${\delta }_{\mathrm{CP}}=-\pi /2$. The matter effect resonance is visible in the normal ordering for neutrinos (upper left) or the inverted ordering for antineutrinos (lower right) between 2 GeV and 10 GeV, and for $\cos {\theta }_z\lesssim -0.5$.

Figure 2

Event display of a multi-ring atmospheric neutrino cadidate event in SK V data. Hit ID PMTs are displayed on an unrolled view of the cylindrical detector, with the color and radius of each hit PMT corresponding to the detected charge. The reconstruction algorithm apfit identifies three Cherenkov rings, indicated by dashed outlines: one bright $\mu$-like ring, with $p_{\mu }\approx 1010\mathrm{MeV}/c$, and two fainter $e$-like rings, each with $p_e\approx 320\mathrm{MeV}/c$.

Figure 3

Performance of energy reconstruction for various sources across all SK periods. Solid points indicate measurements made within the conventional fiducial volume (vertex is greater than 200 cm from the detector walls), while dashed points correspond to measurements in the additional fiducial volume (vertex is between 100 cm and 200 cm from the detector walls). Michel-$e$ refers to the stopping muon decay electron spectrum calibration.

Figure 4

Average event rates for the primary SK neutrino samples, fully contained (FC), partially contained (PC), and upward-going muons (Up-$\mu$). Error bars are statistical. The five pure-water data-taking phases, SK I–V, are labeled. The FC event rates include events in the additional FV volume region; see Sec. 2b4.

Figure 5

Zenith angle or momentum distributions for the 19 analysis samples without neutron tagging. The first column shows the momentum bins for samples which are not also binned by zenith angle, while the second through fifth columns show the 1D zenith angle distributions for samples which use 2D momentum and zenith angle binning. The MC distributions are shown at the best-fit point in the normal ordering, cf. Table 4, with best-fit systematic pulls applied. Different colors in the MC histograms correspond to the true neutrino flavors present in each sample. Panels beneath each distribution show the data-MC ratio, and all error bars are statistical. FC (non-PC and non-Up-$\mu$) sub-GeV and multi-GeV single-ring samples, marked with an asterisk (*), contain events from only SK I–III, while the corresponding events from SK IV–V are separated into samples using tagged neutron information, shown in Fig. 6.

Figure 6

Zenith angle distributions for the SK IV and SK V FC sub-GeV and multi-GeV single-ring samples using the number of tagged neutrons. The MC configuration and the meaning of the colors are identical to Fig. 5.

Figure 7

Monte Carlo distributions of input variables for the FC multi-GeV, multi-ring BDT. Distributions are area-normalized. ${\mathrm{L}}_{\text{Decay}\mathrm{e}}$ is the maximum distance of any decay electron from the event’s primary vertex. $p_{\mathrm{T}}$ is the momentum transverse to the most energetic ring, $p_{\mathrm{Max}}$. is the momentum of the most energetic ring, and $p_{\text{Tot}}$ is the sum of the momenta from all reconstructed rings.

Figure 8

Data and MC distributions of the multi-ring BDT classifier scores for multi-ring ${\nu }_e$ and ${\overline{\nu }}_e$ events. The BDT makes a final classification decision for each event based on the class with the highest score: Negative values correspond to ${\overline{\nu }}_e$-like events, and positive values correspond to ${\nu }_e$-like events. Distributions are shown for the SK IV–V phases, including events in the expanded fiducial volume region. MC events are shown with oscillations applied, and without the effect of any fitted systematic uncertainty parameters. The “MC total” distribution includes contributions from true ${\nu }_{\mu }$, ${\nu }_{\tau }$, and NC events.

Figure 9

SK IV–V data and MC distributions of the likelihood variables used to classify events into the different analysis samples. The top row shows events in the conventional fiducial volume region, while the bottom row shows events in the additional fiducial volume region. The first and third columns show sub-GeV events, and the second and fourth columns show multi-GeV events. The left four panels show the PID likelihood for the most energetic ring in each event: Negative values indicate the ring is $e$-like, while positive values indicate the ring is $\mu$-like. The right four panels show the ring-counting likelihood: Negative values indicate the event has a single ring, while positive values indicate the event has multiple rings. In these panels, the “CC QE” histograms include both 1p1h and 2p2h processes, and “CC Other” refers to single, nonpion hadron production. All MC distributions are calculated assuming neutrino oscillations and without the effect of any systematic uncertainties.

Figure 10

Simulated neutrino energy spectra by interaction modes for the different SK event categories: fully contained (FC), partially contained (PC), and upward-going muon (Up-$\mu$). The simulated event rates are for an oscillated MC, with oscillation parameters set to the Particle Data Group best-fit values [31], except for ${\delta }_{\mathrm{CP}}$, which is set to 0. “CC Other” modes refer to the production of single, nonpion hadrons.

Figure 11

Updated zenith angle bin edges for this analysis (black, solid lines) compared to equally spaced bins (red, dashed lines). The updated bin edges are symmetric about zero and align with the matter-enhanced ${\nu }_{\mu }\to {\nu }_e$ resonance regions present assuming the PREM. The oscillation probabilities and corresponding color scale are the same as in Fig. 1 for neutrinos in the normal ordering.

Figure 12

Estimated fractional uncertainty on the ratio of upward-going, $\cos {\theta }_z<0$, versus downward-going, $\cos {\theta }_z>0$, events in the multi-GeV $e$-like samples (both single-ring and multi-ring) from statistical and systematic uncertainties. The fractional uncertainties are estimated by randomly fluctuating the nominal MC counts either by Poisson statistics for the “Statistics” entry, or by Gaussian fluctuations of one or more systematic uncertainties. Uncertainties on the up/down ratio in the multi-GeV $e$-like samples have the largest impact on the sensitivity to the neutrino mass ordering.

Figure 13

1D $\mathrm{\Delta }{\chi }^2$ sensitivity profile of ${\delta }_{\mathrm{CP}}$ for the normal and inverted mass-ordering scenarios, with (solid lines) and without (dashed lines) neutron-based event classification for SK IV and SK V data. The sensitivity is computed assuming the true neutrino oscillation parameters are the global best-fit parameters from [31] and the normal mass ordering. The parameters $\mathrm{\Delta }{m}_{32}^2$, ${\sin }^2{\theta }_{23}$, and ${\delta }_{\mathrm{CP}}$ are free parameters in the fit, while the other oscillation parameters are fixed.

Figure 14

1D $\mathrm{\Delta }{\chi }^2$ profiles of oscillation parameters in the analysis, with ${\sin }^2{\theta }_{13}$ treated as a free parameter. Solid lines correspond to the data fit result, while dashed lines correspond to the MC expectation at the data best-fit oscillation parameters, cf. Table 4. Dotted lines show critical values of the ${\chi }^2$ distribution for 1 degree of freedom, with the lowest to highest corresponding to 68%, 90%, 95%, and 99% probabilities.

Figure 15

Up-down asymmetry for multi-GeV $e$-like events. The $y$ axis is the asymmetry parameter, the ratio between the difference and sum of upward-going ($\cos {\theta }_z<0.6$) and downward-going ($\cos {\theta }_z>0.6$) events. The $x$ axis is the reconstructed neutrino energy: For single-ring events, the reconstructed energy is the visible energy of the ring assuming the reconstructed ring is an electron, while for mult-iring events, it is the total visible energy of the event. All error bars are statistical. MC lines for the normal and inverted orderings are drawn assuming the best-fit oscillation parameters of the analysis with ${\sin }^2{\theta }_{13}$ constrained. SK IV-V multi-GeV single-ring events are selected using the number of tagged neutrons, and so they are separated from the SK I–III multi-GeV single-ring samples.

Figure 16

1D $\mathrm{\Delta }{\chi }^2$ profiles of oscillation parameters in the analysis with ${\sin }^2{\theta }_{13}$ constrained. Solid lines correspond to the data fit result, while dashed lines correspond to the MC expectation at the data best-fit oscillation parameters, cf. Table 4. Dotted lines show critical values of the ${\chi }^2$ distribution for 1 degree of freedom corresponding to 68%, 90%, 95%, and 99% probabilities.

Figure 17

2D constant $\mathrm{\Delta }{\chi }^2$ contours of neutrino oscillation parameters $\mathrm{\Delta }{m}_{32}^2$ and ${\sin }^2{\theta }_{23}$ for the normal mass ordering. Contours are drawn for a 90% critical ${\chi }^2$ value assuming 2 degrees of freedom, with the $\mathrm{\Delta }{\chi }^2$ computed for each experiment with respect to the best-fit point in the normal mass ordering. The Super-K contour shows the result of this analysis, and other contours are adapted from publications by MINOS+ [53], NOvA [4], T2K [3], and IceCube [54]. Best-fit points are indicated with markers for each experiment.

Figure 18

Distribution of the mass-ordering preference statistic, $\mathrm{\Delta }{\chi }_{\mathrm{I}.\mathrm{O}.-\mathrm{N}.\mathrm{O}.}^2$, for ensembles of simulated datasets, assuming either the normal or inverted mass orderings. The data result from the atmospheric analysis with ${\sin }^2{\theta }_{13}$ constrained is shown as the vertical black line. The blue and orange histograms indicate the distribution of this statistic for toy datasets assuming the normal and inverted ordering, respectively. The filled areas to the left of the data result for inverted toy datasets and to the right of the data result for normal toy datasets indicate the $p$-values.