Measurement of atmospheric neutrino oscillation parameters by Super-Kamiokande I

We present a combined analysis of fully-contained, partially-contained and upward-going muon atmospheric neutrino data from a 1489 d exposure of the Super-Kamiokande detector. The data samples span roughly five decades in neutrino energy, from 100 MeV to 10 TeV. A detailed Monte Carlo comparison is described and presented. The data is fit to the Monte Carlo expectation, and is found to be consistent with neutrino oscillations of ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ with ${sin}^{2}2\theta >0.92$ and $1.5\times {10}^{-3}<\Delta m^2<3.4\times {10}^{-3}{\mathrm{eV}}^2$ at 90% confidence level.

Figure 1

The parent neutrino energy distributions for the fully-contained, partially-contained, upward stopping-muon and upward through-going muons samples. Rates for the fully-contained and partially-contained samples are for interactions in the 22.5 kt fiducial volume. Taken together, the samples span five decades in neutrino energy.

Figure 2

(a) The direction averaged atmospheric neutrino energy spectrum for ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ calculated by several authors are shown by solid line [28], dashed line [29], and dotted line [25]. (b) The ratio of the calculated neutrino flux. The fluxes calculated in [29] (solid line) and [25] (dashed line) are normalized by the flux in [28].

Figure 3

The flux ratio of ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ to ${\nu }_e+{\overline{\nu }}_e$ averaged over all zenith and azimuth angles versus neutrino energy. Solid, dashed, and dotted lines show the prediction by [25, 28, 29], respectively.

Figure 4

The flux ratios of ${\nu }_{\mu }$ to ${\overline{\nu }}_{\mu }$ and ${\nu }_e$ to ${\overline{\nu }}_e$ versus neutrino energy. Solid, dashed, and dotted lines show the prediction by [25, 28, 29], respectively, (same key as Fig. 3).

Figure 5

The flux of atmospheric neutrinos versus zenith angle. Solid, dashed, and dotted lines show the prediction by [25, 28, 29], respectively, (same key as Fig. 3).

Figure 6

The flux of upward-going atmospheric neutrinos versus zenith angle for higher energy region. Solid, dashed and dotted lines show the prediction by [25, 28, 29], respectively, (same key as Fig. 3).

Figure 7

The calculated flight length of neutrinos for vertically down-going ($\cos \Theta =0.95–1.00$) and near horizontal-going ($\cos \Theta =0.05–0.10$) directions. Distributions are made for both muon neutrinos and electron neutrinos and for three energy intervals [28].

Figure 8

A drawing of the Super-Kamiokande detector. The cut-away shows the inside lined with photomultiplier tubes comprising a photocathode coverage of about 40%. The support structure is stainless steel beams. The thin outer region is shown with sparser density of outward-facing PMTs: 2 outer PMTs for every unit of $3\times 4$ inner PMTs. The top of the detector, under the hemisphere, consists of electronics huts and open work area.

Figure 9

The invariant mass distribution of fully-contained events with two $e$-like rings and no muon-decay electron, for SK data (points) and atmospheric neutrino Monte Carlo (histogram). A peak from neutrino induced ${\pi }^0$ is clearly observed.

Figure 10

The determination of the absolute energy scale of Super-Kamiokande based on in situ calibration with $\mu$-decay electrons, ${\pi }^0\to \gamma \gamma$ invariant mass, and the Cherenkov light of stopping cosmic ray muons.

Figure 11

The mean reconstructed energy of cosmic ray stopping muons divided by their range (upper) and muon-decay electron (lower) as a function of elapsed days. Vertical axes in both figures are normalized to mean values and each data point corresponds to two month period. The variation is within $\pm 2\%$.

Figure 12

The gain uniformity of the Super-Kamiokande detector as determined by the mean value of the reconstructed decay electron momentum (a) as a function of zenith angle, and (b) as a function of azimuthal angle. Vertical axes in both figures are normalized to the mean values.

Figure 13

The gain uniformity of the Super-Kamiokande detector as determined by the fitted peak of the ${\pi }^0\to \gamma \gamma$ mass distribution as a function of zenith angle. Vertical axis is normalized to the mean value.

Figure 14

The scattering angle distribution by neutrino interactions off the ${\mathrm{H}}_2\mathrm{O}$ target from the K2K experiment (data are from Fig. 1(b) of Ref. [19]). Single Cherenkov ring events observed by the 1 kton water Cherenkov detector are used. The histogram shows the prediction by the Monte Carlo used in the present analysis.

Figure 15

Charged-current total cross section divided by $E_{\nu }$ for (a) neutrino and (b) antineutrino nucleon charged-current interactions. Solid line shows the calculated total cross section. The dashed, dot, and dash-dotted lines show the calculated quasielastic, single-meson and deep-inelastic scatterings, respectively. Data points are taken from the following experiments: (▵)ANL [75], (◯)GGM77 [76], ($●$) GGM79(a) [77],(b)[78], (*)Serpukhov [79], (⋄)ANL82 [80], (★)BNL86[53], (■)CCFR90 [81], (▾)CDHSW87 [82], (𝔛)IHEP-JINR96 [83], (+)IHEP-ITEP79 [84], (□)CCFRR84 [85], and (▴)BNL82 [86].

Figure 16

The number of hits in the largest outer detector cluster, which is used to separate the fully-contained and partially-contained event samples. The histogram shows the MC prediction with neutrino oscillations.

Figure 17

The distribution of fully-contained event vertices in the (a) $z$-coordinate and (b) $r^2$-coordinate, comparing SK data and atmospheric neutrino Monte Carlo. The points show the data and the histogram shows the Monte Carlo prediction. The Monte Carlo includes neutrino oscillation with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$.

Figure 18

The distribution of the likelihood difference between a single-ring assumption and a multi-ring assumption for sub-GeV (top) and multi-GeV (bottom) FC events. The points show the data and the histograms show the Monte Carlo prediction. The Monte Carlo includes neutrino oscillation with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$. The hatched histograms show the charged-current quasielastic interactions.

Figure 19

The distribution of the number of identified Cherenkov rings, comparing SK data and atmospheric neutrino Monte Carlo. The Monte Carlo includes neutrino oscillation with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$. The hatched histogram shows the charged current quasielastic interactions.

Figure 20

An example event display of a single-ring $e$-like event. Each small circle represents a hit PMT and the size of the circle represents the number of photons to hit it. In this event the boundary of the Cherenkov light is smeared over many PMTs as the light comes from numerous positrons and electrons in the electromagnetic shower.

Figure 21

An example event display of a single-ring $\mu$-like event. In this event the boundary of the Cherenkov light is sharp as the muon travels relatively straight as it comes to a stop. Distant hit PMTs come from scattered light and Cherenkov light from delta-rays.

Figure 22

The distribution of particle identification likelihood for sub-GeV (top) and multi-GeV (bottom) FC single-ring events, comparing SK data (points) and atmospheric neutrino Monte Carlo (histograms). The Monte Carlo includes neutrino oscillation with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$. The hatched histograms show the ${\nu }_{\mu }$ charged-current interactions.

Figure 23

Particle ID likelihood distribution for sub-GeV (top) and multi-GeV (bottom) FC multi-ring events and the brightest ring of the multi-ring events. Points show the data and the histograms show the Monte Carlo results. The Monte Carlo includes neutrino oscillation with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$. The hatched histograms show the ${\nu }_{\mu }$ charged-current interactions.

Figure 24

The distribution of partially-contained event vertices in the (a) $z$-coordinate and (b) $r^2$-coordinate, comparing SK data and atmospheric neutrino Monte Carlo. The Monte Carlo includes neutrino oscillation with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$.

Figure 25

The zenith versus azimuth directions for a 641.4 d sample of upward muons used to estimate background contamination. The dense regions of events near the horizon correspond to thin regions of the mountainous overburden. The upper panel is for upward stopping muons and the lower panel is for upward through-going muons.

Figure 26

The zenith-angle distribution of upward muon candidates near the horizon for two different regions in azimuth. Regions (1) and (2) are thin and thick overburden, respectively. The live-time of upward and downward events is 1645.9 days and 641.4 days, respectively. The number of downward events is normalized to be 1645.9 days live-time. The upper panel is for upward stopping muons and the lower panel is for upward through-going muons.

Figure 27

Event rates as a function of elapsed SK running time for contained events.

Figure 28

Momentum distribution of FC single-ring $e$-like (top) and $\mu$-like (bottom) events. The sharp cut in the muon momentum spectrum in the high energy end is due to the requirement on full containment. The points show the data, solid lines show the Monte Carlo prediction without neutrino oscillation and dashed lines show the oscillated Monte Carlo events with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$.

Figure 29

Visible energy distribution of multi-ring $\mu$-like events (top) and PC events (bottom). The points show the data, solid lines show the Monte Carlo prediction without neutrino oscillation and dashed lines show the oscillated Monte Carlo events with $({sin}^{2}2\theta =1.00,\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2)$.

Figure 30

Expected $(\mu /e{)}_{\mathrm{Data}}/(\mu /e{)}_{\mathrm{MC}}$ for single-ring sub- and multi-GeV $+\mathrm{PC}$ samples as a function of $\Delta m^2$ for full ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ mixing. The values for the data together with $\pm 1\sigma$ statistical errors are shown by the horizontal lines. The systematic errors are shown by the band in the expectation.

Figure 31

The zenith-angle distribution for fully-contained 1-ring events, multi-ring events, partially-contained events and upward muons. The points show the data, box histograms show the nonoscillated Monte Carlo events and the lines show the best-fit expectations for ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ oscillations with ${sin}^{2}2\theta =1.00$ and $\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2$. The best-fit expectation is corrected by the 39 systematic error terms, while the correction is not made for the nonoscillated Monte Carlo events. The height of the boxes shows the statistical error of the Monte Carlo.

Figure 32

Angular resolution of the neutrino direction as a function of the outgoing charged lepton momentum. The angular resolution is defined as the angular difference between the parent neutrino and the reconstructed direction for which 68% of the events are included.

Figure 33

The azimuth distribution of the sample of events selected for analysis of the east-west effect. The Monte Carlo histogram is normalized to the total number of the real data. $0^{°}$, ${90}^{°}$, ${180}^{°}$ and $270°$ azimuthal angles show particles going to north, west, south and east, respectively.

Figure 34

Expected $U/D$ ratio for FC single-ring $\mu$-like $+\mathrm{PC}$ events as a function of $\Delta m^2$ for full ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ mixing. The data sample is divided into FC sub-GeV with $P_{\mu }<400\mathrm{MeV}/c$, FC sub-GeV with $P_{\mu }>400\mathrm{MeV}/c$, and FC multi-GeV $+\mathrm{PC}$ events. The ratio for the data together with the $\pm 1\sigma$ statistical error are shown by the horizontal lines. The systematic errors are shown by the band in the expectation.

Figure 35

Event rates as a function of elapsed SK running time for upward-going muon data.

Figure 36

Expected ratio of vertical to horizontal upward through-going muons as a function of $\Delta m^2$ for full ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ mixing. Vertical and horizontal are defined to be the number of events in $-1<\cos \Theta <-0.5$ and $-0.5<\cos \Theta <0.0$, respectively. The ratio for the data together with $\pm 1\sigma$ combined statistical and systematic error is also shown by the horizontal lines. The systematic error is shown by the band in the expectation.

Figure 37

Expected ratio of stopping to through-going upward muons as a function of $\Delta m^2$ for full ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ mixing. The ratio for the data together with $\pm 1\sigma$ combined statistical and systematic error is also shown by the horizontal lines. The systematic error is shown by the band in the expectation.

Figure 38

Allowed oscillation parameters for ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ oscillations. Three contours correspond to the 68% (dotted line), 90% (solid line) and 99% (dashed line) C.L. allowed regions.

Figure 39

${\chi }^2-{\chi }_{\min }^2$ projected onto the ${sin}^{2}2\theta$ and $\Delta m^2$ axes. The minimum value at each ${sin}^{2}2\theta$ and $\Delta m^2$ is plotted.

Figure 40

90% confidence level allowed oscillation parameter regions for ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ oscillations from six subsamples. In this plot, 90% confidence interval is defined to be ${\chi }^2={\chi }_{\min }^2+4.61$, where ${\chi }_{\min }^2$ is the minimum ${\chi }^2$ value including the unphysical parameter region.

Figure 41

Left: 90% confidence level allowed oscillation parameter regions for ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ oscillations, based on the NEUT neutrino interaction model, from different flux models (solid line; [28], dashed line; [25], dotted line; [29]). Right: The 90% C.L. allowed regions based on a different neutrino interaction model (NUANCE [48]) for $\mathrm{FC}+\mathrm{PC}$ events with the flux model of Ref. [28] (dashed line) is compared with that based on NEUT with the same flux. In this plot, Monte Carlo events from NEUT were used for upward-going muons.

Figure 42

The 68%, 90% and 99% confidence level allowed oscillation parameter regions obtained by an $L/E$ analysis [72] and by the present analysis are compared.