Limits on sterile neutrino mixing using atmospheric neutrinos in Super-Kamiokande

We present limits on sterile neutrino mixing using 4,438 live-days of atmospheric neutrino data from the Super-Kamiokande experiment. We search for fast oscillations driven by an ${\mathrm{eV}}^2$-scale mass splitting and for oscillations into sterile neutrinos instead of tau neutrinos at the atmospheric mass splitting. When performing both of these searches we assume that the sterile mass splitting is large, allowing ${\sin }^2(\mathrm{\Delta }{m}^{2}L/4E)$ to be approximated as 0.5, and we assume that there is no mixing between electron neutrinos and sterile neutrinos ($|U_{e4}{|}^2=0$). No evidence of sterile oscillations is seen and we limit $|U_{\mu 4}{|}^2$ to less than 0.041 and $|U_{\tau 4}{|}^2$ to less than 0.18 for $\mathrm{\Delta }{m}^2>0.1{\mathrm{eV}}^2$ at the 90% C.L. in a $3+1$ framework. The approximations that can be made with atmospheric neutrinos allow these limits to be easily applied to $3+\mathrm{N}$ models, and we provide our results in a generic format to allow comparisons with other sterile neutrino models.

Figure 1

The true energy distribution from simulation without oscillations of the fully contained (sub-GeV and multi-GeV), partially contained (stopping and through-going), and up-going muon (stopping, through-going nonshowering, and through-going showering) samples.

Figure 2

(a) The ${\nu }_{\mu }$ survival probability without sterile neutrinos, plotted versus zenith angle and neutrino energy. This includes the standard ${\nu }_e\mathrm{CC}$ matter effect, which creates the distortion around a few GeV in the most upward-going zenith angles ($\cos {\theta }_z$ near $-1$), which correspond to neutrinos that pass through the core of the Earth. (b) The ${\nu }_{\mu }$ survival probability calculated using the no-${\nu }_e$ approximation with $|U_{\mu 4}{|}^2=0.0018$ and $|U_{\tau 4}{|}^2=0.33$. The distortion due to the ${\nu }_e\mathrm{CC}$ matter effects is gone, but there is now a more pronounced distortion introduced by the sterile matter effects which reduces the amount of ${\nu }_{\mu }$ disappearance for the most upward-going bins in the 10’s of GeV region. There is also a small amount of extra disappearance away from the standard oscillations introduced by the nonzero $|U_{\mu 4}{|}^2$ which is most visible in the slight darkening of the upper-right part of the plot corresponding to the higher energy downward-going events ($\cos {\theta }_z$ near 1).

Figure 3

The ${\nu }_{\mu }$ survival probability without sterile neutrinos (black) and with $|U_{\mu 4}{|}^2=0.058$ (red), calculated using the sterile vacuum oscillation probability, plotted versus $L/E$. The oscillation probability is not unique for a given $L/E$ since the ${\nu }_e\mathrm{CC}$ matter effect dependence on $L$ and $E$ is more complicated. So, many points corresponding to simulated neutrino events are plotted versus $L/E$, but with oscillation probabilities calculated using the individual simulated $L$ and $E$ values, to show the band of possible oscillation probabilities. While the standard atmospheric oscillation pattern and the smaller variation due to ${\nu }_e\mathrm{CC}$ matter effects are persistent, introducing a sterile neutrino reduces the maximum survival probability at all values of $L/E$. The effect is most visible in regions without standard atmospheric oscillations.

Figure 4

Zenith angle distributions summed across SK-I through SK-IV of the PC through-going and UP-$\mu$ stopping subsamples shown for the data (black points with statistical error bars), the MC prediction without sterile neutrinos (black solid line), and the MC prediction with a large (approximately $5\sigma$ sensitivity) sterile signal of $|U_{\tau 4}{|}^2=0.31$. Both MC predictions are shown after fitting the systematic uncertainties to the data. These two subsamples are shown because they contain the 10’s of GeV neutrinos most sensitive to the sterile matter effect. The prediction with a sterile component shows an up-turn for the most up-going events which corresponds to the distortion of the oscillogram shown in Fig. 2.

Figure 5

The 90% and 99% upper limits on $|U_{\tau 4}{|}^2$ vs $|U_{\mu 4}{|}^2$ from the no-${\nu }_e$ fit are shown by the solid and dashed lines, respectively. The best fit point is marked by a black dot. The light gray region is excluded at 90% and the dark gray region is disallowed by unitarity.

Figure 6

Ratios to the MC prediction without sterile neutrinos, binned in zenith angle and summed across SK-I through SK-IV, for three $\mu$-like subsamples at low (FC sub-GeV), medium (FC multi-GeV), and high energies (though-going UP-$\mu$). The prediction without sterile neutrinos has been fit to the data using the systematic uncertainties. The black points represent the data with statistical error bars and the solid red line shows the MC prediction with the best fit for sterile neutrinos ($|U_{\mu 4}{|}^2=0.016$), including the best fit systematic uncertainties. In all the samples it lines up close to unity, meaning the prediction is nearly identical to the prediction without sterile neutrinos. The dashed red line shows the MC prediction with the same sterile component ($|U_{\mu 4}{|}^2=0.016$), but now with the same systematic uncertainty parameters as the denominator, showing the effect of just the sterile oscillations: the normalization is shifted downward by approximately 3% in every $\mu$-like sample.

Figure 7

The 90% and 99% upper limits on $|U_{\mu 4}{|}^2$ from the sterile vacuum fit to Super-K is shown in the solid and dashed and vertical lines, respectively. The gray filled region is excluded at 90%. This analysis is not sensitive to $\mathrm{\Delta }{m}^2$, but the experiments who also measure $|U_{\mu 4}{|}^2$ are, so here the one-dimensional Super-K result is shown in two dimensions. The dotted line is the 90% limit placed by the joint analysis of MiniBooNE and SciBooNE [35] and the dot-dashed line is the 90% limit placed by the CCFR experiment [34].

Figure 8

The $\mathrm{\Delta }{\chi }^2$ from the fit to the atmospheric neutrino data in the no-${\nu }_e$ approximation, plotted versus the two effective parameters, $A_s$ and $\sin (2{\theta }_s)$, with the third free parameter, $d_{\mu }$, profiled out.

Figure 9

The 90% sensitivity contour for the sterile vacuum fit with the effect $P_{ee}$ from Eq. (b1) included. Allowing the freedom in the electron sample normalization reduces the sensitivity to $|U_{\mu 4}{|}^2$ as can be seen from the bowing outward on the right side of the contour. Note that on this plot $|U_{\mu 4}{|}^2$ is shown in linear scale so the correlation with $|U_{e4}{|}^2$ is clear.

Figure 10

The average of ${\sin }^2(\mathrm{\Delta }{m}^{2}L/4E)$ calculated event-by-event for a range of values of $\mathrm{\Delta }{m}^2$ in four SK samples: (a) FC sub-GeV, (b) FC multi-GeV, (c) PC, and (d) UP-$\mu$. When the event-by-event average deviates significantly (here defined as 5%) from $⟨{\sin }^2⟩=0.5$, the “fast-oscillation” assumption is no longer valid.

Figure 11

Distributions of zenith angle or energy, summed across SK-I through SK-IV, for the $\mu$-like FC, PC, and UP-$\mu$ subsamples. They are projected into zenith angle when binned in both angle and energy and the sub-GeV 2 decay-e sample is binned only in momentum. The black points represent the data with statistical error bars, while the solid blue line represents the no-${\nu }_e$ best fit, the dashed red line represents the sterile vacuum best fit, and the solid black line represents the MC prediction without sterile neutrinos.

Figure 12

Distributions of zenith angle or energy, summed across SK-I through SK-IV, of the $e$- and $\mathrm{NC}{\pi }^0$-like FC subsamples. They are projected into zenith angle when binned in both. In the fits for sterile neutrinos, these samples serve primarily to control the normalization of the atmospheric neutrino flux. As in Fig. 11, the black points represent the data with statistical error bars, while the solid blue line represents the no-${\nu }_e$ best fit, the dashed red line represents the sterile vacuum best fit, and the solid black line represents the MC prediction without sterile neutrinos. The small deviation of the no-${\nu }_e$ best fit in the multi-GeV and multiring $e$-like samples is from setting ${\theta }_{13}$ to zero.