Searching for eV-scale sterile neutrinos with eight years of atmospheric neutrinos at the IceCube Neutrino Telescope

We report in detail on searches for eV-scale sterile neutrinos, in the context of a $3+1$ model, using eight years of data from the IceCube Neutrino Telescope. By analyzing the reconstructed energies and zenith angles of 305,735 atmospheric ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ events we construct confidence intervals in two analysis spaces: ${\sin }^2(2{\theta }_{24})$ vs $\mathrm{\Delta }{m}_{41}^2$ under the conservative assumption ${\theta }_{34}=0$; and ${\sin }^2(2{\theta }_{24})$ vs ${\sin }^2(2{\theta }_{34})$ given sufficiently large $\mathrm{\Delta }{m}_{41}^2$ that fast oscillation features are unresolvable. Detailed discussions of the event selection, systematic uncertainties, and fitting procedures are presented. No strong evidence for sterile neutrinos is found, and the best-fit likelihood is consistent with the no sterile neutrino hypothesis with a $p$ value of 8% in the first analysis space and 19% in the second.

Figure 1

Disappearance probability calculated using NuSQuIDS [105] for several sterile neutrino parameters. The ${\overline{\nu }}_{\mu }$ disappearance probability in terms of true neutrino energy and cosine of the zenith is shown for several sterile neutrino parameters. Top row has fixed ${\sin }^2(2{\theta }_{24})=0.1$ and increasing mass-squared differences from left to right. Bottom row has fixed $\mathrm{\Delta }{m}_{41}^2=1{\mathrm{eV}}^2$ and increasing mixing from left to right. There are visible discontinuities between inner to outer core [$\cos ({\theta }_{\nu }^{\mathrm{true}})=-0.98$] and outer core to mantle [$\cos ({\theta }_z^{\mathrm{true}})=-0.83$]. Note that the peak of the IceCube flux is at around 1 TeV.

Figure 2

Number of observed events per bin in the full eight-year dataset used in this work.

Figure 3

Reconstructed muon energy (top) and cosine of the zenith (bottom) distributions. Data points are shown in black with error bars that represent the statistical uncertainty. The solid blue and red lines show the best-fit sterile neutrino hypothesis and the null (no sterile neutrino) hypothesis, respectively, with nuisance parameters set to their best-fit values in each case.

Figure 4

Expected composition of the energy and zenith distributions in the absence of sterile neutrinos. Top: the reconstructed energy distribution for signal (conventional atmospheric, prompt atmospheric, and astrophysical ${\nu }_{\mu }$ flux) and backgrounds (atmospheric muons, ${\nu }_{\tau }$, and ${\nu }_e$). Bottom: the corresponding reconstructed zenith direction.

Figure 5

Predicted true conventional neutrino energy distribution in the absence of sterile neutrinos. The distribution is shown as an orange histogram for the conventional atmospheric component for default nuisance parameters. The translucent regions indicate the area that contains 90% (solid lines), 95% (dashed), and 99% (dotted) of the data.

Figure 6

Distributions of variables used in the diamond filter. Four different variables are shown: event charge excluding DeepCore (Qtot NoDC), number of triggered DOMs (NChan NoDC), number of DOMs that see direct light (DNDoms), and the cosine of the zenith angle ($\cos {\theta }_z$). The signal (conventional ${\nu }_{\mu }$) is shown in orange, while the backgrounds are shown in blue, teal, and green (cosmic-ray muons, electron neutrinos, and tau neutrinos respectively). The vertical-dashed line in each plot shows the location of the cut, and the shaded region is rejected.

Figure 7

Cuts on variables used to reduce the atmospheric shower background. The ${\nu }_{\mu }$ signal is shown in orange, while the backgrounds are shown in blue, teal, and green representing expectations from cosmic-ray muons, electron neutrinos, and tau neutrinos, respectively. The vertical-dashed line in each plot shows the location of the cut, and the shaded region is rejected. The notable depth dependent structure is primarily due to the ice optical properties.

Figure 8

Two-dimensional cuts on overburden and reconstruction quality variables. The top figure uses ParaboloidSigma, while the bottom uses BLLHR. In these figures the atmospheric muon background is shown with the rainbow color scale labeled corsika, while the signal is shown with the light gray color. The dashed lines represent the delineation of the cut function described in the text. For more details, see Ref. [116].

Figure 9

Two-dimensional cuts on overburden for RLL and DNDOMs. These cuts are used to remove residual background contamination in the final sample.

Figure 10

Cuts used in clean-up step. Top two plots show the 1D cuts used in the clean-up step. In these plots the color coding is the same as in Fig. 7 where, again, the vertical-dashed line in each plot shows the location of the cut, and the shaded region is rejected.

Figure 11

Energy distribution ice uncertainty covariance (top) and correlation matrix (bottom). The color scale shows the covariance and correlation between energy bins.

Figure 12

DOM angular efficiency variations. Different allowed angular acceptance curves are shown as a function of the incident photon angle.

Figure 13

Contribution of different parent particles to the atmospheric neutrino flux. The neutrino flux from a given parent particles—pion in blue, kaon in red, muon in teal, and $D$ meson in green—is compared to the total ${\nu }_{\mu }$ and antineutrino flux at IceCube. The right panel is for horizontal neutrinos while the left column is for vertically upward-going neutrinos.

Figure 14

Effects of atmosphere temperature variations in the atmospheric neutrino angular distribution. The change in neutrino flux relative to the average flux at 8.932 TeV given temperature variations from the airs satellite data (black). The standard deviation of the distribution of temperature fluctuations is shown as a dashed red line.

Figure 15

Results from three measurements of the astrophysical neutrino flux performed by IceCube [130]. The vertical axis shows the overall six-neutrino normalization at 100 TeV assuming an unbroken power-law and uniformly distributed neutrino flavor composition at Earth. The horizontal axis shows single-power law spectral index. The stars correspond to the location of the best-fit point of each measurement, while the solid (dashed) lines correspond to the 68.3% (95.4%) confidence regions. The color scale shows the shape of the correlated two-dimensional Gaussian constraint (prior) at the 68.3% (white solid), 95.4% (white dashed), and 99.7% (white dotted) levels used in the frequentist (Bayesian) analysis.

Figure 16

Effects of different systematic groups on the sensitivity. The analyses sensitivity at 90% C.L., estimated using an Asimov set, are shown as a solid gray line. The color lines show the estimated sensitivity when a given systematic uncertainty category is removed (within analysis II the effect of astrophysical and cross section uncertainties are sufficiently small that their contours are effectively superposed).

Figure 17

Nuisance parameters posterior distributions at best-fit sterile parameter point. Each subplot shows the posterior distribution for analysis I (red) and analysis II (blue) as histograms. In each of them we also show the cumulative distribution as solid lines, as well as the standard deviation as a horizontal error bar.

Figure 18

Correlation between nuisance parameters. The correlation matrix has been calculated for the best-fit point of analysis I.

Figure 19

Frequentist result for analyses I and II. The result of analysis I (top) and analysis II (bottom). The best-fit points are marked with white stars, and the 90% (solid), 95% (dashed), and 99% (dotted) C.L. contours are drawn assuming Wilks’s theorem with two degrees of freedom. The color scale shows the likelihood difference with respect to the best-fit point scaled by two in both analyses.

Figure 20

Best-fit points distribution from null hypothesis pseudodata for analyses I and II. The distribution of the best-fit points given 2000 null realizations (blue) throughout the physics parameter space. Also shown is the location of the analyses best-fit points, as white stars.

Figure 21

Data pull distribution with at analyses best-fit points. The observed statistical-only pull distribution in reconstructed energy and $\cos ({\theta }_{\mathrm{z}})$ for analysis I (top) and analysis II (bottom) at their respective best-fit points.

Figure 22

Nuisance parameter pulls at best-fit point. The systematic uncertainty nuisance parameters pulls for both analyses at their respective best-fit points.

Figure 23

Expected dominant systematic across the parameter space. The expected strongest-pulling nuisance parameter at each point in the physics space for each analysis. The white solid, dashed, and dotted lines indicate the 90%, 95%, and 99% C.L. respectively.

Figure 24

Analyses frequentist result with expected sensitivities. The 99% C.L. Brazil bands for analysis I (top) and analysis II (bottom), overlaid with the analysis result shown as a black line. The yellow band corresponds to the 95% spread, while the green to the 68%. The median sensitivity is shown as a dashed white line, while the bet fit points for each analysis are shown as a white star.

Figure 25

Effect of removing a systemic category on the frequentist results. Each color line corresponds to the analysis performed without a single systematic group and the star of the same color is the corresponding best-fit point. Left: analysis I; right: analysis II. The solid (dashed) lines show the 90% C.L. (99% C.L.). The solid black lines represent the frequentist result using all years.

Figure 26

Effect of removing a given year on the frequentist results. Each color line corresponds to the analysis performed without a given year. Left: analysis I; right: analysis II. The solid (dashed) lines show the 90% C.L. (99% C.L.) and the stars represent the best-fit point. The solid black lines represent the frequentist result using all years.

Figure 27

Comparison to other ${\nu }_{\mu }$ disappearance results. The solid blue line in the top (bottom) panel shows the analysis I frequentist result at 90% C.L. (99% C.L.) compared to other experiments’ results shown as thin black lines [67, 68, 69, 70, 71, 72, 73, 74, 75, 209]. Where results were not available at 99% C.L., methods of Ref. [53] were applied using public data releases.

Figure 28

Analysis II frequentist result compared with other experiments’ results. The solid blue line in the top (bottom) panel shows the analysis II frequentist result at 90% C.L. (99% C.L.) compared to other experiments’ results shown as thin black lines.