Atmospheric Neutrino Unblinding Proposal
AMANDA-II 2000-2006

John Kelley, UW-Madison, May 2008



Analysis Methodology

Data Selection


Systematic Errors





8. Excess



After the original unblinding, we examined the observable distributions, Nch and cos(Zenith). The data are consistent with the predicted conventional atmospheric neutrino flux models, with the exception of a 1.5% excess in the (60 < Nch < 120) region. This is slightly higher than the estimated 0.5% background contamination, and more importantly, it is not distributed evenly across the observable space (which is how we model background contamination in the systematic errors). In this section, we discuss the impact of the excess, and how we have chosen to address it.

Figure 8.1: Data vs. atmospheric MC, cos(Zenith) for (20 <= Nch <= 120) (2000-2006 Zeuthen+original purity cuts). MC is generated with Photonics AHA and 85% OM sensitivity.

Figure 8.2: Data vs. atmospheric MC, Number of channels hit (2000-2006 Zeuthen+original purity cuts). MC is generated with Photonics AHA and 85% OM sensitivity.


Limits on VLI and Quantum Decoherence


Initial limits on VLI (violation of Lorentz invariance) and quantum decoherence are quite reasonable, and better than the median sensitivity, because of the small excess at high Nch. This is because the data are less compatible with a small new-physics signal, which would show up first as a deficit at high Nch. Because the excess is not modeled in the systematic errors, these limits are artifically low.

Figure 8.4: Allowed region of VLI parameter space (90%, 95%, and 99% contours), preliminary limits from 2000-2006 data. The star marks the best-fit point. The red dashed curve is the best previous limit (90% CL, SuperK+K2K), and the yellow dotted curve the IceCube sensitivity (90% CL, 10 years of IC80).

Figure 8.5: Allowed region of QD parameter space (90%, 95%, and 99% contours), preliminary limits from 2000-2006 data. The star marks the best-fit point.

A note on the decoherence limits: the shape of the allowed region looks different than the test sensitivity shown in figure 7.2, but this is not necessarily unexpected. The confidence level of the region along the y-axis is particularly sensitive to the systematic errors, and in some test cases with MC, we see results which look qualitatively like the contours shown above.


Constraints on the Conventional Flux


Unfortunately, the conventional analysis is significantly impacted by the high-Nch excess. This is because the background is modeled in the likelihood only as a uniform normalization error, not as something which is energy-dependent. The likelihood analysis therefore models the atmospheric flux as significantly harder (a change of spectral index of +0.1) to compensate for the extra events. We do not believe this is a meaningful result.


Analysis of the Excess


What is the excess?

An analysis of the events in the Nch (60,120) region suggests that the excess (about 85 events compared to MC normalized to the low-Nch region) consists of misreconstructed muons. Salient observations about the excess include:


To illustrate the last point we show the distribution of paraboloid error and JAMS/Pandel space angle for high-Nch events. Note the excess is concentrated at poor values of both --- what one would expect for misreconstructed background. We therefore have chosen to isolate and remove the excess, developing a well-motivated procedure which is not biased simply to force data-MC agreement (since we have already unblinded).

Figure 8.6a: Paraboloid error for events with Nch>65.

Figure 8.6b: JAMS/Pandel space angle, events with Nch>65.

Isolating the excess

In order to isolate the excess we note another point from the previous section: the excess is concentrated at poor up-to-down likelihood ratio. We can therefore first roughly isolate the population via their likelihood ratio, and only then apply any cuts to paraboloid error and space angle difference. Instead of using a constant value we note that the likelihood ratio is very dependent on the zenith angle, so instead we follow the median LR as a function of cos(zenith), as derived from MC.

Figure 8.7a: Bayes/Pandel likelihood ratio, events with Nch>65.

Figure 8.7b: Median profile of Bayes/Pandel likelihood ratio as a function of zenith angle, atmospheric neutrino MC, events with Nch > 50. Error bars are 25%-75% range. The red line indicates our parametrization used for event selection, LR_median(theta).

To reiterate what we are doing: we perform this as a first selection on which to then apply Nch-dependent cuts on the other quality variables.

To determine how to tighten the cuts as a function of Nch, we examine 2D plots of paraboloid error and space angle vs. Nch, only for the events below LR_median(theta) (see figure 8.7b). A 2D cut is shown superimposed on the distributions for atmospheric MC (left), data (center), and the ratio of data to MC (right).

Figure 8.8a: Paraboloid error vs. Nch, atmospheric neutrino MC.

Figure 8.8b: Paraboloid error vs. Nch, data from 2000-2006.

Figure 8.8c: Paraboloid error vs. Nch, ratio of data to atmospheric neutrino MC. Note excess in upper right region of plot.

Figure 8.9a: JAMS/Pandel space angle difference vs. Nch, atmospheric neutrino MC.

Figure 8.9b: JAMS/Pandel space angle difference vs. Nch, data from 2000-2006.

Figure 8.9c: JAMS/Pandel space angle difference vs. Nch, ratio of data to atmospheric neutrino MC. Note excess in upper right region of plot.

Applying these test cuts reduces the data in the analysis region from 5638 to 5511 events (-2.3%), while reducing the (not normalized) atmospheric MC from 5399 to 5341 events (-1.1%). After applying these cuts, the agreement in the Nch distribution is significantly improved, with little loss in sensitivity to atmospheric neutrinos.

Figure 8.10a: Original Nch distribution showing excess at Nch>60.

Figure 8.10b: Revised Nch distribution after 2D Nch-dependent cuts.

Although we designed the cuts to be zenith-agnostic, we find that most of the events removed are more horizontal than vertical. The small number of events removed does not, however, appreciably change the zenith angle distribution.

Figure 8.11: Zenith angle distribution of events removed by 2D Nch-dependent cuts.


As a note, we had previously posted an event we considered bad because it was not tracklike: event 2166924 (Quicktime MOV or AVI). After designing these cuts we noted that this event is one of those removed. In general, we note a high correlation with randomly selected, high-Nch events classified by eye as questionable (in the event viewer) and the events removed by the 2D cuts.


A Note on COGz

There is also an excess in the COGz peaks: however, the COGz structure over the whole sample is not well-reproduced by the simulation. We feel it not unreasonable that just as in level 3 data, misreconstructed muons at this high purity level are more likely to show up in the COGz peaks.

Figure 8.12: Z-coordinate center of gravity for all events.

Figure 8.13: Z-coordinate center of gravity for events removed by 2D Nch-dependent cuts.

We also show the COGz distribution for various zenith angle ranges (before the Nch-dependent purity cuts described above -- distributions look the same after the cuts):

Figure 8.14a: Z-coordinate center of gravity for near-vertical events (cos(zenith) < -0.7).

Figure 8.14b: Z-coordinate center of gravity for events with -0.7 < cos(zenith) < -0.3.

Figure 8.14c: Z-coordinate center of gravity for near-horizontal events (cos(zenith) > -0.3).

The differences between data and MC in the rightmost plot (horizontal events that are primarily probing one ice layer) mirror the discrepancies found in our ice model timing residual analysis.


A Note on the Cascade Likelihood Ratio

As part of this investigation, we seriously considered using the cascade-to-track likelihood ratio as a cut parameter, as many of the questionable events are not very tracklike. However, this variable is not well-reproduced in MC. If we scale the MC variable by a factor of 0.775 (determined via Kolmogorov test), the distribution agrees much better, but there is a still an excess in the data at low values (less tracklike). We were not comfortable that this excess was truly misreconstructed background to remove it. We mention it here for completeness and as a avenue of further investigation -- if it is background, this could be another 3% of contamination that is undetectable by the existing cuts described here. It is also possible that understanding the MC scaling factor could lead to insights about the ice model.

Figure 8.14: Cascade-to-track likelihood ratio (higher values are more tracklike).

Figure 8.15: Cascde-to-track likelihood ratio, MC value scaled by 0.775.


Alternate Hypotheses

One other hypothesis that we have examined and rejected is that the events are misreconstructed neutral current cascades that are not simulated in our nusim MC. While there is a clear excess of cascade-like events in ANIS L3 relative to nusim, this does not really persist to the final cut level, and the Nch distributions are nearly identical:

Figure 8.16: ANIS and nusim nu_mu MC cascade to Pandel likelihood ratio, 2005 final cut level.

Figure 8.17: ANIS and nusim nu_mu MC number of channels hit, 2005 final cut level.