Study of the background

An important component to this analysis is understanding the background. The two main sources of our background are misreconstructed tracks of down-going muons and up-going neutrino-induced muons from the atmosphere. Understanding the nature of the events that pass our selection criteria, will enable us to improve signal to noise in the next version of cut optimization. Such an exercise will also give us consistency checks of results produced by Monte Carlo. In this section, the number of events from atmospheric neutrinos are investigated, a classification of the events passing this analysis, and a comparison with the neutrino candidates found by Zeuthen group.

 

Atmospheric neutrinos produce one background to the point source search, but the energy spectrum is much softer ( $\gamma \sim 3.7$ above 1 TeV). The differential atmospheric neutrino flux derived by Volkova [13] was used to calculate the energy spectrum for this background that survive the full analysis. Figure 31 shows the differential flux of atmospheric neutrinos detected by AMANDA in 138.2 days of live-time. The results are repeated in figure 32 and figure 33. The total number of events for the point source neutrinos range from 0.012 to 0.78 events and between 1.4 to 1.9 atmospheric neutrinos are in the bin. There are two main conclusions from these results. First, a reliable energy variable is needed to remove the atmospheric neutrino background. Second, $\sim 75$ to 90% of the events that pass the optimized set of cuts must be misreconstructed tracks of down-going muons.

  

Figure 32: differential energy spectra for two sources, NGC4151 and atmospheric neutrinos. (left) The NGC4151 calculation assumes a model by Szabo and Protheroe in $1<E_{\nu}<10^{3}$ TeV energy range. (right) The NGC4151 calculation assumes a model by Stecker et al. in the same energy range. The two models represent two extremes of event rate for hadronic acceleration in NGC4151.

Figure 34 shows the experimental data and the expected number of atmospheric neutrinos in bins of cosine zenith. The total of 307 events are expected from atmospheric neutrinos. The first bin near vertical (cos(zenith)=-1) may be exclusively atmospheric neutrinos. However visual inspection of the 61 experimental events revealed that most possess cascade-like topologies (table 7). There are only 18 clearly identified neutrino candidates in this bin, but 12 of those events coincide with the neutrino candidates (shown in appendix A) found by the Zeuthen group [6]. Another 6 other events have hit distributions expected from up-going neutrino-induced muons. Since the Monte Carlo predicts 50 events, only $\sim$ 2/5 of neutrinos are observed. Most of these cascade-like events are down-going muons with energetic stochastic events (ie. bright bremsstrahlung, pair production, or nuclear interaction). However, inspection of signal events reveal that the neutrino interaction locations of low energy events ( $E_{\mu}<100$ GeV) tend to be near or inside the detector volume. These events often deposit more light from the cascade at the muon vertex than the muon. Thus the event appears cascade-like and it would be very difficult to distinguish these events from those containing a down-going cascade. There is still a possibility that a large fraction of these cascade like events in table 7 could be low energy atmospheric neutrinos whose vertices are near or inside the array. This could remove the discrepancy between the number of observed neutrinos and the number predicted by Monte Carlo. There are at least two additional possibilities to explain the discrepancy. First, the predicted flux may be in error. MACRO finds a factor of 2 discrepancy between measured flux and the Bartol prediction (although Super-Kamiokande finds less). Neutrino oscillation may reduce the flux of muon neutrinos and generate more tau neutrinos (which would look like a electron neutrino interaction in AMANDA). Another possibility involves errors in the absolute photon efficiencies in the simulation.

    

Figure 33: (right) The Mk421 calculation assumes a model by Szabo and Protheroe in $1<E_{\nu}<10^{3}$ TeV energy range.
Figure 34: (right) The 1997 experimental data (138.2 days) and the expected number of atmospheric neutrinos.

 

Table 7: Visual inspection, using eview of the nearly up-going ( $-1 < \cos \theta(2) < -.91667$), which remain after the applying selection criteria of table 2. A Neutrino candidate appears to have the characteristics of up-going neutrino-induced muons. Cascade-like events exhibit more of a spherical hit distribution expected from high energy stochastic processes that lead to electromagnetic cascades along the track. The timing of the hits appear down-going muon are more consistent with an atmospheric muon. Noise/? are events whose leading edge times and peak amplitudes are not consistent with the topology expected from muon or cascade-like. All or part of the information contained in the event may be electronic artifacts. The ievent numbers for each of these events is given in appendix E.

Category	Number of events
Neutrino Candidate	18
Cascade Like	35
Down going muon	1
Noise/?	7

  

Figure 35: effective area versus declination for different muon energies. Muon effective presented in the internal report from Zeuthen [6] is superimposed with our results (UCI).

Instead of concentrating on the vertical bin we now compare our results to the Zeuthen group's level 4 atmospheric neutrino candidates. Only 32 out of the their 116 candidates (or 27.6%) pass our cuts. They are listed in appendix E. Assuming all their candidates are true neutrino events, this result appears to be inconsistent with the 307 atmospheric neutrinos predicted by the Monte Carlo. The muon effective area at 0.1 TeV, 1.0 TeV, 10.0 TeV, and 100.0 TeV was calculated to investigate the sensitivity at different muon energies (figure 35). Detectable muons (i.e., muons that reach the detector before ranging out) with these energies at their vertex where selected out of the Monte Carlo signal sample to calculate the effective areas. The information figure 35 was superimposed with the muon effective area found in the analysis done by the Zeuthen group [6]. At higher energies our muon effective area of this analysis is significantly larger than at their level 4 cuts [6]. Most of the detected atmospheric neutrino events are low energy (due tot he steep power law behavior of the energy spectrum). At these energies, the effective area for the point source search is only marginally larger than theirs (figure 35). This is mainly due to our greater acceptance at large zenith angles. The Zeuthen analysis predicts 223 atmospheric events at level 4, while the estimate for the analysis in this report is 307, which is with larger effective area. One observation taken from table 14 in appendix E is only 38.7% of the their events pass our jkrchi(3) cut, while all the other cuts have greater than 90% passing efficiency. Hence this one variable is efficiently cutting out a lot of atmospheric neutrino candidates. This may be related to the energy dependence of this variable (figure 1), where more of the low energy events (atmospheric neutrinos) are being cut out. This will need further investigation.

The majority of events are poorly reconstructed down-going muons. The issue of removing low energy atmospheric neutrinos background is not critical. Clearly, efficient removal of poorly reconstructed tracks is the primary concern. The most common type of event that survive the point source analysis are cascade-like events, necessitating the development of selection criteria to remove these events. Lastly, there are two items that need to be understood. The atmospheric neutrino simulation appears to be overestimating the event rate by a factor of $\sim 2$, yet only $\sim 30$% of the neutrino candidates of the atmospheric neutrino analysis done in Zeuthen are in our data set.