2008 IceCube Update - Section 8
VIII. EVENT RECONSTRUCTION
In the Northern hemisphere, events are reconstructed using maximum-likelihood fitting techniques. Events are fitted to templates representing different decay modes. Figure 5 shows examples of three different interaction topologies in IceCube .
Figure 5 (top) shows an actual (data) muon or muon bundle (group of parallel muons from an air shower). The tracks are visible over more than 1 km. This long lever arm allows for good directional reconstruction, better than 1 degree. Of course, for shorter tracks, the resolution degrades. It is also possible to estimate muon energies by either the length of their tracks, or by measuring the specific energy loss; at energies above 1 TeV, muon energy loss (dE/dx) is proportional to the muon energy.
Figure 5 (middle) shows a simulated νe interaction which produces a compact deposition of energy; this is known as a 'cascade.' Cascades are also produced by neutral current neutrino interactions and low-energy (below 1 PeV) ντ interactions. Although there is very little directional information, cascade energies may be determined to within a factor of 2.
Figure 5 (bottom) shows a simulated few-PeV ντ interaction forming a classic 'double-bang' topology. The interaction produces one cascade when the ντ interacts. That interaction produces a τ, which, at PeV energies, can travel hundreds of meters before decaying. The second cascade comes when the τ decays. Several other τ decay modes are under study in IceCube.
Other topologies are also being studied. For example, a νμ interacting in the detector will produce a hadronic shower from the struck nucleus, in addition to the μ track. Muons can also stop in the detector.
Of course, the most common events are downward going muons produced in cosmic-ray air showers. In triggered events, cosmic-ray muons outnumber neutrino induced muons by about 500,000:1. Rejection of this background is a significant difficulty which must be dealt with in event reconstruction.
Events are reconstructed by fitting them to one of these hypotheses. The starting points for these fits are the results of 'first guess' methods. For muons, the main first guess method fits a moving plane to the launch times in the DOMs . For a muon, the plane should have a velocity near the speed of light. An alternate approach uses the measured charge deposition to the 'long axis' in events such as in Fig. 5 (top).
The maximum likelihood fitter finds the likelihood for different track positions and directions, and, optionally, energy. To do this, it uses functions which model the light propagation, giving the probability distribution for a photon radiated from a track with a given orientation to reach a DOM at a given perpendicular distance and orientation as a function of time. These functions are precalculated using a simulation that tracks photons through the ice, and stored in a 7-dimensional histogram . One of the dimensions is depth, incorporating the depth dependence of the optical properties of the ice.
Because of the high rate of downward going muons, it is not enough to select events with the most likely reconstruction as upward going . Fairly stringent cuts must be applied to eliminate tracks with reasonable likelihoods for being downward going. This can be done by cutting on the estimated errors from the likelihood fit, which can act as a stand-in for the depth of the minimum in the likelihood function. Alternately, one can perform a Bayesian reconstruction, weighting fits to different zenith angles by the relative size of the signal in that direction (effectively requiring that the upward going hypothesis be much more likely). The exact cuts are analysis-dependent, since different analyses are interested in signals from different energy ranges and zenith angles.
IceCube is big enough that there is also a significant background due to random coincident muon events, whereby two (or more) muons from independent cosmic-ray air showers traverse the detector in the course of one event. Specific algorithms have been developed to find and reject these events, by separating hits from the two tracks based on their separation in space and/or time.
After these cuts, a relatively clean sample of well-reconstructed neutrino events remains, as is shown in Fig. 6. There remains an irreducible background of atmospheric neutrinos produced by cosmic-ray air showers in the northern hemisphere. In 1 year (about 320 live days) of IC40 data, we expect about 5,000 atmospheric νμ interactions. The atmospheric νe background is about two orders of magnitude lower and the atmospheric ντ background is almost absent.
The lower backgrounds make the two latter channels attractive avenues to search for extraterrestrial neutrinos. In searches for point sources of neutrinos, off-source regions are used to directly measure the background level . Diffuse neutrino analyses use the fact that the energy spectrum of the atmospheric neutrinos is much softer than for extra-terrestrial neutrinos; by selecting high energy events, one can largely remove the atmospheric background . Current diffuse searches have most of their sensitivity above 100 TeV.