1. Unfolding performance Data - Monte Carlo comparison
XXX International Cosmic Ray Conference, July 2007, Mérida, Mexico
Muon Energy Reconstruction and Atmospheric Neutrino Unfolding with the IceCube Neutrino Telescope
Juan-de-Dios Zornoza and Dmitry Chirkin on behalf of the IceCube Collaboration
Data collected during the year 2006 by the first 9 strings of IceCube can be used to measure the energy spectrum of the atmospheric muon neutrino flux. Atmospheric neutrinos, an important scientific output by itself (for instance, to understand the high-energy hadronic interaction models), are also fundamental in order to check the performance of the detector and to estimate the background for the extraterrestrial high-energy neutrinos searches. A full reconstruction of the neutrino-induced muon tracks provides both directional and energy information. The reconstructed energy-correlated parameter, the photon density emitted by the muon along its track, can be used to calculate the energy spectrum, which is reconstructed by using unfolding techniques. We will discuss the unfolding procedure to be applied to data from the 9-string configuration of IceCube
IceCube
Energy resolution
Muon energy reconstruction
IceCube will be the first neutrino detector with an effective volume of 1 km3, which is the “natural” size for this kind of detectors, given the low flux expected.
Like AMANDA, it will be located in the South Pole, with 80 strings containing 4800 PMTs.
The first 22 lines have been already installed and it will be finished by The analysis presented here uses data obtained with the first 9 lines of the detector.
Photon density parameter
In ice muon energy loss is dE/dx=a+bE with
a=0.26 GeV / mwe
b= / mwe
(1 mwe = 1/0.917 m of ice)
The number of Cherenkov photons generated by a bare muon is
number of channels
reconstructed
photon density
total charge
Likelihood function
The full log likelihood function contains terms which depend on the muon energy and describe the probabilities to observe more or less or no hits in each sensor.
The number of photons vs. distance to the track is constructed by merging 2 approximations: for the near and far (diffuse) regions. This is fitted/verified with data.
The reconstructed parameter is number of photons per unit length of the muon track times the effective PMT area.
The probability (likelihood) that an event is described by a particular track hypothesis is
When comparing the energy of the muon at the point of the closest approach to the COG (center of gravity, weighted with charge) of hits, we see that the best correlation is obtained with the reconstructed photon density
When convolved with ice and sensor glass transmission curves, this is about Cherenkov photons per meter of muon track.
From Geant-based simulations each cascade left by a muon generates as much light as a bare muon with the length of track of
4.37 m E / GeV for electromagnetic cascades
3.50 m E / GeV for hadronic cascades
For a typical muon the average is ~ 4.22 meters E/GeV
A typical cascade emits 4.22x32440 = photons/GeV
For a muon track the “photon density parameter” is
Area x Nc [m] = [m-1] ( x 10-3 E/[GeV]) x 81 cm2
number of channels
total charge
reconstructed photon density
7 Tev
32 TeV
150 TeV
680 TeV
3.2 PeV
14 PeV
Log likelihood may be rewritten to emphasize the energy term:
number of
channels
total harge
Average quantum efficiency ~ 17%
PMT area = cm2 
81 cm2 effective area
reconstructed
photon density
hit positional/timing likelihood
energy density term
Linearity holds and rms is 30% in log10(E) from 25 TeV to 25 PeV
Spectrum Unfolding
Motivation
The atmospheric neutrino spectrum is one of the basic measurements of neutrino telescopes>
Fundamental for understanding background in other analysis, in particular point-like source searches
Intrinsic interest for the study of atmospheric neutrino studies
The aim of this analysis is to set up the basis for the reconstruction of the energy spectrum of atmospheric neutrinos using unfolding techniques.
Unfolding techniques are needed for neutrino spectrum reconstruction because of the combination of two features of this problem:
The energy resolution is limited, since the energy loss of the muon is stochastic (and moreover only part of the muon energy is observable, which is turn is only part of the neutrino energy).
Second, the spectrum falls very quickly with the neutrino energy. Therefore, the low-energy events for which the energy is overestimated "bury" the regions at higher energies.
Unfolding performance
We have checked the robustness of the unfolded results as function of the spectral index used when creating the smearing matrix and the initial assumption made for the solution of the system.
As a spectral index of gamma=-2 is far from gamma=-3.7, the dependence on the uncertainty of the smearing matrix is small.
We used rather different shapes for the initial assumption on the solution and could show that the algorithm converges towards the expected solution.
Input for the algorithm: distribution of estimator for one year (obtained by Poison randomization of a larger MC sample)
Analysis procedure
The main steps of the analysis are the following:
Cleaning of the bad OMs (based on abnormal noise rates)
Feature extraction (determination of the times and charges of the pulses)
Energy reconstruction with the RIME algorithm
Track reconstruction in a two-step procedure (prefit based on the + likelihood maximization fit)
Unfolded spectrum (blue) compared with the real one (black). This result is preliminary, since no coincident muons are included.
Data - Monte Carlo comparison
The comparison between data and Monte Carlo simulation allows us to check that the detector simulation is under control. This comparison has be to be done at a level at which the blindness policy of the experiment is respected.
Conclusions
IceCube is a neutrino detector being built at the South Pole (22 out of 80 lines already installed and smoothly working)
A method for reconstructing the muon energy based on the estimation of the photon density emission along the track has been developed
The energy resolution using this estimator is better than other estimations based on the number of channels or the total charge
The application of the Single Value Decomposition Method using this photon density is proposed for the unfolding of the 9-line configuration of the IceCube detector
The preliminary results (no coincident muon background included) are promising in terms of stability and convergence
References: [1] A. Achterberg et al., submitted to PRD (2007), arXiv: v1
[2] A. Hoecker and V. Kartvelishvili, Nucl. Instr. & Meth. A372, (1996)
Acknowledgments: J.D. Zornoza acknowledges the support of the Marie Curie OIF program.