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## Energy Reconstruction Algorithms for the ANTARES Neutrino Telescope

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**International Workshop on UHE Neutrino Telescopes**Chiba July 28-29, 2003 Energy Reconstruction Algorithms for the ANTARES Neutrino Telescope J.D. Zornoza1, A. Romeyer2, R. Bruijn3 on Behalf of the ANTARES Collaboration 1IFIC (CSIC-Universitat de València), Spain 2CEA/SPP Saclay, France 3NIKHEF, The Netherlands**Introduction**Neutrinos could be a powerful tool to study very far or dense regions of the Universe, since they are stable and neutral. The aim of the ANTARES experiment is to detect high energy neutrinos coming from astrophysical sources (supernova remnants, active galactic nuclei, gamma ray bursts or micro-quasars). At lower energies, searches for dark matter (WIMPs) and studies on the oscillation parameters can be also carried out. The background due to atmospheric neutrinos is irreducible. However, at high energies, this background is low, so energy reconstruction can be used to discriminate it. Juan-de-Dios Zornoza - IFIC**ANTARES Layout**12 lines 25 storeys / line 3 PMT / storey 14.5 m 350 m Junction box 100 m 40 km to shore ~60-75 m Juan-de-Dios Zornoza - IFIC Readout cables**Energy loss**Energy loss vs. muon energy: • The muon energy reconstruction is based on the fact that the higher its energy, the higher the energy loss along its track. • There are two kinds of processes: • Continuous: ionization • Stochastic: Pair production, bremstrahlung, photonuclear interactions • Above the critical energy (600 GeV in water) stochastic losses dominate. Juan-de-Dios Zornoza - IFIC**Time distribution**• There is also an effect of the energy on the arrival time distribution of the photons. • The higher the energy, the more important the contribution to the time distribution tail. • The ratio of the tail hits over the peak hits gives information about the muon energy. Photon arrival time distributions Juan-de-Dios Zornoza - IFIC**Reconstruction algorithms**• Three algorithms have been developed to reconstruct the muon energy: • MIM comparison method • Estimation based on dE/dx • Neural networks Juan-de-Dios Zornoza - IFIC**MIM Comparison method**• 1. An estimator is defined, based on a comparison between the light produced by the muon and the light it would have produced if it was a Minimum Ionizing Muon: 2. A large MC sample is generated to calculate the dependence between the muon energy and the estimator. 3. This dependence is parameterized by the fit to a parabola: log x = p0 + p1 logE + p2 (logE)2 4. This parameterization is used to estimate the energy of a new MC sample. Juan-de-Dios Zornoza - IFIC**Reconstructed energy**Estimator distributions • Two energy regimes have been defined, in order to optimize the dynamic range of the method. In the calculation of the estimator, we only take the hits which fulfill: • Low energy estimator: 0.1 < Ahit/AMIP < 100 • High energy estimator: 10 < Ahit/AMIP < 1000 Erec vs Egen • There is a good correlation between the reconstructed and the generated energy. • The resolution is constrained by the stochastic nature of the energy loss process. Juan-de-Dios Zornoza - IFIC**MIM Results**vs. muon generated energy: • Each x-slice of the log10(Erec/Egen) distribution is fitted to a Gaussian. • The mean of the distribution is close to zero. • The resolution at high energies is a factor 2-3. vs. muon reconstructed energy: Juan-de-Dios Zornoza - IFIC**Estimation based on dE/dx**• This method also uses the dE/dx dependence on the muon energy. • An new estimator is defined as follows: Lμ = muon path length in the sensitive volume A = ∑A=total hit amplitude R = detector response • R(r, θ, φ) is the ratio of light seen by the overall detector, i.e. a kind of detector efficiency to a given track. It is independent of the reconstruction, but a function of: • track parameters (x, y, z, θ, φ) • light attenuation and diffusion (att ~ 55 m) • PMT angular response Juan-de-Dios Zornoza - IFIC**µ**N Detector volume N N N Detector response and sensitive volume • The detector response is defined as: NPMT=number of PMTs in the detector θj=PMT angular response r=distance to the PMT • The sensitive volume is the volume where the muon Cherenkov light can be detected. • It is defined as the detection volume + 2.5 att in each direction Juan-de-Dios Zornoza - IFIC**RMS with mean at zero**log10 Egen (GeV) Results of the dE/dx method Above 10 TeV, the energy resolution is a factor 2-3. Juan-de-Dios Zornoza - IFIC**Neural networks**• There are 11 inputs in this method: • Hit amplitude and time • Hit time residue distribution • Reconstructed track parameters Only events with energy above 1 TeV have been used to train the NN. After studying several topologies, the best performances were obtained by a two layer network with 20 units in each layer. Juan-de-Dios Zornoza - IFIC**Results of neural network method**After fitting each x-slice of the log10 Erec/Egen distribution to a Gaussian, we can plot the mean and the sigma: The energy resolution is a factor ~2 above 1 TeV. From 100 GeV to 1 TeV, the energy resolution is ~3. Juan-de-Dios Zornoza - IFIC**Spectrum reconstruction (I)**Using the methods previously presented, muon spectra can be reconstructed. The aim is to compare the atmospheric and the signal spectra. Atmospheric muon background has been rejected in the selection process (quality cuts). Atmospheric neutrinos Diffuse flux in E-2 (Waxman & Bahcall) dE/dx energy reconstruction method Juan-de-Dios Zornoza - IFIC**P(Xj|Ei)**Smearing Matrix (MC) Reconstructed Spectrum P(Ei|Xj) n(Ei) P(Ei) no(E) Po(E) Initial Hypothesis n(Xj) Experimental Data Spectrum reconstruction (II) • Another approach to reconstruct the spectra is to use a deconvolution algorithm. • An iterative method1 based on the Bayes’ theorem has been used. preliminary Cause: E log10 Eμ Effect: X log10 xlow (MIM method) Juan-de-Dios Zornoza - IFIC 1 G. D'Agostini NIM A362(1995) 487-498**ANTARES Sensitivity**The reconstructed energy can be used as a threshold to calculate the sensitivity of the experiment. The optimum value is the one for which we need the lowest number of signal events to exclude the background hypothesis at a given confidence level (i.e. 90%) • The expected sensitivity is: - 7.7·10-8E-2 GeV-1 cm-2 s-1 sr-1 with Eµ > 50 TeV, after 1 year - 3.9·10-8 E-2 GeV-1 cm-2 s-1 sr-1 with Eµ > 125 TeV, after 3 years • These values are comparable with AMANDA II Juan-de-Dios Zornoza - IFIC**Conclusions**• Three methods have been developed to reconstruct the muon energy, based on the stochastic muon energy loss. • The energy resolution is a factor 2-3 above 1 TeV. • The expected sensitivity after 1 year is ~8x10-8 E-2 GeV-1 cm-2 s-1 sr-1 with Eµ > 50 TeV. • This value will be similar to AMANDA II. Juan-de-Dios Zornoza - IFIC