1. Energy Reconstruction Algorithms for the ANTARES Neutrino Telescope J.D. Zornoza 1, A. Romeyer 2, R. Bruijn 3 on Behalf of the ANTARES Collaboration 1 IFIC (CSIC-Universitat de València), Spain 2 CEA/SPP Saclay, France 3 NIKHEF, The Netherlands International Workshop on UHE Neutrino Telescopes Chiba July 28-29, 2003

2. Juan-de-Dios Zornoza - IFIC 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.

3. Juan-de-Dios Zornoza - IFIC ANTARES Layout 12 lines 25 storeys / line 3 PMT / storey ~60-75 m 350 m 100 m 14.5 m Junction box Readout cables 40 km to shore

4. Juan-de-Dios Zornoza - IFIC Energy loss The muon energy reconstruction is based on the fact that the higher its energy, the higher the energy loss along its track. 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: 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. Above the critical energy (600 GeV in water) stochastic losses dominate. Energy loss vs. muon energy:

5. Juan-de-Dios Zornoza - IFIC Time distribution There is also an effect of the energy on the arrival time distribution of the photons. 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 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. The ratio of the tail hits over the peak hits gives information about the muon energy. Photon arrival time distributions

6. Juan-de-Dios Zornoza - IFIC Reconstruction algorithms Three algorithms have been developed to reconstruct the muon energy: Three algorithms have been developed to reconstruct the muon energy: –MIM comparison method –Estimation based on dE/dx –Neural networks

7. 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: 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. 2. A large MC sample is generated to calculate the dependence between the muon energy and the estimator. log x = p 0 + p 1 logE  + p 2 (logE  ) 2 4. This parameterization is used to estimate the energy of a new MC sample. 4. This parameterization is used to estimate the energy of a new MC sample. 3. This dependence is parameterized by the fit to a parabola: 3. This dependence is parameterized by the fit to a parabola:

8. Juan-de-Dios Zornoza - IFIC Reconstructed energy 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: 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 < A hit /A MIP < 100 –High energy estimator: 10 < A hit /A MIP < 1000 There is a good correlation between the reconstructed and the generated energy. 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. The resolution is constrained by the stochastic nature of the energy loss process. E rec vs E gen Estimator distributions

9. Juan-de-Dios Zornoza - IFIC MIM Results vs. muon generated energy: vs. muon reconstructed energy: Each x-slice of the log 10 (E rec /E gen ) distribution is fitted to a Gaussian. Each x-slice of the log 10 (E rec /E gen ) distribution is fitted to a Gaussian. The mean of the distribution is close to zero. The mean of the distribution is close to zero. The resolution at high energies is a factor 2-3. The resolution at high energies is a factor 2-3.

10. Juan-de-Dios Zornoza - IFIC Estimation based on dE/dx An new estimator is defined as follows: An new estimator is defined as follows: L μ = 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: 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) track parameters (x, y, z, θ, φ) light attenuation and diffusion ( att ~ 55 m) light attenuation and diffusion ( att ~ 55 m) PMT angular response PMT angular response This method also uses the dE/dx dependence on the muon energy. This method also uses the dE/dx dependence on the muon energy.

11. Juan-de-Dios Zornoza - IFIC Detector response and sensitive volume The detector response is defined as: The detector response is defined as: N PMT =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. 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 It is defined as the detection volume + 2.5 att in each direction Detector volume N N N N µ

12. Juan-de-Dios Zornoza - IFIC Results of the dE/dx method log 10 Egen (GeV) RMS with mean at zero Above 10 TeV, the energy resolution is a factor 2-3.

13. Juan-de-Dios Zornoza - IFIC Neural networks There are 11 inputs in this method: 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. 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. After studying several topologies, the best performances were obtained by a two layer network with 20 units in each layer.

14. Juan-de-Dios Zornoza - IFIC Results of neural network method The energy resolution is a factor ~2 above 1 TeV. The energy resolution is a factor ~2 above 1 TeV. From 100 GeV to 1 TeV, the energy resolution is ~3. From 100 GeV to 1 TeV, the energy resolution is ~3. After fitting each x-slice of the log 10 E rec /E gen distribution to a Gaussian, we can plot the mean and the sigma: After fitting each x-slice of the log 10 E rec /E gen distribution to a Gaussian, we can plot the mean and the sigma:

15. Juan-de-Dios Zornoza - IFIC Spectrum reconstruction (I) Atmospheric neutrinosDiffuse flux in E -2 (Waxman & Bahcall) dE/dx energy reconstruction method 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).

16. Juan-de-Dios Zornoza - IFIC Spectrum reconstruction (II) Another approach to reconstruct the spectra is to use a deconvolution algorithm. Another approach to reconstruct the spectra is to use a deconvolution algorithm. An iterative method 1 based on the Bayes’ theorem has been used. An iterative method 1 based on the Bayes’ theorem has been used. preliminary Reconstructed Spectrum P(X j |E i ) P o (E) P(E i |X j ) n(X j ) n(E i )P(E i ) Initial Hypothesis n o (E) Experimental Data Smearing Matrix (MC) Cause: E  log10 E μ Effect: X Effect: X  log 10 x low (MIM method) 1 G. D'Agostini NIM A362(1995) 487-498

17. Juan-de-Dios Zornoza - IFIC 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 -8 E -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

18. Juan-de-Dios Zornoza - IFIC Conclusions Three methods have been developed to reconstruct the muon energy, based on the stochastic muon energy loss. 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 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 E µ > 50 TeV. The expected sensitivity after 1 year is ~8x10 -8 E -2 GeV -1 cm -2 s -1 sr -1 with E µ > 50 TeV. This value will be similar to AMANDA II. This value will be similar to AMANDA II.