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

Energy Reconstruction Algorithms Energy Reconstruction Algorithms for the ANTARES Neutrino Telescopefor the ANTARES Neutrino Telescope

J.D. ZornozaJ.D. Zornoza11, A. Romeyer, A. Romeyer22, R. Bruijn, R. Bruijn33

on Behalf of the ANTARES Collaborationon Behalf of the ANTARES Collaboration

1IFIC (CSIC-Universitat de València), Spain2CEA/SPP Saclay, France3NIKHEF, The Netherlands

International Workshop on UHE Neutrino Telescopes

Chiba July 28-29, 2003

Juan-de-Dios Zornoza - IFICJuan-de-Dios Zornoza - IFIC

IntroductionIntroduction•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.


ANTARES LayoutANTARES Layout• 12 lines• 25 storeys / line• 3 PMT / storey

~60-75 m

350 m

100 m

14.5 m

Junctionbox

Readout cables

40 km toshore


Energy lossEnergy loss• The muon energy The muon energy

reconstruction is based on reconstruction is based on the fact that the higher its the fact that the higher its energy, the higher the energy, the higher the energy lossenergy loss along its track. along its track.

• There are two kinds of There are two kinds of processes:processes:– ContinuousContinuous: ionization: ionization– StochasticStochastic: Pair production, : Pair production,

bremstrahlung, photonuclear bremstrahlung, photonuclear interactions interactions

• Above the critical energy Above the critical energy (600 GeV in water) (600 GeV in water) stochasticstochastic losses losses dominatedominate..

Energy loss vs. muon energy:

E

dx

dE


Time distributionTime distribution

• There is also an effect There is also an effect of the energy on the of the energy on the arrival timearrival time distribution distribution of the photons.of the photons.

• The higher the energy, The higher the energy, the more important the the more important the contribution to the time contribution to the time distribution distribution tailtail..

• The ratio of the The ratio of the tailtail hits hits over the over the peakpeak hits hits gives information about gives information about the muon energy.the muon energy.

Photon arrival time distributions


Reconstruction algorithmsReconstruction algorithms

• Three algorithms have been developed Three algorithms have been developed to reconstruct the muon energy:to reconstruct the muon energy:

– MIM comparison methodMIM comparison method

– Estimation based on dE/dxEstimation based on dE/dx

– Neural networksNeural networks


MIM Comparison methodMIM Comparison method

• 1. An 1. An estimatorestimator is defined, based on a comparison between the is defined, based on a comparison between the light produced by the muon and the light it would have produced light produced by the muon and the light it would have produced if it was a if it was a Minimum Ionizing MuonMinimum Ionizing Muon::

1MIP

hithits A

Anx

• 2. A large 2. A large MC sampleMC sample is generated to calculate the is generated to calculate the dependencedependence between the muon energy and the estimator.between the muon energy and the estimator.

log x = p0 + p1 logE + p2 (logE)2

• 4. This 4. This parameterizationparameterization is used to estimate the energy of a new is used to estimate the energy of a new MC sample.MC sample.

• 3. This dependence is parameterized by the fit to a 3. This dependence is parameterized by the fit to a parabolaparabola::


Reconstructed energyReconstructed energy

• Two energy regimesTwo energy regimes have been defined, in have been defined, in order to optimize the dynamic range of the order to optimize the dynamic range of the method. In the calculation of the estimator, method. In the calculation of the estimator, we only take the hits which fulfill:we only take the hits which fulfill:

– Low energyLow energy estimator: 0.1 < A estimator: 0.1 < Ahithit/A/AMIPMIP < 100 < 100

– High energyHigh energy estimator: 10 < A estimator: 10 < Ahithit/A/AMIPMIP < 1000 < 1000

• There is a There is a good correlationgood correlation between the reconstructed between the reconstructed and the generated energy.and the generated energy.

• The resolution is The resolution is constrained by the constrained by the stochastic nature of the stochastic nature of the energy loss process.energy loss process.

EErecrec vs E vs Egengen

Estimator distributionsEstimator distributions


MIM ResultsMIM Resultsvs. muon generated energy:vs. muon generated energy:

vs. muon reconstructed energy:vs. muon reconstructed energy:

•Each x-slice of the Each x-slice of the loglog1010(E(Erecrec/E/Egengen) ) distribution is fitted distribution is fitted to a Gaussian. to a Gaussian.

•The The meanmean of the of the distribution is close distribution is close to to zerozero..

•The resolution at The resolution at high energies is a high energies is a factor 2-3factor 2-3..


Estimation based on dE/dxEstimation based on dE/dx

• An new An new estimatorestimator is defined as follows: is defined as follows:

R

ΔA

L

1ρ

µ

LLμ μ = muon path length in the = muon path length in the

sensitive volumesensitive volume

A = ∑A=total hit amplitudeA = ∑A=total hit amplitude

R = detector responseR = detector response

• R(r, R(r, θθ, , φφ) is the ratio of light seen by the overall ) is the ratio of light seen by the overall detector, i.e. a kind of detector efficiency to a detector, i.e. a kind of detector efficiency to a given track. It is independent of the given track. It is independent of the reconstruction, but a reconstruction, but a functionfunction of: of:

•track parameters (x, y, z, track parameters (x, y, z, θθ, , φφ))

•light attenuation and diffusion (light attenuation and diffusion (attatt ~ 55 m) ~ 55 m)

•PMT angular responsePMT 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.


Detector response and sensitive Detector response and sensitive volumevolume• The The detector responsedetector response is defined as: is defined as:

PMTatt

jN

1j

λ

r

j

jθ

PMT

er

α

N

1R

NNPMTPMT=number of PMTs =number of PMTs in the detectorin the detector

θθjj=PMT angular =PMT angular responseresponse

r=distance to the PMTr=distance to the PMT

• The sensitive volume is the The sensitive volume is the volume where the muon volume where the muon Cherenkov light can be Cherenkov light can be detected.detected.

• It is defined as the It is defined as the detection volume + 2.5 detection volume + 2.5 attatt in each directionin each direction

Detector volume

N

N

N

N µ


Results of the dE/dx methodResults of the dE/dx method

log10 Egen (GeV)

RM

S w

ith

mean

at

zero

•Above 10 TeV, the energy resolution is a factor 2-3.


Neural networksNeural networks

• There are There are 11 inputs11 inputs in this method:in this method:– Hit amplitude and Hit amplitude and

timetime– Hit time residue Hit time residue

distributiondistribution– Reconstructed track Reconstructed track

parametersparameters

• Only events with energy above 1 TeV have been used to train Only events with energy above 1 TeV have been used to train the NN.the NN.

• After studying several topologies, the best performances After studying several topologies, the best performances were obtained by a two layer network with 20 units in each were obtained by a two layer network with 20 units in each layer.layer.


Results of neural network methodResults of neural network method

• The energy resolution is a The energy resolution is a factor ~2 above 1 TeVfactor ~2 above 1 TeV..

• From From 100 GeV to 1 TeV100 GeV to 1 TeV, the energy resolution is , the energy resolution is ~3~3..

• After fitting each x-slice of the logAfter fitting each x-slice of the log1010 E Erecrec/E/Egengen distribution to a Gaussian, we can plot the mean distribution to a Gaussian, we can plot the mean and the sigma:and the sigma:


Spectrum reconstruction (I)Spectrum reconstruction (I)

Atmospheric neutrinos Diffuse 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).


Spectrum reconstruction (II)Spectrum reconstruction (II)

• Another approachAnother approach to to reconstruct the reconstruct the spectra is to use a spectra is to use a deconvolution deconvolution algorithm.algorithm.

• An An iterative methoditerative method11 based on the Bayes’ based on the Bayes’ theorem has been theorem has been used.used.

prelim

inar

y

Reconstructed Spectrum

P(Xj|Ei)

Po(E)

P(Ei|Xj)

n(Xj)

n(Ei) P(Ei)

Initial Hypothesis

no(E)

Experimental Data

Smearing Matrix (MC)Cause: E log10 Eμ

Effect: X Effect: X log10 xlow

(MIM method)

1 G. D'Agostini NIM A362(1995) 487-498


ANTARES ANTARES SensitivitySensitivity• 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


ConclusionsConclusions

• Three methodsThree methods have been developed to reconstruct have been developed to reconstruct the muon energy, based on the stochastic muon the muon energy, based on the stochastic muon energy loss.energy loss.

• The energy The energy resolutionresolution is a is a factor 2-3factor 2-3 above 1 TeV. above 1 TeV.

• The expected The expected sensitivitysensitivity after 1 year is ~ after 1 year is ~8x108x10-8-8 E E-2-2 GeVGeV-1-1 cm cm-2-2 s s-1-1 sr sr-1 -1 with Ewith Eµµ > 50 TeV. > 50 TeV.

• This value will be similar to This value will be similar to AMANDA II.AMANDA II.

Documents

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