A neural network approach to high energy cosmic rays mass identification at the Pierre Auger Observa

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A neural network approach to high energy cosmic
rays mass identification at the Pierre Auger
Observatory
Amsterdam - April 23-27, 2007

• S. Riggi, R. Caruso, A. Insolia, M. Scuderi

Department of Physics and Astronomy, University
of CataniaINFN, Section of Catania
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Open questions in UHECR physics

• Origin and nature of the cosmic radiation at the
  highest energy
• (AGNs? GRBs? Pulsars? Exotic scenarios?...)
• Cutoff or not cutoff?

3 principal research fields, interconnected each
other

• Energy spectra and mass composition
• Propagation through galactic and intergalactic
  medium
• Arrival direction and anisotropies

ACAT 2007
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Open questions in UHECR physics

• Origin and nature of the cosmic radiation at the
  highest energy
• (AGNs? GRBs? Pulsars? Exotic scenarios?...)
• Cutoff or not cutoff?

3 principal research fields, interconnected each
other

• Energy spectra and mass composition
• Propagation through galactic and intergalactic
  medium
• Arrival direction and anisotropies

ACAT 2007
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Open questions in UHECR physics

• Origin and nature of the cosmic radiation at the
  highest energy
• (AGNs? GRBs? Pulsars? Exotic scenarios?...)
• Cutoff or not cutoff?

3 principal research fields, interconnected each
other

• Energy spectra and mass composition
• Propagation through galactic and intergalactic
  medium
• Arrival direction and anisotropies

ACAT 2007
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Why to study mass composition?

• Discrimination between different models advanced
  to explain the cosmic rays origin
• (Different energy spectra predicted to be
  observed at ground from model to model, according
  to the mass of the primary)
• Importance of event-by-event mass analysis
• Study possible correlations between the mass of
  the event and the arrival direction at ground
• Correct the reconstructed energy of the shower
  with the right missing energy factor (reduce
  systematic uncertainties in the measurement of
  the energy)

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How to study mass composition?

• Indirect methods
• Need some shower observables sensitive to the
  primary mass
• Need to rely on simulation codes and
  parameterizations of the interactions in the low
  and high energy regime

Heavy nuclei-induced cascades develop faster in
atmosphere than light nuclei-induced ones (at the
same energy and zenith), due to their higher
interaction cross section with air. This
behaviour results in a set of mass-discriminating
parameters

• Longitudinal shower profiles
• (number of particles in the cascade vs
  atmospheric depth)
• Shifts of ?100 g/cm2 in the depth at which the
  cascade has its maximum

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How to study mass composition?

• Number of muons and electrons at a given
  distance from the shower core (usually 1000 m)
• Less muons in a proton shower than in an iron one.

Other parameters so far have been used steepness
of the lateral distribution function, rise time
of the signals in ground detectors, shower
curvature parameters,
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How to study mass composition?

• Mass identificationa very difficult task
• Any parameter does not show a strong correlation
  to the mass
• Correlation to the mass is reduced by intrinsic
  shower-to-shower fluctuations and by detector
  response
• In any case any prediction is always extremely
  dependent on the adopted interaction model
• Combine different observables to perform a
  multidimensional analysis
• Event-by-event case in a multicomponent primary
  flux is prohibitive.

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The Pierre Auger Experiment

• Auger Sud (Malargue Argentina)
• 1600 Cherenkov detectors
• 4 fluorescence sites
• (6 telescope each)
• Tank spacing 1.5 km
• 100 efficiency above 1018.5 eV

• Auger North (Lamar USA)
• Still in project phase

Extension ?3000 km2
Actual status of Auger Sud SD About 1164 tanks
running To be completed at the end of
2007 FD Completed
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Experimental techniques
Hybrid Detection

• Calorimetric energy calibration (FD) high event
  collecting power (SD)
• Cross-check between the two techniques

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Mass Analysis

• Simulation strategy
• Parameters sensitive to the primary mass
• Neural network application

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Mass Analysis

• Simulation strategy
• Parameters sensitive to the primary mass
• Neural network application

Heavy nuclei-induced cascades develop faster in
atmosphere than light nuclei-induced ones. The
longitudinal profiles, measurable with the FD,
could show this behaviour.
7 features as NN inputs
Xmax depth of shower maximum
Nmax number of charged particles at shower
maximum
E, ? primary energy and zenith angle
p10, p50, p90 depths at which the 10, 50, 90
of the integral profile are reached
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Mass Analysis

• Simulation strategy
• Parameters sensitive to the primary mass
• Neural network application

Data sets 3 input data sets (learn, cross
validation, test) Patterns random-selected
Feature preprocessing normalization in the range
-11
Error function Mean Square Error
Learning algorithm quasi-Newton with BFGS
minimization formula
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Mass Analysis

• Simulation strategy
• Parameters sensitive to the primary mass
• Neural network application

• Net Architecture
• Optimize the net architecture (neurons per
  layer, number of hidden layers) to our specific
  problem
• Use tgh as activation functions in hidden layers
  and linear function in output layer
• No appreciable differences with logistic
  functions

• Identification procedure
• Train the network to assign 0,1,2,3,4 to proton,
  helium, oxigen, silicon, iron events
• Stop the training phase when overfitting appear
  in the cross validation set
• Cut over the net outputs to separate the mass
  classes
• Estimate the results in terms of identification
  efficiency and purity

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Results 2 components
Efficiency
Purity
protons
VERY GOOD IDENTIFICATION
irons
NN design 7-15-15-1 Good results even with only
one hidden layer
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Results 5 components
Efficiency
Purity
p/Fe BETTER RECOGNIZED STRONGER CONTAMINATION IN
INTERMEDIATE COMPONENTS
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Determining the mean composition
Given the classification matrix Cij, we determine
the mean composition of a data sample, by solving
this linear system
nirec number of reconstructed events in the
sample for the given i-th mass cij elements of
the classification matrix nirec true number of
events in the sample for the given i-th
mass Passing to the fraction notation
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Determining the mean composition
We work with the fractions of event (abundances)
for a given mass instead of using the number of
events, scaling the ni with the total number of
events N in the sample
The linear system becomes
with the constraints
We solve the system minimizing with MINUIT the
following function
? Lagrange multiplier
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Determining the mean composition
where the error is given by
MINUIT solve the non-linear fit with the given
constraints and returns the estimates of the true
abundances.
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Results Composition 1
Reconstructed fractions
Mass classes
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Results Composition 2
Reconstructed fractions
Mass classes
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Results Composition 3 (iron most abundant)
Reconstructed fractions
Mass classes
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Results Composition 4 (proton most abundant)
Reconstructed fractions
Mass classes
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Taking into account FD response

• Shower simulation and reconstruction with the
  Auger official Offline tool
• Simulate the shower core in the field of view of
  FD (say LosLeones)
• Generation of fluorescence and Cherenkov light
  and propagation to the telescope aperture
• Simulation of PMT responses and trigger levels
• Reconstruction of shower parameters (energy,
  direction, longitudinal profile,)

Several quality cuts have been applied to the
reconstructed events Require a good fit of the
longitudinal profiles, observation of Xmax,
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Results 2 components
Early loss of NN generalization capabilities
during the training
Add a regularization term to MSE to avoid larger
value weights
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Results 2 components
Deviations from true fractions are around 56
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Conclusions and future plans
Pure simulated data

• Mass identification for p-Fe components
  performed with efficiency of nearly 100
• Mass identification for 5-components performed
  with misclassification of 22-30 for p-Fe
  component and 40 for intermediate components.
• Reconstructed mean mass composition deviates
  from the true one of about 5

Reconstructed data

• Mass identification for p-Fe components
  performed with misclassification of 20-25
• Reconstructed mean mass composition deviates
  from the true one of about 5

WORK IN PROGRESS

• Improve classification efficiency by adding
  parameters from SD
• Full hybrid simulation is required in this case
  using Corsika or Aires codes
• Better event quality cuts definition, analysis
  with multi-components flux, restrict analysis in
  smaller energy bin
• application of the method over the Auger
  experimental data

ACAT 2007