A neural network approach to high energy cosmic rays mass identification at the Pierre Auger Observatory S. Riggi, R. Caruso, A. Insolia, M. Scuderi Department of Physics and Astronomy, University of Catania INFN, Section of Catania Amsterdam - April 23-27, 2007 Amsterdam - April 23-27, 2007

ACAT 2007 ACAT 2007 Open questions in UHECR physics Origin and nature of the cosmic radiation at the highest energyOrigin and nature of the cosmic radiation at the highest energy (AGNs? GRBs? Pulsars? Exotic scenarios?...) Cutoff or not cutoff?Cutoff or not cutoff? 3 principal research fields, interconnected each other

Open questions in UHECR physics Origin and nature of the cosmic radiation at the highest energyOrigin and nature of the cosmic radiation at the highest energy (AGNs? GRBs? Pulsars? Exotic scenarios?...) Cutoff or not cutoff?Cutoff or not cutoff? ACAT 2007 ACAT principal research fields, interconnected each other

Open questions in UHECR physics Origin and nature of the cosmic radiation at the highest energyOrigin and nature of the cosmic radiation at the highest energy (AGNs? GRBs? Pulsars? Exotic scenarios?...) Cutoff or not cutoff?Cutoff or not cutoff? ACAT 2007 ACAT principal research fields, interconnected each other

Why to study mass composition? ACAT 2007 ACAT 2007 Discrimination between different models advanced to explain the cosmic rays originDiscrimination 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 groundStudy 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)Correct the reconstructed energy of the shower with the right missing energy factor (reduce systematic uncertainties in the measurement of the energy)

How to study mass composition? ACAT 2007 ACAT 2007 Indirect methods 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 Longitudinal shower profiles (number of particles in the cascade vs atmospheric depth) Shifts of  100 g/cm 2 in the depth at which the cascade has its maximum

Number of muons and electrons at a given distance from the shower core (usually 1000 m) 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. How to study mass composition? ACAT 2007 ACAT 2007 Other parameters so far have been used: steepness of the lateral distribution function, rise time of the signals in ground detectors, shower curvature parameters,…

How to study mass composition? ACAT 2007 ACAT 2007 Mass identification…a very difficult task: Any parameter does not show a strong correlation to the mass 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 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 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.

The Pierre Auger Experiment ACAT 2007 ACAT 2007 Actual status of Auger Sud SD: About 1164 tanks running To be completed at the end of 2007 To be completed at the end of 2007 FD: Completed Auger Sud (Malargue – Argentina) 1600 Cherenkov detectors1600 Cherenkov detectors 4 fluorescence sites4 fluorescence sites (6 telescope each) (6 telescope each) Tank spacing: 1.5 kmTank spacing: 1.5 km  100% efficiency above eV Extension  3000 km 2 Auger North (Lamar – USA) Still in project phaseStill in project phase

Experimental techniques Surface Detection Cherenkov detectorsCherenkov detectors Shower front observation at groundShower front observation at ground 100% duty cycle100% duty cycle Fluorescence Detection Telescope with a PMTs cameraTelescope with a PMTs camera Fluorescence light observation in atmosphereFluorescence light observation in atmosphere 10% duty cycle10% duty cycle Hybrid Detection  Calorimetric energy calibration (FD) + high event collecting power (SD)  Cross-check between the two techniques ACAT 2007 ACAT 2007

Mass Analysis Data sets: protons helium nuclei oxygen nuclei silicon nuclei iron nuclei Simulation code: CONEX 1.4 (1-dimensional shower simulation, appropriate for FD analysis Hadronic interaction model: QGSJET II-03 Energy range: eV Zenith range: 0-60 degrees Uniform distributions

Mass Analysis 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 p10, p50, p90: depths at which the 10%, 50%, 90% of the integral profile are reached; X max : depth of shower maximum; E,  : primary energy and zenith angle; N max : number of charged particles at shower maximum; ACAT 2007 ACAT 2007

Mass Analysis ACAT 2007 ACAT 2007 Data sets: 3 input data sets (learn, cross validation, test) Patterns random-selected Feature preprocessing: normalization in the range [-1;1] Error function: Mean Square Error Learning algorithm: quasi-Newton with BFGS minimization formula

Mass Analysis ACAT 2007 ACAT 2007 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

Results – 2 components ACAT 2007 ACAT 2007 Efficiency: Purity: protons irons VERY GOOD IDENTIFICATION NN design: Good results even with only one hidden layer

ACAT 2007 ACAT 2007 Results – 5 components Efficiency: Purity: p/Fe BETTER RECOGNIZED STRONGER CONTAMINATION IN INTERMEDIATE COMPONENTS

ACAT 2007 ACAT 2007 Determining the mean composition Given the classification matrix C ij, we determine the mean composition of a data sample, by solving this linear system: n i rec : number of reconstructed events in the sample for the given i-th mass; c ij : elements of the classification matrix; n i rec : true number of events in the sample for the given i-th mass; Passing to the “fraction” notation… M.Ambrosio et al, Astropart. Phys. 24 (2005) 355

ACAT 2007 ACAT 2007 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 n i 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: standard chisquareconstraint term Lagrange multiplier

ACAT 2007 ACAT 2007 Determining the mean composition where the error is given by: variance of a multinomial distributionuncertainty over the classification matrix MINUIT solve the non-linear fit with the given constraints and returns the estimates of the true abundances.

ACAT 2007 ACAT 2007 Results – Composition 1 Reconstructed fractions Mass classes

Results – Composition 2 ACAT 2007 ACAT 2007 Reconstructed fractions Mass classes

Results – Composition 3 (iron most abundant) ACAT 2007 ACAT 2007 Reconstructed fractions Mass classes

Results – Composition 4 (proton most abundant) ACAT 2007 ACAT 2007 Reconstructed fractions Mass classes

Taking into account FD response ACAT 2007 ACAT 2007 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, …

Results – 2 components ACAT 2007 ACAT 2007 Early loss of NN generalization capabilities during the training Add a regularization term to MSE to avoid larger value weights

Results – 2 components ACAT 2007 ACAT 2007 Deviations from true fractions are around 5÷6 %

Conclusions and future plans ACAT 2007 ACAT 2007 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% Pure simulated data Reconstructed data Mass identification for p-Fe components performed with misclassification of % Reconstructed mean mass composition deviates from the true one of about 5% 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 WORK IN PROGRESS…