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Physics Laboratory School of Science and Technology Hellenic Open University KM3NeT detector optimization with HOU simulation and reconstruction software A. G. Tsirigotis WP2 - Paris, 10-11December 2008 In the framework of the KM3NeT Design Study

The HOU software chain • Underwater Detector • Generation of atmospheric muons and neutrino events (F77) • Detailed detector simulation (GEANT4-GDML) (C++) • Optical noise and PMT response simulation (F77) • Filtering Algorithms (F77 –C++) • Muon reconstruction (C++) • Calibration (Sea top) Detector • Atmospheric Shower Simulation (CORSIKA) – Unthinning Algorithm (F77) • Detailed Scintillation Counter Simulation (GEANT4) (C++) – Fast Scintillation Counter Simulation (F77) • Reconstruction of the shower direction (F77) • Muon Transportation to the Underwater Detector (C++) • Estimation of: resolution, offset (F77)

Event Generation – Flux Parameterization μ ν ν • Atmospheric Muon Generation • (CORSIKA Files, Parametrized fluxes ) • Neutrino Interaction Events • Atmospheric Neutrinos • (Bartol Flux) • Cosmic Neutrinos • (AGN – GRB – GZK and more) Earth Shadowing of neutrinos by Earth Survival probability

GEANT4 Simulation– Detector Description • Any detector geometry can be described in a very effective way Use of Geomery Description Markup Language (GDML-XML) software package • All the relevant physics processes are included in the simulation • (NO SCATTERING) Fast Simulation EM Shower Parameterization • Number of Cherenkov Photons Emitted (~shower energy) • Angular and Longitudal profile of emitted photons Detector components Particle Tracks and Hits Visualization

Arrival Pulse Time resolution Single Photoelectron Spectrum Quantum Efficiency Πρότυπος παλμός mV Simulation of the PMT response to optical photons Standard electrical pulse for a response to a single p.e.

Prefit, filtering and muon reconstruction algorithms d L-dm (x,y,z) θc dγ Track Parameters θ : zenith angle φ: azimuth angle (Vx,Vy,Vz): pseudo-vertex coordinates dm (Vx,Vy,Vz) pseudo-vertex • Local (storey) Coincidence (Applicable only when there are more than one PMT looking towards the same hemisphere) • Global clustering (causality) filter • Local clustering (causality) filter • Prefit and Filtering based on clustering of candidate track segments (Direct Walk) • Χ2fit without taking into account the charge (number of photons) • Kalman Filter (novel application in this area) • Charge – Direction Likelihood

Kalman Filter application to track reconstruction State vector Initial estimation Update Equations Kalman Gain Matrix Updated residual and chi-square contribution (timing uncertainty)

Kalman Filter – Muon Track Reconstruction - Algorithm Filtering Prediction Update the state vector Extrapolate the state vector Update the covariance matrix Extrapolate the covariance matrix Calculate the residual of predictions Decide to include or not the measurement (rough criterion) Calculate the contribution of the filtered point Decide to include or not the measurement (precise criterion) Initial estimates for the state vector and covariance matrix

Charge Likelihood Hit charge in PEs Mean expected number ofPes (depends on distance form track and PMT orientation) Not a poisson distribution)

Geometry: 10920 OMs in a hexagonal grid. 91 Towers seperated by 130m, 20 floors each. 30m between floors Tower Geometry Floor Geometry 20 floors per tower 30m seperation Between floors 10,8,6,3m 30m 45o 45o

Optical Module • 10 inch PMT housed in a 17inch benthos sphere • 35%Maximum Quantum Efficiency • Genova ANTARES Parametrization for angular acceptance 50KHz of K40 optical noise

Results Neutrino Angular resolution (no cuts applied)

Results Neutrino effective area (no cuts applied)

Results Efficiency of cuts Min compatible tracks = 25 Min compatible tracks = 10 Min compatible tracks = 40 Number of misreconstructed muons per day Number of reconstructed atmospheric neutrinos per day Ratio = (muons)/(neutrinos) (%) 1 hour of generated atmospheric muons

Results Effective Area and angular resolution : Without applying any cuts Applying the cuts that give zero misreconstructed atmospheric muons per day: Likelihod < 1.0 and Minimum number of combatible tracks 40

Results Number of reconstructed atmospheric neutrinos per day vs Neutrino Energy: Without applying any cuts Applying the cuts that give zero misreconstructed atmospheric muons per day: Likelihod < 1.0 and Minimum number of combatible tracks 40

Conclusions Kalman Filter is a promising new way for filtering and reconstruction for KM3NeT However for the rejection of badly misreconstructed tracks additional cuts must be applied Presented by Apostolos G. Tsirigotis Email: tsirigotis@eap.gr

Kalman Filter – Basics (Linear system) Definitions Vector of parameters describing the state of the system (State vector) a priori estimation of the state vector based on the previous (k-1) measurements Estimated state vector after inclusion of the kth measurement (hit) (a posteriori estimation) Measurement k Equation describing the evolution of the state vector (System Equation): Track propagator Process noise (e.g. multiple scattering) Measurement equation: Projection (in measurement space) matrix Measurement noise

Kalman Filter – Basics (Linear system) Prediction (Estimation based on previous knowledge) Extrapolation of the state vector Extrapolation of the covariance matrix Residual of predictions (criterion to decide the quality of the measurement) Covariance matrix of predicted residuals

Kalman Filter – Basics (Linear system) Filtering (Update equations) where, is the Kalman Gain Matrix Filtered residuals: Contribution of the filtered point: (criterion to decide the quality of the measurement)

Kalman Filter – (Non-Linear system) Extended Kalman Filter (EKF) Unscented Kalman Filter (UKF) A new extension of the Kalman Filter to nonlinear systems, S. J. Julier and J. K. Uhlmann (1997)

Kalman Filter Extensions – Gaussian Sum Filter (GSF) • Approximation of proccess or measurement noise by a sum of Gaussians • Run several Kalman filters in parallel one for each Gaussian component t-texpected

Kalman Filter – Muon Track Reconstruction Pseudo-vertex Zenith angle State vector Azimuth angle Hit Arrival time Measurement vector Hit charge System Equation: Track Propagator=1 (parameter estimation) No Process noise (multiple scattering negligible for Eμ>1TeV) Measurement equation:

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