1. KM3NeT detector optimization with HOU simulation and reconstruction software A. G. Tsirigotis In the framework of the KM3NeT Design Study WP2 - Paris, 10-11 December 2008

2. 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)

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

4. 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 SimulationEM Shower Parameterization Number of Cherenkov Photons Emitted (~shower energy) Angular and Longitudal profile of emitted photons Visualization Detector components Particle Tracks and Hits

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

6. Prefit, filtering and muon reconstruction algorithms 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) Χ 2 fit without taking into account the charge (number of photons) Kalman Filter (novel application in this area) Charge – Direction Likelihood dmdm L-d m (V x,V y,V z ) pseudo-vertex dγdγ d Track Parameters θ : zenith angle φ: azimuth angle (Vx,Vy,Vz): pseudo-vertex coordinates θcθc (x,y,z)

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

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

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

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

11. Optical Module 10 inch PMT housed in a 17inch benthos sphere 35%Maximum Quantum Efficiency Genova ANTARES Parametrization for angular acceptance 50KHz of K 40 optical noise

12. Neutrino Angular resolution (no cuts applied) Results

13. Neutrino effective area (no cuts applied) Results

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

15. 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

16. Results 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 Number of reconstructed atmospheric neutrinos per day vs Neutrino Energy:

17. 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

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

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

21. 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)

22. 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)

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

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