Physics Laboratory

1. Physics Laboratory School of Science and Technology Hellenic Open University Progress report of the HOU contribution to TDR (WP2) A. G. Tsirigotis WP2 - Demokritos, 31March 2009 In the framework of the KM3NeT Design Study

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++) • Effective areas, resolution and more (scripts) • 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 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

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 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

5. 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) • Compination of Χ2fit and Kalman Filter (novel application in this area) using the arrival time information of the hits • Charge – Direction Likelihood using the charge (number of photons) of the hits

6. Kalman Filter application to track reconstruction State vector Initial estimation Update Equations timing uncertainty Kalman Gain Matrix Updated residual and chi-square contribution (rejection criterion for hit) Many (40-200) candidate tracks are estimated starting from different initial conditions The best candidate is chosen using the chi-square value and the number of hits each track has accumulated.

7. Charge Likelihood Hit charge in PEs Probability depends on muon energy, distance from track and PMT orientation Not a poisson distribution, due to discrete radiation processes E=1TeV D=37m θ=0deg Ln(F(n)) Ln(n) Log(E/GeV)

8. Working Example 60 meters maximum abs. length no scattering Detector Geometry: 10920 OMs in a hexagonal grid. 91 Towers seperated by 130m, 20 floors each. 30m between floors Floor Geometry Tower Geometry 20 floors per tower 30m seperation Between floors 8m 30m 45o 45o

9. Working Example 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

10. Results Atmospheric Muons (Corsika files - 1 hour of generated showers) (Time in days) Without any cuts (21000/day misrec. as upgoing) With optimal cuts (0 misrec. as upgoing) #hit>=12 #solutions>=20 #compatible>=10 #compatible / #sol >0.5 Mild likelihood cut depended on reconstructed energy Cos(theta)

11. Results Neutrino effective area (E-2 spectrum) Without any cuts Effective area (m2) With optimal cuts Neutrino Energy (log(E/GeV))

12. Results Neutrino Angular resolution (median in degrees) Without any cuts Angular resolution (median degrees) With optimal cuts Neutrino Energy (log(E/GeV))

13. Results Atmospheric neutrinos (Bartol Flux) Without any cuts (200/day rec.) 65% cut efficiency With optimal cuts (130/day rec.) (Time in days) (Time in days) Cos(theta) Neutrino Energy (log(E/GeV))

14. Results Muon energy reconstruction (at the closest approach to the detector) Simulation data from E-2 neutrino flux Log(Erec/GeV) Log(Etrue/GeV)

15. Results Muon energy reconstructionresolution Δ(Log(E/GeV)) RMS(Log(E/GeV)) Log(Etrue/GeV)

16. Work to be done • Calculation of point source sensitivities for varius depths (~ 2 weeks) • Simulation of more Geometries (Benchmark – MultiPMT string detector and more) (~ 2 weeks) • Optical photon scattering in GEANT4 simulation (~ 1 month)

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) 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

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 (criterion to decide the quality of the measurement) Covariance matrix of predicted residuals

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

24. 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:

25. 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.

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

27. 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