Physics Laboratory

1. Physics Laboratory School of Science and Technology Hellenic Open University HOU contribution to KM3NeT TDR (WP2) A. G. Tsirigotis EESFYE - Demokritos, 22May 2009 In the framework of the KM3NeT Design Study

2. The HOU software chain • Underwater Neutrino 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) • Extensive Air Shower Calibration Detector (Sea Top) • 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 • (OPTICAL PHOTON SCATTERING ALSO) 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. 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.

6. 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 technique) • Combination 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

7. 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.

8. Charge Likelihood – Used in muon energy estimation 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)

9. Working Example 60 meters maximum abs. length no optical photon 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

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

11. 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) #hits>=12 #solutions>=20 #compatible solutions>=10 #compatible / #sol >0.5 Mild likelihood cut depended on reconstructed energy Cos(theta)

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

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

14. Results Muon Angular resolution (For the neutrino induced muon at impact point) With optimal cuts Neutrino Angular resolution (median degrees) Muon Energy (log(E/GeV))

15. 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))

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

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

18. Use of Extensive Air Shower detector stations forthe calibration of KM3NeT The General Idea… • Angular offset • Efficiency • Position Physics ? C.R. composition UHE ν - Horizontal Showers Veto atmospheric background – Study background

19. SeaTop Detector – Station Setup Station 5m 19m 1 m2 Scintillation Counter 19m - Three Floating Stations operating independently above KM3NeT- Distance between stations 150m- 16m2 Scintillator Each Station

20. Simulation Results Position calibration resolution σc(na) [degrees] na minimum number of active EAS detectors per shower event. na Angular calibration resolution minimum number of active EAS detectors per shower event. For 3 EAS detector stationsabove KM3NeT and 10 days of operation the proposed calibrationsystem will be able to measure a possible zenith angle offsetwith an accuracy of ~0.05o and can estimate the absoluteposition of the neutrino telescope with an accuracy ~0.6m.

21. Application of the Sea-Top calibration method for ANTARES Neutrino Telescope Simulation Results 5 days sea campaignwith a surface arraymadeof 10 scintillators distributed on an area of 13 × 23m2 will reveal asystematic error ofabout 0.5 degrees on the zenith angle reconstructed by thetelescope.

22. We are finalizing • Calculation of point source and diffuse flux sensitivities for varius depths (with energy cut application) • Simulation of more KM3NeT Detector Geometries • Calibration of ANTARES Neutrino Telescope with Sea-Top More work to be done

23. 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 Charge Likelihood can be used effectively in energy reconstruction The operation of 3 SeaTop stations (3x16 counters) for 10 days will provide the determination of a possible angular offset of the KM3NeT with an accuracy ~ 0.05 deg Presented by Apostolos G. Tsirigotis Email: tsirigotis@eap.gr

25. 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

26. 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

27. 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)

28. 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)

29. 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

30. 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:

31. 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