1. HOU Reconstruction & Simulation (HOURS): A complete simulation and reconstruction package for Very Large Volume underwater neutrino Telescopes. A.Leisos, A. G. Tsirigotis, S.E.Tzamarias In the framework of the KM3NeT Design Study VLVnT 2009 - Athens, 15 October 2009

2. The HOURS software chain Underwater Neutrino Detector Generation of atmospheric muons and neutrino events (F77–CORSIKA,Pythia) Detailed detector simulation (GEANT4-GDML) (C++) Optical noise and PMT response simulation (F77) Filtering Algorithms (F77 –C++) Muon reconstruction (C++) Effective areas, angular resolution and sensitivities calculation (scripts) Extensive Air Shower Calibration Detector (Sea Top) Atmospheric Shower Simulation (CORSIKA) – Unthinning Algorithm (F77) Detailed EAS detector response Simulation (GEANT4) (C++) Reconstruction of the shower direction (F77) Muon Transportation to the Underwater Detector (C++) Estimation of: resolution, offset (F77)

3. CORSIKA (Extensive Air Shower Simulation) All Flavor Neutrino Interaction Events (Secondary Particles Generation) Atmospheric Muon Generation from CORSIKA GEANT4 (KM3NeT Detector Description and Simulation) GEANT4 (Muon Propagation to KM3NeT) Optical Noise, PMT response and Electronics Simulation Prefit & Filtering Algorithms Muon Reconstruction EAS detector Simulation Shower direction reconstruction The HOURS software chain Flow Chart SeaTop Calibration Neutrino Telescope Performance

4. Event Generation – Flux Parameterization Neutrino Interaction Events (PYTHIA) Atmospheric Muon Generation (CORSIKA) μ Atmospheric Neutrinos (Bartol Flux) ν ν Cosmic Neutrinos (AGN – GRB – GZK and more) Earth

5. Event Generation – Shadowing of neutrinos by Earth Earth Density Profile Column Depth Survival probability Nadir Angle Probability of a ν μ to cross Earth

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

7. 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

8. 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 technique) Combination of Χ 2 fit 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 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)

9. 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

10. State vector Initial estimation Update Equations Kalman Gain Matrix Updated residual and chi- square contribution (rejection criterion for hit) timing uncertainty 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. Kalman Filter – Muon Track Reconstruction - Algorithm

11. Muon Track Reconstruction Chi-square probability Energy (log(E/GeV)) Neutrino Muon Angular resolution

12. 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 Ln(F(n)) Ln(n) E=1TeV D=37m θ=0deg Log(E/GeV)

13. Log(E true /GeV) Log(E reco /GeV) Log(E/GeV) Simulation data from E -2 neutrino flux and SeaWiet detector (300 Strings, 130m between strings, 20 MultiOMs/string, 40m MultiOM distance) True muon energy at the closest approach to the detector center (impact point) Δ(Log(E/GeV)) True and reconstructed muon energy distribution Muon energy reconstruction Results 1

14. Muon energy reconstruction Results 2 Log(E true /GeV) RMS(Δ(Log(E/GeV))) Mean(Δ(Log(E/GeV)))

15. Neutrino Detector Performance Atmospheric Muon background + Atmospheric Neutrino Background signal Point Source Sensitivity m2m2 Neutrino Energy (log(E/GeV)) Angular resolution (median) degrees Neutrino Energy (log(E/GeV)) Neutrino Effective area

16. Sea top Detector Simulation Tools CORSIKA (Extensive Air Shower Simulation) GEANT4 (Scintillation, WLS & PMT response) Fast Simulation also available Unthinning Algorithm

17. DAQSIM (DAQ Simulation) HOUANA (Analysis & Track Reconstruction) Zentih (degrees) Sea top Detector Simulation Tools Charge (in units of mean p.e. charge) At the Detector Center  Data - Monte Carlo Prediction

18. GEANT4 Muon Propagation to KM3 HOU-KM3 Muon track (s) reconstruction 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) Sea top Detector Simulation Tools

19. Conclusions The study of the response of a km3-scale underwater neutrino telescope is a crucial point both for the design of the detector and for the experimental analysis. The HOU Reconstruction & Simulation (HOURS) software package is a complete simulation package of the detector response from the expected neutrino fluxes to the event reconstruction and sensitivity estimation for different neutrino sources.

20. GEANT4 Simulation – Detector Description Any detector geometry can be described in a very effective way Use of Geomery Description Markup Language (GDML, version 2.5.0) software package All the relevant physics processes are included in the simulation ParticlePhysical Processes AllDecays (unstable), multiple scattering (charged), continuous energy loss, ionization and δ-ray production (charged), Cherenkov effect (charged) μ-/μ+μ-/μ+ Bremsstrahlung, photonuclear interaction, direct (e +,e - ) pair production e - /e + Bremsstrahlung, e + e - annihilation γγ conversion, photoelectric effect, Compton scattering HadronsHadronic Interactions Optical Photons Absorption, medium boundary interactions