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Physics Laboratory

Physics Laboratory. School of Science and Technology. Hellenic Open University. Calibration, filtering and reconstruction strategies for KM3NeT. G. Bourlis , N. A. B. Gizani , A. Leisos , A. G. Tsirigotis , S.E. Tzamarias.

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  1. Physics Laboratory School of Science and Technology Hellenic Open University Calibration, filtering and reconstruction strategies for KM3NeT G. Bourlis, N. A. B. Gizani, A. Leisos, A. G. Tsirigotis, S.E. Tzamarias • Use of floating surface detector stations forthe calibration of KM3NeT • Estimation of the angular resolution of the KM3NeT by applying inter-calibration techniques • New filtering and reconstruction strategies WP2 Collaboration Meeting, 30-31 October 2007, Catania Italy In the framework of the KM3NeT Design Study

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

  3. Isotropic on the top of the atmosphere BUT … ~4km ~20km

  4. EAS Calibration Method - The Concept A floating array of EAS detectors can be used as a sea-topcalibration infrastructure, on top of the KM3NeT neutrino telescope. Such anarray can detect atmospheric showers and the collected data can be used for thereconstruction of the direction and the estimation of the impact parameter of the shower axis. Cosmicshowers with energiesabove 1014eV contain energetic muons able topenetrate the 4000m deep sea water and reach the KM3NeT detector. Thecomparison of the reconstructed muontrack parameters with the estimated shower axis: Floating stations Atmospheric Muon • Revealsany possible systematic angular error of the neutrino telescope and, • Providesthe absoluteposition of the undersea detector. Underwater Neutrino Telescope

  5. The SeaTop Detector – HELYCON Station • The EAS array used in this study consists of floating HELYCON (HEllenic LYceum Cosmic Observatories Network) scintillation counters. • Each HELYCON stationincludesa GPS antenna,digitization and controlelectronics and the data acquisition system controlled by a PC. • A single station is able to detectatmospheric showers initiatedby cosmic particles of energy more than 1014–1015 eV. • The reconstruction of the shower axis is based on the measurement of: • a) the arrival times and • b) the amplitude of the detector signals. Scintillator-PMT GPS Triangulation Shower Direction 1 m2 ~20 m Station Server DAQ

  6. The EAS Charged Particle Detector - DAQ • 1 m2active area scintillation counter. • The ReadOut system is based on aHPTDC chip, designed at CERN,with 5 analogue inputs. • The input signals are compared to sixadjustable thresholds and the corresponding times of thePMT waveform-threshold crossings are digitized with an accuracy of 100ps. • Thesynchronization between the HELYCONstations relies on theGPS time-signal which is incorporated in the data. Scintillator 1 Station Server Scintillator 2 Scintillator 3 GPS timestamp Scintillator 4

  7. Calibration and Test Results Global time resolution and slewing Slewing Scintillator A discriminators Lead Scintillator B Inputs Resolution Trigger Response to MIP • Data -Monte Carlo Prediction σ=2.8ns Local time resolution Charge (in units of mean p.e. charge) ΔT [ns]

  8. Observations of Extensive Air Showers - Resolution The performance of HELYCON in detecting andreconstructing showershas been studied by operatinga system of eight HELYCON detectors in thelaboratory. σ= 7.2ο±0.2ο MC Estimated resolution group A σAMC=4.5ο±0.5o , group B σBMC=5.2ο±0.6o, all six detectors σ6MC=3.5ο±0.3o. These resolutions can be evaluated solely from thereal data, by comparing the resultsobtained by the two detector groups (A andB) on an event by event basis. The distribution of the difference (Δθ=θΑ-θΒ) ofthese two estimations of the zenith angle has a spread of σDATA =7.2ο±0.2ο. This spread is consistent with the above MCpredictionsof the detector resolution:

  9. 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

  10. Monte Carlo Studies- Outlook1014 - 5·1015 eV E~ 1014 - 5·1015 eV: 2500 showers/m2/year Single station detection: 360m2 geometrical area (effective area depends strongly on selection cuts) E> 1016 eV: 1 shower/m2/year TO BE STUDIED 35% of the detected showers include a muon which arrives at the Neutrino Telescope (depth 4000m) with an energy >300GeV General Remark: 3 stations operating for 10 days can identify an angular offset of the KM3NeT with an accuracy of 0.05o Specifically…..

  11. Investigation for a systematic angular offset of the KM3NeT σ1(na) Aeff(na) [m2] na na We use EAS that contain at least one energetic muon reconstructed by the KM3NeT and compare the estimated zenith angles of the shower axis andthe muon track on an event by event basis.The difference between these two angles should follow a normal distributionwith mean zero.A possible statistically significant deviation from zeroindicatesthat the estimations of the KM3NeT suffer from a systematicangularoffset. The spread of thisdistribution expressesthe calibration resolution per shower event. Calibration resolution per single shower event (degrees) Effective area of a floating detector station na : minimum number of active detectors per shower event

  12. Investigation for a systematic angular offset of the KM3NeT σc(na) [degrees] na The calibration resolutionper single shower decreases when events with more active detectors areselected, as shown before, because the reconstruction accuracy of theshower’s direction improves. However, the requirement of more active detectorsperevent results to a reduction of the effective area of the floating detectorarray. The calibration resolution, σc(na), in identifying a possible angular offset inthe neutrino telescope estimations using the three floating detector arrays, is: For 3 EAS detector stationsand 10 days of operation the calibration resolution has a minimum for na≤5 . The proposed calibrationsystem will be able to measure a possible zenith angle offsetwith an accuracy of ~0.05o. minimum number of active detectors per shower event.

  13. Determination of the KM3NeT Absolute Position (a) na (b) na The resolution in estimating the (X-Y) coordinates of the under-water detector, as afunction of the number of active detectors per shower event, using: (a)single reconstructedEAS and (b) showers collected by three floating arrays during 10 days of operation. The proposed technique can estimate the absoluteposition of the neutrino telescope with an accuracy ~0.6m.

  14. Estimation of the angular resolution of the KM3NeT – (Inter-Calibration) KM3NeT’s resolution measurement Impossible using EAS array KM3NeT resolution ~ 0.1 deg EAS Detector resolution ~ 1 deg (Inter-Calibration) • Divide the detector in 2 identical sub detectors • Reconstruct the muon separately for each sub detector • Compare the 2 reconstructed track directions Working Example IceCube Geometry 9600 OMs looking up & down in a hexagonal grid. 80 Strings, 60 storeys each. 17m between storeys MultiPMT Optical Module 125m

  15. Resolution Estimation (1 TeV Muons, isotropic flux, IceCube Geometry, 9600 OMs) Mean 12 hits Number of active OMs in one subdetector Mean 24 hits Number of active OMs in whole detector • Simulatedevents with at least 14 active OMs, after filtering out the background hits. • The selected sample consisted, in average, of 24active OMs per event, whilst the remaining contamination from K40 backgroundhits was less than 0.5 OM per event. • Each muon track was reconstructed usingthe information from the whole set of the active OMs as well as using the datafrom the two sub-groups, each containing the half of the selected OMs.

  16. Resolution Estimation (1 TeV Muons, isotropic flux, IceCube Geometry, 9600 OMs) σ=0.07o±0.003o σ=0.095o ±0.005o Zenith angle resolution of subdetectors (degrees) Zenith angle resolution of whole detector (degrees)

  17. Resolution Estimation (1 TeV Muons, isotropic flux, IceCube Geometry, 9600 OMs) σ=0.14o±0.01o Zenith angle difference between the 2 reconstructed directions (degrees) Space angle difference between the 2 reconstructed directions (degrees) ≈ 0.095o ±0.005o

  18. 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 • Χ2fit without taking into account the charge (number of photons) • Kalman Filter (novel application in this area)

  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 – 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:

  24. 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

  25. Chi-square vs Kalman Filter – Comparison (1TeV muons isotropic flux) With initial background filtering Space angle resolution Zenith angle resolution σ=0.081±0.004 σ=0.074±0.004 KF KF degrees degrees degrees degrees efficiency = 56% KF efficiency = 54%

  26. Chi-square vs Kalman Filter – Comparison (1TeV muons isotropic flux) Without initial background filtering Space angle resolution Zenith angle resolution KF KF degrees degrees degrees degrees efficiency = 11% KF efficiency = 38%

  27. Conclusions The operation of 3 stations (3x16 counters) for 10 days will provide: • The determination of a possible angular offset of the KM3NeT with an accuracy ~ 0.05 deg • The determination of the absolute position of the KM3NeT with an accuracy ~ 0.6 m • Efficiency vs Energy and Zenith angle… Resolution can be estimated through the inter-calibration technique Kalman Filter is a promising new way for filtering and reconstruction for KM3NeT Presented by Apostolos G. Tsirigotis Email: tsirigotis@eap.gr

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