Pixel TPC simulation and reconstruction Kees Ligtenberg, Peter Kluit, Jan Timmermans ILD Software and Technical Meeting Lyon 25 April 2017 Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 1 / 21
Outline Introduction 1 Simulation 2 Pads Pixels Reconstruction 3 Pads Pixels Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 2 / 21
Readout of the ILD TPC Baseline TPC endplate Micromegas or GEM amplification Readout with ≃ 6mm × 1mm sized pads Endplate with timepix3 chip with integrated grid under development Integrated amplification grid Readout with a 256 × 256 grid of 55 µ m × 55 µ m pixels New timepix3 chip offers improved time resolution and data-acquisition Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 3 / 21
Simulation of pads within ilcsoft version 01-17-09, ILD o1 v5 Detector is described by DD4HEP geometry y Pads have ideal 100% coverage Geant4 processes interactions of particle(s) from gun or event x Single hit in TPC is deposited if energy is above threshold (32eV) in a single pad. Position of pad centre crossing is recorded Volumes are organised as Diffusion and hit resolution is simulated by tube shaped layers, smearing the hits by the expected resolution in there are no pad columns r φ and z directions Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 4 / 21
Simulation of pixels Pixels are described by the same cylindrical volumes in DD4HEP Pixels also have ideal 100% coverage Multiple hits per row can be deposited In order to simulate diffusion, hits are smeared transverse to track in x , y and z directions Interpolate the track with a parabola over a volume of 0 . 99 mm (18 pixel rows) x 2 φ 2 ∆ s x 1 φ 1 Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 5 / 21
Distribution of hits along the track Ionization in gas follows roughly a Landau distribution Approximate by a combination of a Poisson and a triangle (for now) normalised frequency 0.9 µ 55x55 m pixels Interpolation depositing single hits (Poisson-like) 0.8 Interpolation with a 0.1 chance to draw from a triangle distribution 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 number of hits Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 6 / 21
Pad simulation of a 700 MeV muon Simulated pad hits are only at layer centre crossing Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 7 / 21
Pixel simulation of a 700 MeV muon Interpolated pixel hits are placed everywhere along the track Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 8 / 21
Simulation of pad hits compared to pixel hits 6 mm 55 µ m 18 rows 990 µ m Pad hits Pixel hits 6 mm × 1 mm 55 µ m × 55 µ m Exactly one hit per layer Multiple or no hits per layer 22 electrons per hit 1 electron per hit Only diffusion in r φ and z Diffusion in x , y and z ∼ 200 hits per track ∼ 10 000 hits per track Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 9 / 21
Track finding for pads using Clupatra Tracker hits Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 10 / 21
Track finding for pads using Clupatra 1 Seed finding ◮ Uses nearest neighbour clustering by distance in a pad row range of 15 rows Seeds Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 10 / 21
Track finding for pads using Clupatra 1 Seed finding ◮ Uses nearest neighbour clustering by distance in a pad row range of 15 rows 2 Fit track to seeds ◮ use first, middle and last hit to initialise track parameters 3 Extend track inwards (and outwards) ◮ Uses Kalman filter (Kaltest) in MarlinTrk Seed fit and extended Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 10 / 21
Track finding for pads using Clupatra 1 Seed finding ◮ Uses nearest neighbour clustering by distance in a pad row range of 15 rows 2 Fit track to seeds ◮ use first, middle and last hit to initialise track parameters 3 Extend track inwards (and outwards) ◮ Uses Kalman filter (Kaltest) in MarlinTrk Track fit 4 Merge split segments Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 10 / 21
Fit tracks by Extended Kalman filter Fit track by an Extended Kalman Filter: a recursive fitting algorithm working in steps: Predict state at next site using propagator a k − 1 = f k ( a k ) k ◮ a k contains track parameters ( d ρ , φ 0 , κ, d z , tan λ ) Update with measurement m k using state-to-measurement projector h k ( a k − 1 ) k ◮ Add hit and update if χ 2 < χ 2 threshold (=35) ◮ m k are coordinates of a cylindrical surface ( r φ, z ) Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 11 / 21
Issues when applying pad-track-reconstruction to pixel-hits Seed finding: CPU time of nearest neighbour clustering scales as O ( N 2 ) Unsuitable for many thousands of pixel hits Track fit: initialise Kalman filter with first, middle and last hit 3 hits do not fix the track tight enough, first hits can pull the track fit in the wrong direction Hits restricted to a cylindrical surface For pixel another representation is more suitable Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 12 / 21
Track finding for pixel TPC Perform clustering by φ (Hough-transform like) ◮ Fill histogram of hits by φ in pad row range of 750 pixel rows ◮ Maximum bin is cluster with track candidate if more than 200 hits ◮ construct a straight line from the detector center to the average position ◮ Cut hits on distance from this line (10mm in r φ and 3mm rz ) ◮ initialise track fit with this line Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 13 / 21
Track fitting for pixel hits d 0 hit φ track Define alternative measure with m k as a function of a k − 1 k � d 0 � � � ∆ x sin( φ track ) − ∆ y cos( φ track ) m k ( a k − 1 ) = = k z hit + tan λ (∆ x cos( φ track ) + ∆ y sin( φ track )) , z The distance to the track d 0 better represents the measurement Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 14 / 21
Fit of straight track 50 GeV muon Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 15 / 21
Fit of curled track 1 GeV muon without energy loss Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 16 / 21
Fit of curled track 1 GeV muon without energy loss Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 17 / 21
Momentum resolution from track fit 50 GeV muon ] -1 − 1 10 [GeV pixel (without deltas) pad 1/pT − 2 10 σ − 3 10 − 4 10 − 5 10 6 ratio 4 2 0 0 10 20 30 40 50 60 70 80 90 θ [degree] Pixels hits simulated with delta’s, but rejected before reconstruction Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 18 / 21
Pull of 1 / p T from 8 × 1000 tracks of 50 GeV muons 0.2 2.2 of pull of pull Pad 0.15 µ σ 2 Pixel 0.1 1.8 0.05 1.6 0 1.4 − 0.05 1.2 − 0.1 − 1 0.15 − 0.2 0.8 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 θ θ [degrees] [degrees] σ of pull is too large at Mean µ does not indicate any angles with the best biases momentum resolution Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 19 / 21
Distortion of σ of pull 0.8 [GeV] Pixel expected resolution (without deltas) Pad expected resolution 0.7 pT Pixel resolution without smearing σ Pad resolution without smearing 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 80 90 θ [degrees] p T difference between input and fit to unsmeared hits is ∼ 40 MeV σ of pull is increased by precision settings or a bug in the code Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 20 / 21
Conclusion A muon track was successfully simulated and reconstructed with a pixel readout First estimates of the pixel readout performance show a factor ∼ 2 − 6 improvement over to the pad readout Next steps: ◮ Fix pull of track fit ◮ Do delta rejection using an algorithm ◮ Continue studies of performance of pixel readout ◮ Investigate dE / dx performance ◮ Implement an endplate layout with more realistic coverage ( ∼ 80%) ◮ Simulate and reconstruct physics events with a pixel readout Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 21 / 21
Momentum resolution from track fit covariance matrix 50 GeV muon 1 [GeV] pad pixel (without deltas) 0.9 pT σ 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 80 90 θ [degree] Kees Ligtenberg (Nikhef) Pixel TPC simulation and reconstruction 25 April 2017 22 / 21
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