C Ainsley

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Published on October 15, 2007

Author: Gourmet

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Cluster finding in CALICE calorimeters:  Cluster finding in CALICE calorimeters Chris Ainsley University of Cambridge, UK <ainsley@hep.phy.cam.ac.uk> General CALICE meeting: simulation/reconstruction session 28-29 June 2004, CERN, Switzerland Motivation:  Motivation Desire for excellent jet energy resolution at future LC  calorimeter needs to be highly granular to resolve individual particles within jets;  calorimeter will have tracker-like behaviour: unprecedented;  novel approach to calorimeter clustering required. Aim to produce a flexible clustering algorithm, independent of ultimate detector configuration and not tied to a specific MC program. Develop within an LCIO-compatible framework  direct comparisons with alternative algorithms can be made straightforwardly. Order of service:  Order of service Tracker-like clustering algorithm in outline. Generalisation of the full detector geometry. Application to single-particle cluster reconstruction. Application to multi-particle cluster reconstruction: Z event at 91 GeV (W-Si Ecal, Fe-RPC Hcal); W+W- event at 800 GeV (W-Si Ecal, Fe-RPC Hcal). Summary and outlook. Tracker-like clustering algorithm in outline:  Tracker-like clustering algorithm in outline Sum energy deposits within each cell. Retain cells with total hit energy above some threshold (⅓ MIP; adjustable). Form clusters by tracking closely related hits layer-by-layer through calorimeters: for a given hit j in a given layer l, minimize the angle b w.r.t all hits k in layer l-1; if b < bmax for minimum b, assign hit j to same cluster as hit k which yields minimum; if not, repeat with all hits in layer l-2, then, if necessary, layer l-3, etc.; after iterating over all hits j, seed new clusters with those still unassigned; calculate centre-of-energy of each cluster in layer l; assign a direction cosine to each hit along the line joining its clusters’ seed (or {0,0,0} if it’s a seed) to its clusters’ centre-of-energy in layer l; propagate layer-by-layer through Ecal, then Hcal; retrospectively match any backward-spiralling track-like cluster fragments with the forward-propagating cluster fragments to which they correspond using directional and proximity information at the apex of the track. Geometry generalisation (1):  Geometry generalisation (1) Layers Pseudolayers Layer index changes discontinuously at: (i) Ecal barrel stave boundaries; (ii) barrel/endcap boundaries. Define “pseudolayers” as surfaces of coaxial octagonal prisms  discontinuities removed; pseudolayer indices vary smoothly. Geometry generalisation (2):  Geometry generalisation (2) Staves Pseudostaves Stave = plane of parallel layers Pseudostave = plane of parallel pseudolayers Geometry generalisation (3):  Geometry generalisation (3) Clustering algorithm works as described earlier, but with layers replaced by pseudolayers  pseudolayer index changes smoothly;  clusters are tracked with continuity across stave boundaries. Pseudolayers/pseudostaves are defined automatically by the intersection of the real, physical layers  only need distances of layers from {0,0,0} and their angles w.r.t. each other to construct these;  idea applies to ANY detector design comprising an n-fold rotationally symmetric barrel closed by a pair of endcaps! Single-particle reconstruction:  Single-particle reconstruction 15 GeV e- 15 GeV p- 91 GeV Z event: Full detector:  91 GeV Z event: Full detector Reconstructed clusters True particle clusters 91 GeV Z event: Zoom 1:  91 GeV Z event: Zoom 1 Reconstructed clusters True particle clusters 91 GeV Z event: Zoom 2:  91 GeV Z event: Zoom 2 Reconstructed clusters True particle clusters 91 GeV Z event: Performance:  Fraction of true cluster energy in each reconstructed cluster 91 GeV Z event: Performance Fraction Reconstructed cluster ID True cluster ID True cluster ID True cluster ID Reconstructed cluster ID Reconstructed cluster ID Fraction Fraction Fraction of event energy in each true-reconstructed cluster pair Fraction of reconstructed cluster energy in each true cluster 15 highest energy reconstructed and true clusters plotted. Reconstructed and true clusters tend to have a 1:1 correspondence. Averaged over 100 Z events at 91 GeV: – 87.7 ± 0.5 % of event energy maps 1:1 from true onto reconstructed clusters; – 97.0 ± 0.3 % of event energy maps 1:1 from reconstructed onto true clusters. 800 GeV W+W- event: Full detector:  800 GeV W+W- event: Full detector Reconstructed clusters True particle clusters 800 GeV W+W- event: Zoom 1:  800 GeV W+W- event: Zoom 1 Reconstructed clusters True particle clusters 800 GeV W+W- event: Zoom 2:  800 GeV W+W- event: Zoom 2 Reconstructed clusters True particle clusters 800 GeV W+W- event: Performance:  Fraction of true cluster energy in each reconstructed cluster 800 GeV W+W- event: Performance Fraction Reconstructed cluster ID True cluster ID True cluster ID True cluster ID Reconstructed cluster ID Reconstructed cluster ID Fraction Fraction Fraction of event energy in each true-reconstructed cluster pair Fraction of reconstructed cluster energy in each true cluster 15 highest energy reconstructed and true clusters plotted. Reconstructed and true clusters tend to have a 1:1 correspondence. Averaged over 100 W+W- events at 800 GeV: – 83.3 ± 0.5 % of event energy maps 1:1 from true onto reconstructed clusters; – 80.2 ± 1.0 % of event energy maps 1:1 from reconstructed onto true clusters. Summary & Outlook:  Summary & Outlook R&D on clustering algorithm for calorimeters at a future LC in progress. Approach mixes tracking and clustering aspects to utilize the high granularity of the calorimeter cells. Starts from calorimeter hits and builds up clusters – a “bottom up” approach (cf. “top down” approach of G. Mavromanolakis). Can be applied to any likely detector configuration  straightforward to try out alternative geometries. Works well for single-particles events. Good performance for 91 GeV Z events. Encouraging signs for 800 GeV W+W- events. Runs in the LCIO (v.1.0) framework: hits collection → clusters collection (awaiting next version to make full use of cluster object methods)  straightforward to try out alternative algorithms.

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