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Clustering and Track Association in Digital Calorimeters for Multi-Particle Events

This study presents a novel approach for clustering and track association in digital calorimeters, specifically focusing on charged pions with a 10 GeV energy level. The methodology involves analyzing energy-weighted resolutions and local density maxima to enhance hadronic position resolution. By iteratively refining centroids and employing distance functions for membership determination, we achieved promising results. This algorithm shows potential for broader applications in multi-particle events and could provide valuable feedback into calorimeter design and particle identification strategies.

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Clustering and Track Association in Digital Calorimeters for Multi-Particle Events

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  1. EF with simple multi-particle states Vishnu V. Zutshi NIU/NICADD

  2. Hadron Position Resolution • Since Eflow invariably involves associating clusters near an extrapolated track … • How to do this in a digital calorimeter ? • Study this using charged pions • Resolution is defined w.r.t. the MC extrapolated position

  3. 10 GeV charged pions Energy weighted unweighted Density weighted

  4. 10 GeV charged pions

  5. “Density” • Need a hierarchy in the absence of an energy measurement • Clumpiness of the surrounding • A simple-minded realization of this used here: di = S (1/dRij) where dRij is the angular distance between cell ‘i’ and cell ‘j’

  6. Thanks Ben 10 GeV p unweighted Measured relative to the energy weighted resolutions Cell area at first layer=0.64cm2 Density weighted

  7. 10 GeV p unweighted Measured relative to the energy weighted resolutions Cell area at first layer=4cm2 Density weighted

  8. 10 GeV p unweighted Measured relative to the energy weighted resolutions Cell area at first layer=6cm2 Density weighted

  9. 10 GeV p unweighted Measured relative to the energy weighted resolutions Cell area at first layer=9cm2 Density weighted

  10. 10 GeV p unweighted Measured relative to the energy weighted resolutions Cell area at first layer=12cm2 Density weighted

  11. 10 GeV p unweighted Measured relative to the energy weighted resolutions Cell area at first layer=16cm2 Density weighted

  12. 2GeV Photons maxima maxima maxima

  13. Clustering • Local ‘density’ maxima chosen as seed clusters • Membership of each cell in the seed clusters decided with a distance function • Calculate centroids • Iterate steps 2 and 3 till distortion is below some threshold Could be unique or shared

  14. Parameters • Cell thresholds • How many layers to lump together • Neighborhood for maxima search • Minimum no. of layers hit • Neighborhood for membership • Proto-cluster definition • Uniqueness of membership

  15. 10 GeV p0 Density weighted q-f High asymmetry

  16. 10 GeV p0 Density weighted q-f Medium asymmetry

  17. 10 GeV p0 Density weighted q-f Low asymmetry

  18. 10 GeV p0 Density weighted q-f Low asymmetry

  19. 10 GeV p0 Recon. energy Recon. mass 18%

  20. 10 GeV p0 Recon. energy Recon. mass

  21. Energy asymmetry A = abs(Eg1 – Eg2)/(Eg1 + Eg2)

  22. S+ pp0 p Density weighted q-f p0

  23. S+ pp0 p Density weighted q-f

  24. S+ pp0 Eflow Cal only E/Egen

  25. S+ np+ p+ EMCal n HCal p

  26. S+ np+ n EMCal p HCal

  27. S+ np+ Not reliable due to noncompensation recE (p) genE (p)

  28. S+ np+ • Get the e/pi for the SD detector • Scale the MC truth with that function • Take the ratio of the reconstructed pion energy with the scaled MC truth • This should have a mean of 1.0 (with an atrocious resolution) if things are working ok

  29. S+ np+

  30. Summary/Outlook • A first pass clustering/track association algorithm exists applicable to EM/HAD, both analog/digital • Encouraging results for multiparticle events • More detailed study to expand and enhance (for instance particle id) • Move to jets • Feedback into calorimeter design

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