A Study on Cluster Resolution Neighborhood hit density gradients are proposed as a means for -- identifying cluster boundaries -- implementing a cluster split/merge strategy Relies on the inspection of “calorimeter domains” – collections of connected cells gang’ed as projective towers. Currently coded in “box form”  ( n x m x l ) cells as segmented in ( theta,phi,layer ). A tool to be used as a sup- port to clustering algorithms. Equally applicable to both analogue and digital readouts. A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002 γ1γ1 γ2γ2 neighborhood hit density gradients

EM shower profiles suggest pre-clustering box of 4x4 cells. Locate (4 x 4 x all) domain with highest energy (or #hits). Inspect neighborhood w/ grads; i.e. find (Rmin, Gmin) and (Rmax,Gmax). If Gmax > k *Gmin, then a secondary cluster is declared found (currently using k = 2 ). Rmin & Rmax determine a search area for “next-hottest” (4 x 4 x all) domain. Cross check that γ 2 cluster also “sees” γ 1 Use both sets of R & G(min,max) to re-size clusters. γ1γ1 search area for γ 2 Cluster ID Calorimeter Domain Methods Rmin+1 RminRmax Rmax + size Gmin Gmax A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002

γ γ distance, generated (cm) γ γ distance, reconstructed (#of cells) 5000 events superimposed (#of cells) 1= layers = layers π 0 ( 10GeV )  γ γ 5K single- π 0 events neighborhood 2 is tested if neighborhood 1 fails 1 cell = 0.5 cm A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002

inefficiency GeV Generated (upper).vs. “Reconstructed” (lower) A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002

Domain (Projective Box) Energy Resolution A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002

Layer energy centroid position fluctuations across layers (distances in cell units) γ 1 pre-cluster γ 1 re-sized γ 2 pre-cluster γ 2 re-sized A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002

A series of event displays for 10GeV π 0  γ γ with the associated neighborhood gradients analysis as an illustration of the method.

Event 81 Evt# 81 Gamma1: ThetaBin=420 PhiBin=213 Reco Energy = 4.87 MC Energy = 5.28 Gamma2: ThetaBin=417 PhiBin=204 Reco Energy = 4.39 MC Energy = 4.72 Example of a ~symmetric decay Neighborhood Grads

Event 81 γ 1 “looks at” γ 2 layers used: 0--9 γ 2 “looks at” γ 1 layers used: 0--9 distance, in number of cells

Event 36 Example of an asymmetric decay Evt# 36 Rmin1 = 4, Rmax1 = 9 Rmin2 = 36, Rmax2 = 9, DeltaR = 10 Gamma1: ThetaBin=420 PhiBin=288 Box-Reco Energy=8.09 ( MC = 8.88 ) Gamma2: ThetaBin=410 PhiBin=289 Box-Reco Energy=1.33 ( MC = 1.12 ) Neighborhood Grads

Event 36 γ 1 “looks at” γ 2 layers used: 0--9 γ 2 “looks at” γ 1 layers used: 0--9 distance, in number of cells

Event 48 Evt# 48 (how it can get tricky...) Gamma1 Energy=8.10 MC = 9.50 Gamma2 Energy=0.31 MC = 0.50 γ1γ1 γ2γ2 “dirt” Neighborhood Grads

Event 48 γ 1 “looks at” γ 2 layers used: 0--9 γ 2 “looks at” γ 1 layers used: 0--9 distance, in number of cells “dirt” γ1γ1 γ2γ2 γ2γ2 γ1γ1 Note: “Grads” search was cylindrical (as opposed to directional, in theta and phi)

Event 184 Neighborhood Grads Evt# 184 ( A case of extreme asymmetry ) Gamma1: ThetaBin=419 PhiBin=1603 Reco Energy=9.45 MC Energy = 9.98 Gamma2: ThetaBin=414 PhiBin=1588 Reco Energy=0.050 MC Energy=0.021

Event 184 γ1γ1 γ2γ2 γ2γ2 layers 0—9 cannot detect gamma_2 layers 10—19 layers 20—29 layers 0—9 Rmin1 = 10, Rmax1 = 13 hsize1 = 13, DeltaR = 15 (*) clearly, any level of noise here turns this into an inefficiency... (*)

Event 284 Evt# 284 (Gamma_2 is a late shower) Gamma1: ThetaBin=419 PhiBin=1492 Reco Energy=7.91 MC Energy=8.04 Gamma2: ThetaBin=417 PhiBin=1483 Reco Energy=2.15 MC Energy=1.96 Neighborhood Grads

Event 284 Rmin2 = 4 Rmax2 = 8 DeltaR = 9 Rmin1 = 4 Rmax1 = 7 hsize1 = 5 γ1γ1 layers 0—9 cannot detect gamma_2 γ1γ1 γ2γ2 γ2γ2 γ1γ1 layers 20—29 layers 10—19 layers 0—9 γ1γ1 γ2γ2

EM Shower Characteristics in the “SD” Detector Model The next two slides display shower profiles for electrons and gammas respectively Profiles are averaged over samples of 5000 monochromatic single particles (10GeV) All plots are longitudinal profiles, where the x-axis labels the layer number -- Energy deposition per layer-- Layer hosting hottest cell -- Number of hits per layer-- Layer mean square radius (*) (*) definition; A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002

SD – 10GeV single γ’s in Em-Cal (5k evts.) GeV n.of cells energy-weighted transverse shower radius (in #of cells) shower-max hit-max A. Maciel (NIU), Simulation & E-flow Wshop, NIU, November 7-9, 2002