1. Adam Para, October 14, 2005 First look at PFA/clustering with RPC-based calorimeter Progress Report

2. Step 1: Gas calorimetry GEANT 3.21 modeling Hadron shower simulation (GCALOR+GFLUKA) consistent with MINOS test calorimeter 2 cm iron, 1x1 cm 2 readout pads Pad multiplicity = 1  + with p = 2,5,10,20,50,100 GeV/c, 1000events at each momentum Significant non—linearity of the response (~20% @ 100 GeV) Large constant term (~10%) for the energy resolution Why ?

3. Gas calorimetry ctnd 20 GeV:  E/E  0.132, or  E/E=0.59 /√ E Fairly gaussian response 2 GeV (‘low energy’): long tail towards higher response It is caused by particles traversing long distance before the interaction Expect very large difference in the response to charged and neutral particles 100 GeV (‘high energy’): long tail towards low energies caused by multiply hit cells inside EM showers saturation leads to degradation of energy (constant term, non-linearity)

4. PFA: what do we want? PFA Challenge: identify and discard all red/green points Identify and count all blue points Chief (?) difficulties: identify ‘blue’ cluster in the midst of the red/green one Properly identify the disconnected red cluster (a.k.a. ‘fragment’)

5. PFA: is it obviously impossible? Yes? Hadrons impact the calorimeter at ~ 10 cm distance Hadronic shower has transverse dimension of  ~40-50 cm Hadronic showers are extremely irregular, they do not follow ‘shower profile’ No? Hadronic showers are extremely irregular, they do not follow ‘shower profile’ Shower develops in 3 dimensions. ALL displays are projections on 2D plane and they convey unnecessarily pessimistic picture Although to contain the shower energy one needs a ‘cylinder’  ~40-50 cm, L=100 cm for any particular hadron shower this cylinder is very sparsely occupied. Example: such a cylinder contains ~8,000 readout cells, 1 x 1 cm 2. Only ~ 1000 of them are hit. Occupancy is ~12%

6. PFA Challenge: develop a metric in the hit cells space which optimizes the separation of ‘charged hadron cluster’ from ‘neutral hadron clusters’ Figure of merit: minimize fluctuations of the energy in the clusters classified as ’neutral hadrons’ about the true energy of the neutral hadrons Auxiliary information: momentum and spatial position of charged hadrons, possibly energy deposition in the hit cell

7. First try: cartesian distance Find trees of hits with close proximity, d<d cut Here the example of 20 GeV charged pion, d cut =5 cm ‘Objetcs’ found: Clusters Single points

8. Cartesian distance, typical example 20 GeV  + d cut = 20 cm

9. Total energy of the ‘main cluster’ High energy showers are more collimated, hit cells are closer

10. “Fragments” multiplicity and energy Energy of the ‘second’ cluster (~10 hits = 1 GeV) Total number of clusters found

11. Leftovers: single hits ‘free floating’ single hits are probably harmless, there are so few of them that they will not lead to accidental cluster formation Ignoring scattered single one modifies the effective energy calibration (1-2% effect) but induced non-linearity of the response is minimal.

12. This was the simplest choice. Metric closest to ones intuition, but surely not the optimal one. ‘Improvement’: showers are cigars rather than spheres as p t of particles produced in hadronic interaction is limited to ~ 300 MeV/c. Transverse distance between cells less likely than the longitudinal one

13. ‘Transverse metric’ I Significant improvement: better energy containment in the main cluster, smaller secondary cluster

14. ‘Transverse metric’ II Significant improvement: fewer secondary clusters, fewer left-over cells