First look at PFA/clustering with RPC-based calorimeter

1. 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 cm2 readout pads • Pad multiplicity = 1 • p+ 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: • DE/E= 0.132, or • DE/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 F~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’ F~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 cm2. 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<dcut • Here the example of 20 GeV charged pion, dcut=5 cm • ‘Objetcs’ found: • Clusters • Single points

8. Cartesian distance, typical example • 20 GeV p+ • dcut = 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 pt 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