1. Detector Configuration for Simulation (i)
Material: Tungsten powder with polystyrene fibers
Dimensions: 0.52x0.52x1.3 m
Cells: 2.6x2.6 cm, each cell contains 26 rows/columns of scintillating fiber
Detector is rotated 2° with respect to incoming particles
Specify fibers diameter, number of fibers per cell, number of cells in the block. Mention that this is about ¼ of what will require to fill with open FMS configuration.
Radiation length and Molere radius. 1

2. Detector Configuration for Simulation (ii)
Scintillating fibers are 1mm in diameter and run the length of the detector
The radiation length of the mixture of tungsten and polystyrene is 8.7mm and the nuclear interaction length is 21.2 cm. The length of the detector was chosen to be about 6 nucl. int. lengths.
The geometry specified for this simulation is about ¼ what is necessary to fill open FMS configuration

3. Simulation Conditions
Cutoffs are left at their default values (1 mm)
Light attenuation in the scintillating fiber is not included
Particles are fired from a distance of 7.5 meters
Information is stored in a ROOT tree file which tracks the energy deposition in the fibers in each cell
Energy, momentum and impact point from GEANT4 are saved for comparison
GEANT4. 3 3 3

4. Example Events i ii
Energy deposition (GeV) in fibers for a 20 GeV photon (i) and π0 (ii)
Horizontal axes label the cell number 4

5. Molière Radius cm
Radial distribution of shower energy in uniform mixture of tungsten and polystyrene. Molière radius at 90% was determined to be 2.5 cm. This result was also confirmed later for the actual fiber/block geometry. 5 5

6. Position and Energy Resolution (i)
Mention, compensation for lead absorber require sampling fraction ~2.3% for mip
GeV
Energy deposition in the entire volume of fibers for single 10 GeV photons. Shows resolution of ~4% and sampling fraction of 2.4% 6 6

7. Position and Energy Resolution (ii)cm cm
Position as determined by center of gravity method for 1k 10 GeV photons 7

8. Position and Energy Resolution (iii)

9. Identifying 2 Photon Events
We aim to distinguish single photons from 2 photons by computing a weighted moment of the energy in the shower:
Where w is a constant. The best value for w was determined to be .8, which gives 98% rejection of π0 at 80 GeV
Rejection power vs energy. 9 9

10. Rudimentary Attempt to Reconstruct π0
Require two highest cells to be separated, i.e. two highest cells must have a lower cell between them or be diagonal to each other
Use template shower from single photon event scaled to appropriate energy
Divide energy from shared cells based on template shower
Calculate center of gravity for each shower
Apply correction function to center of gravity (see next slide)

11. Position reconstruction (20 GeV shown)

12. Invariant Mass Reconstruction (i)
π0 energy clockwise from top left:
20 GeV, 40 GeV, 50 GeV

13. Invariant Mass Reconstruction (ii)
60 GeV
80 GeV

14. π0 Reconstruction: Mass Peak14

15. π0 Reconstruction: Mass Width
Plot: efficiency of pi0 reconstruction vs energy with this rudimental clusterfinder. 15 15

16. π0 Reconstruction: Efficiency
The pion reconstruction efficiency as a function of energy. There is a distinct dip in efficiency in the GeV range the reason for this is unclear.

17. π0 Reconstruction: Summary
This method provides reasonable results for lower energy π0s.
Noticeably worse in the GeV region. This may be due to the
typical photon separation being around 1.5 cell sizes. CM calculations may then produce large errors in opening angle.
Beyond 80 GeV the photon separation is rarely large enough to have the two high cells be nonadjacent
This method is inherently biased towards highly asymmetric decays 17

18. Fitting the Shower Shape
The previous method used a reference shower from only one impact parameter
This can make it weak at reconstructing showers where the impact point differs significantly from that of the reference
We would prefer to reconstruct the showers by fitting them to a general shower shape function and extracting the relevant parameters from there 18 18

19. Determining the Shower Shape
To determine a shower shape function photons at 50 GeV were fired uniformly over one cell face.
The energy in all cells was recorded as a function of the radial distance from the impact point of the function
This distribution was then normalized to create a single shower energy distribution
Radial shower energy distribution x-axis in cm 19 19

20. Fitting the Shower Shape
Attempted to fit the energy distribution projected onto a single axis (shown at right)
Fitting function uses 4th order exponential to fit the sharp falloff and two Gaussians to fit the broad base
Still have difficulty recreating the shape of the peak at the center
Photon shower shape with fitting function of the form:

21. Conclusions and future work
We have outlined the basic performance characteristics for a tungsten/fiber calorimeter
We have also shown some basic ability to distinguish single and two photon events, and to reconstruct π0s
Still must determine the best method for fitting showers. Appropriate fitting function? How much better is pion reconstruction at higher energies? Will a better procedure fix some of the problems with the current method?
Begin looking at electron/hadron separation