We have begun an effort to simulate spaghetti calorimeters using the GEANT detector simulation package. The goal of this effort is to provide guidance in the design of our calorimeter prototype, and ultimately in the calorimeter used in the experiment.
The complex physical processes at the heart of calorimetry, combined with the fine-grained geometry inherent in fiber calorimetry, make this simulation a formidable task. We thus began by determining whether GEANT could reproduce results from actual spaghetti calorimeter tests performed by the SPACAL collaboration at CERN. So far these results are very encouraging.
We used GEANT to simulate a fiber calorimeter consisting of 1 mm diameter scintillating fibers embedded in lead such that the lead-to-scintillator volume ratio is 4:1. We chose the fiber materials (both scintillator and cladding type), the lead alloy (96% lead, 4% antimony), and other properties of the detector (effective attenuation length of the scintillator, length of the modules, etc.), to match the specifications of the SPACAL prototype detector [12, 76].
The hadronic and electromagnetic energy resolutions estimated by the
GEANT simulation compared favorably to experimental results obtained by the
SPACAL collaboration. Figure 
shows both the Monte-Carlo and the
experimental resolutions. Table compares the fit of the
simulation's resolution curve to the experiment's, assuming the functional
form
where a and b are constants. Our simulation of electromagnetic showers shows slightly more energy deposited in the fibers than the SPACAL results. We are investigating this difference, which we believe is due to differences for incident particles which start to shower in the fiber. Since our requirements are only for hadronic showers, this small effect for electromagnetic showers has negligible influence on results of interest to E864.
Figure: (a)Hadronic and (b) electromagnetic energy resolutions obtained by
the SPACAL collaboration and E864's GEANT simulation. Vertical axis is 
E/E
(best fit Gaussian), horizontal axis is kinetic energy in GeV.
Table: Comparison of fiber calorimeter energy resolutions: Monte-Carlo
vs. data.
The ratio of the electromagnetic and hadronic responses of the
detector, 
, can also be used as a measure of the simulation's
accuracy. We will make this comparison upon completion of GEANT runs
which are currently under way. Further tests of the spatial distributions
and temporal development of showers will also be performed.
The fiber diameter, tower length, volume ratio, and gate length are some of the design parameters to be determined before a prototype is constructed and tested. The GEANT simulation will, given continued success, help ascertain some or all of these parameters.