ClusterID Introduction
We present an approach to reconstructing calorimeter information from cell hits for a modern highly segmented sampling calorimeter system used for measuring high energy particles. This may be thought of as a solution to the “energy flow” problem however it begins with a different set of assumptions than the ones that originally motivated the energy flow concept. The underlying assumption of the energy flow problem is that the hits from highly collimated hadronic jets of particles are such that it is impossible to sort out the hits from different particles into separate clusters. This is partially due to the belief that the cluster of hits from one particle will usually overlay the cluster of hits from other particles due to the close proximity of the particles. The other reason for skepticism about associating hits with particular particles is that even a single isolated particle is seen to produce a set of disconnected cluster of hits. For example, a pion knocks a neutron out of a nucleus of detector material and the neutron travels a large distance before it deposits its energy with a visible cluster of hits elsewhere in the detector. We use the term “fragment” to refer to these secondary clusters of hits.
The belief that these two problems, overlap and fragmentation of clusters, limit our ability to reconstruct calorimeter data is well motivated but incorrect. There are two sources for these beliefs. The calorimeters used at SLC and LEP although state of the art and highly segmented in their day were, in general, unable to isolate hits from different particles into separate sets of clusters in jets. This lead to the development of the energy flow concept that roughly stated is as follows. Tracks from a tracker lying inside the calorimeter system are extended into the calorimeter and hits along the projected trajectory in some cone-like volume are assumed to be due to the charged particle that created the track and they are tagged as such. The remaining hits are then assumed to be due to neutral particles. The “charged” particle calorimeter hits are ignored and the energy of the remaining “neutral” hits is combined with the tracking information about the charged particles to give an “energy flow” level of description of the hadronic jet from which the direction, energy and mass of the underlying jet producing particle is deduced with some considerable resolution error.
The second source of belief in the limitation of calorimeters to sort out particles in jets comes from a cursory perusal of graphic displays of hits from jets as seen in modern event detector event displays. What is seen is a bundle of close but clearly separate tracks in the tracker that lead into a single large cloud of hits in the calorimeter.
This evidence seems compelling, what is wrong with it? Obviously with a very coarsely segmented calorimeter, say projective cells subtending 300 milliradian angles from the IP, nearly all the particles in a tightly collimated jet would pass through the same cells. However, considering the other extreme of say microradian sized cells and remembering that a calorimeter shower is just a large number of particles leaving an ionization trail one can see that there will be almost no overlap of hit energy. So as we move between the extremes of a calorimeter with one readout and a calorimeter with a semi-infinite number of readouts we move from complete overlap of all particles to essentially no overlaps of any particles. The claim we want to demonstrate here is that in the LEP/SLC era the detectors were still insufficiently segmented to get good separation but the next generation of LC detectors can achieve sufficient segmentation to render the overlap problem tractable.
Regarding event displays of next generation detector jet showers one must adjust for two things. First, in any display one is seeing a two dimensional projection of a three dimensional shower which makes matters appear much worse than they are and it is difficult even with zoom and rotate features to convince oneself visually that overlapping is not so common as it appears. One needs to color code hits from different particles and one needs to set hit thresholds to eliminate a pervasive haze of KeV level X-ray hits that permeate the detector. Once this is done it can be made more apparent visually that particle clusters are much more isolated than first appeared. However, analytic techniques are much better suited to demonstrating this claim as we will show in plots to follow.
The second problem, fragmentation, is also not as serious as it seems at first when properly approached. A simple way to demonstrate this is to do simulations with a finely segmented monolithic calorimeter. By monolithic we mean to replace the standard EM and HAD calorimeter separated by a large physical gap which is filled with passive support structures and sometimes a solenoid and instead use a single very deep calorimeter. If one simulates single pions interacting in the standard two calorimeter system with a physical gap and one clusters together hits in adjacent cells one will frequently find many separated clusters containing similar amounts of energy. This occurs in the typical design where the EM section is about one interaction length deep so that about 70% of the pions interact in the EM cal creating an initial fragment and then the secondary particles pass through the gap and each secondary creates a separate cluster in the had cal. The same pion interacting at the same point in the monolithic design typically creates a single cluster of contiguous hits including the primary and secondary particles. The next most energetic fragment that occurs tends to be about 20% the size of the primary. The origin of these fragments is two fold. First, knocked out neutrons as discussed before which because of their large mass compared to pions tend to pick up a relatively small portion of the pions energy due to basic collision kinematics. The second source is gammas from secondary pizero production which may travel a few cells before interacting thus although lying close to the primary cluster are not contiguous with it.
We have tried to suggest that there still may be hope for the idea of reconstructing calorimeter data from the point of view that separate clusters can be associated with individual particles. We call this concept Cluster ID as opposed to the concept of energy flow. In what follows we will demonstrate that this is indeed a promising approach to reconstructing calorimeter data. It is useful to compare to how we approach reconstructing tracking data from trackers that contain many hits, for example a TPC. There we also group hits together and associate those hit sets with single particles. We will try to show that the same approach is viable with calorimeter data, albeit much more complex for reasons that will become clear as we proceed.