J.G. Reid and T.A. Trainor

The purpose of this project is to create fast trigger algorithms which can identify 'interesting' events at different levels in the STAR data stream. For this purpose we have formulated a model-independent correlation analysis system using topological information and entropy measures. Rather than looking for features corresponding to a specific correlation model, we use the entropy and information measures of the data set to determine which events contain information which may be of interest.

Basic to our analysis is a binning of the data set. This yields a list of bin occupancies from which the entropy and information are calculated, but it can also contribute significant systematic errors. In using our analysis chain to find the scaled 'volume' of different simple loci we have observed that the orientation of our simple, square binning system biases our results. Fortunately, the density of STAR Electro Magnetic Calorimeter (EMCAL) data minimizes this effect. This error could be further reduced by use of a more complex binning system, but for triggering purposes the extra time required to use an exotic binning system is prohibitive.

Another element basic to our analysis is the reference entropy. Since topological information is by definition a relative quantity the choice of a baseline (or reference) entropy determines the results of the analysis. For most of the trigger software we have chosen to use the average event ensemble entropy as a reference, but we have found in some situations that it is desirable to use the entropy of a Poisson distribution as a reference since this can be considered to contain the maximum entropy for a given constraint system. This has led us to derive a closed form for the rank-q entropy of a Poisson distribution for use as a general reference in some of our analysis.

In applying our analysis to STAR EMCAL trigger data we have obtained promising results. Using the event generator HIJING and STAR GEANT to generate simulated STAR events we have analyzed EMCAL data for pp, CC, SiSi, pAu, and AuAu. The results look very promising for forming a space out of information values at different scale points. In this space we cut out the 'normal' events and trigger on the remaining 'interesting' events. We also rigorously tested a prototype version of our level-1 trigger software on a set of test events provided by BNL.

Our trigger algorithm shows excellent selection capability. However, there remain several issues in formulating a trigger from our general analysis system. The first and most obvious problem in developing a trigger is the essential issue of runtime. Since this analysis must be able to analyze an event in a time on the order of milliseconds we have developed an approach in which we use a subset of the full analysis which can still identify normal events for rejection (to reasonable accuracy) in a fraction of the time of the full analysis. We have further extended this idea so that this analysis is flexible enough to be applied in some form at every level of triggering (above level 0) and the full analysis can, of course, be used off-line as well.

We have recently begun to apply these techniques to data from CERN experiment NA49. We have created a simulator which gives us distributions in rapidity and transverse mass corresponding to a specified total multiplicity and slope parameter ('temperature'). By comparing our analysis of these events to the analysis of real events we have begun to form a space in which we can map out the systematics related to these thermodynamic quantities. This work has just begun, but it promises to be an important part of our activity in the future.