S.J. Bailey, J.G. Reid and T.A. Trainor

Event-by-event analysis of multiparticle momentum distributions has been an important tool of high-energy physics for about two decades. The principal applications have been in the areas of jet physics at higher energies and collective flow of nuclear matter at lower energies. The concept becomes practicable when detector acceptance and particle multiplicities are sufficiently large to detect the correlation signals of interest above the statistical noise level.

The ultrarelativistic heavy ion programs at the CERN SPS, RHIC and LHC have as their object the study of QCD color deconfinement and the properties of deconfined colored matter, the so-called quark-gluon plasma. It is expected that one manifestation of color deconfinement may take the form of correlated structures in momentum distributions beyond those imposed by global kinematic constraints, and that these correlated structures, differing in form from event to event, would be largely washed out in any ensemble-averaged inclusive distributions. It is therefore essential to characterize each event in terms of its correlation structure in order to develop maximum sensitivity to color deconfinement phenomena.

The program that we have undertaken over the last few years is to develop a universal multiparticle correlation analysis system which can extract all possible information from each event. This system is based on the Renyi entropies, a system of topological measures of which the rank-1 Renyi entropy is identified with the Boltzman-Gibbs entropy of statistical mechanics.

In this work the Renyi entropies are defined as scale-dependent (scaled) quantities, and with each is associated a corresponding scaled dimension. For each event ensemble a reference entropy is determined. The arithmetic difference between the scaled entropy for an individual event and the reference entropy for the event ensemble is the scaled information for the event. The scaled information is then a sensitive measure of differential correlation. (This information is directly related to the Shannon-Wiener information of signal analysis.)

This system can be used in two complimentary ways, either as the basis for event selection, as in an online or offline trigger system, or to carry out a physics analysis on the dynamics of individual collision events. As an event selection mechanism the system would select the (presumably) small fraction of events that may contain an unusual correlation structure, possibly due to fluctuations associated with color deconfinement.

For the study and interpretation of these selected special events one can then use phenomenological event generators to produce simulated events with similar correlation structures, and in this way to sensitively test models of the collision process and aspects of QCD theory. Events from such a generator are passed through a Monte Carlo model of the experimental apparatus, and the resulting simulated particle distributions are passed through the correlation analysis chain. The resulting scaled information system provides a very sensitive measure of differential correlation, presenting a far more demanding test of event generators and physical models than simple ensemble-averaged inclusive distributions.

The correlation analysis system we have developed has been implemented in the C++ programming language and is compatible with the general data processing environment of the NA49 experiment. It has been tested with simulated events and is now being used to analyze real events from the Fall, 1995 NA49 lead beam run at CERN. We expect to analyze several hundred thousand events over the next several months. This analysis will form the basis for a first major search for color deconfinement correlation phenomena in lead-lead collisions at SPS energies.