Using Maximum Likelihood analysis in HBT interferometry: bin-free treatment of correlated errors

Abstract

We present a new procedure, based on the Maximum Likelihood Method, for fitting the space-time size parameters of the particle production region in ultra-relativistic heavy ion collisions. This procedure offers two significant advantages: 1) it does not require sorting of the correlation data into arbitrary bins in the multidimensional momentum space and 2) it applies all available information on the experimental resolution error matrix separately to each correlated particle multiplet analyzed. These features permit extraction of maximum information from the data. The technique may be particularly important in ultra-relativistic heavy ion collisions, because in this energy domain large source radii and long source lifetimes are expected, and high-multiplicity HBT interferometry with a single collision event is a possibility.