Resolving Power of 2-D Pion Interferometry∗

A χ2 analysis is performed to test the resolving power of two-dimensional pion interferometry using for illustration the preliminary E802 data on Si+Au at 14.6 AGeV/c. We find that the resolving power to distinguish two decoupling geometries of different dynamical models is enhanced by studying the variation of the mean χ2 per degrees of freedom with respect to the range of the analysis in the qT , qL plane. The preliminary data seem to rule out dynamical models with significant ω, η resonance formation yields. In this letter, the results of a new multi-dimensional pion interferometric analysis of preliminary E802 ππ correlation data[1]-[3] on central Si+Au reactions at 14.6 AGeV/c are reported. To study the resolving power of multi-dimensional in contrast to the projected one-dimensional interferometry we consider two dynamical scenarios that predict similar correlation functions even though the underlying decoupling geometries differ considerably. We use the non-ideal inside-outside cascade model of Refs. [4, 5]. In one scenario long lived resonances are neglected while in the other the resonance fractions as taken from the Lund model. At higher SPS energies[4], we showed that long lived resonance production predicted by the Lund Model led to similar correlation functions to those expected from models with quark-gluon plasma formation[6], since long lived resonances could mimic the long slow burn of a plasma. Therefore another goal of the present study is to see if a similar ambiguity could exist at the lower AGS range. There is some fragmentary data[7] indicating that resonance production could be suppressed at the AGS, the Lund model predicts similar resonance yields at the two energy ranges. We show below that the two-dimensional χ interferometric 0 *This work was supported by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contract No. DE-FG02-93ER40764. 0 1. Permanent address: IFT/UNESP, Rua Pamplona 145, 01405-900 São Paulo, SP, Brazil. Partially supported by Conselho Nacional de Desenvolvimento Cient́ıfico e Tecnológico (CNPq), Brazil analysis has sufficient resolving power to rule out significant long lived resonance production in the AGS domain, if the preliminary data are confirmed. Recall that under idealized conditions the correlation function, C2(k1,k2), of two identical pions probes the decoupling or freeze-out space-time distribution of pions, ρ(x), through C2(k1,k2) = 1 + |ρ(k1 − k2)|. However, in actual high energy reactions, final state interactions, correlations between coordinate and momentum variables, and resonance production distort this ideal interference pattern due to Bose-Einstein symmetry (see e.g. [4]-[10]). The correlation function in this more general case can be expressed as[4]