N ov 1 99 8 ACCESSING THE SPACE – TIME DEVELOPMENT OF HEAVY – ION COLLISIONS WITH THEORY AND EXPERIMENT

ACCESSING THE SPACE–TIME DEVELOPMENT OF HEAVY–ION COLLISIONS WITH THEORY AND EXPERIMENT By David Alan Brown In this thesis we discuss ways to access the space-time development of heavy-ion reactions using both theory and experiment. From the theoretical side, we discuss modeling ultra-relativistic, parton-dominated, heavy-ion reactions. This discussion is broken into a discussion of transport-like models for massless particles and a discussion of the parton model in phase-space. From the experimental side, we discuss using intensity interferometry to image the relative distribution of emission points. Transport models may offer a way to understand the space-time development of ultra-relativistic, parton-dominated, heavy-ion reactions at RHIC and the LHC. Two key approximations needed to derive semi-classical transport equations, the QuasiParticle and Quasi-Classical approximations, may not be valid for partons. Using QED, we outline a derivation of a transport-like theory which does not rely on these two approximations. This theory rests on the phase-space Generalized FluctuationDissipation Theorem. This theorem and the phase-space particle self-energies give a set of coupled phase-space evolution equations. We illustrate how these evolution equations can be used perturbatively or to derive semi-classical transport equations. To connect the parton phase-space densities to the experimentally measured Parton Distribution Functions, the parton model must be translated into phasespace. Within QED, we study whether two key components of the parton model, factorization and evolution, can be formulated in phase-space. We rewrite the QED analog of the parton model, the Weizsäcker-Williams Approximation, in terms of phase-space quantities, demonstrating factorization in phase-space. Evolution of the parton densities is equivalent to summing a class of ladder diagrams. We study a simplified QED version of these ladders while studying the phase-space photon and electron densities surrounding a classical point charge. We find that the densities take the form given in the phase-space Generalized Fluctuation-Dissipation Theorem. We use the tools developed here to discuss the shape of a nucleon’s parton cloud. We can access the space-time development of a heavy-ion reaction directly by imaging the source function from particle correlation functions. We discuss several methods to perform this inversion. We concentrate on one such method, the Optimized Discretization method, where the source resolution depends on the relative particle separation and is adjusted to available data and their errors. This method can be supplemented using known constraints on the source. We test the inversion methods by restoring simulated pp sources. From the restored sources, one can extract the average freeze-out phase-space density, entropy at freeze-out and the amount of the source that lie outside of the imaged region. We apply the imaging techniques to pion, kaon, proton and Intermediate Mass Fragment (IMF) correlation functions. Significant portions of the pion, proton and IMF sources extend to large distances (r > 20 fm). The results of the imaging show the inadequacy of common Gaussian parameterizations of the source. To Aleida, for her love, To my family, for their support, To my father, whom I will always remember.