Pion Interferometry for Hydrodynamical Expanding Source with a Finite Baryon Density

Abstract

We calculate the two-pion correlation function for an expanding hadron source with a finite baryon density. The space-time evolution of the source is described by relativistic hydrodynamics and the HBT radius is extracted after effects of collective expansion and multiple scattering on the HBT interferometry have been taken into account, using quantum probability amplitudes in a path-integral formalism. We find that this radius is substantially smaller than the HBT radius extracted from the freeze-out configuration. The Bose-Einstein correlation of identical bosons produced in high-energy heavy-ion collisions, also known as the HBT effect, is an important tool for the study of the space-time structure of the emitting source [1]. As the source expands, cools, and freezes out, it is important to know what source distribution the HBT interferometry measures. Is it the freeze-out source distribution, the initial source distribution, or the initial source distribution modified by absorption and expansion? The conventional viewpoint is that the HBT interferometry measures the freeze-out configuration because rescattering of source particles are assumed to lead to a chaotic source. However, the extracted experimental HBT radii are insensitive to the collision energy, and R out /R side ≈ 0.9 − 1.1 at RHIC [2,3]. These general features cannot be understood within the conventional viewpoint [4,5,6].The validity of the conventional assumption on HBT is recently questioned as it was pointed out that because HBT is purely a quantum-mechanical phenomenon, the effects of rescattering and collective dynamics must be investigated within a quantum-mechanical context [7]. As fully quantum treatment of heavy-ion collisions is beyond the scope of our present investigation, we shall describe the gross dynamics of the hadron system with a finite baryon density by classical hydrodynamics. In this letter, we follow Wong's work [7] and take into account the effects of collective expansion and multiple scattering by constructing the quantum probability amplitude using Glauber's multiple scattering model and the trajectories of test particles in the path-integral framework.The hydrodynamics and the composition of the fluid depend on the collision energy. We study in this work the dynamics of heavy-ion collisions in the energy range corresponding to about 10 GeV per nucleon beam energy in fixed target collisions in which nucleons and deltas play an important role and pions are produced dominantly from deltas and absorbed by nucleons.Relativistic hydrodynamics has been extensively applied to high-energy heavy-ion collisions [8]. The energy momentum tensor of a thermalized fluid cell in the centerof-mass frame is [8]

An Explanation of a Phenomenon in Relativistic Heavy-Ion Collisions

“…In this section, we will study two-source pion interferometry in which both sources are in the state of QGP [12] (In Ref. [14], the authors use Monte-Carlo method to resolve the HBT puzzle). The distribution of pion sources is Eq.…”