Pion Dynamics and the RHIC HBT Puzzle

초록

In a transparent source of pions the radius parameter toward the detector, R_O, should be larger than the radius perpendicular to the detector, R_S: R_O^2 \approx R_S^2+\delta \tau^2, with \delta \tau the duration of pion emission. In contrast, two-particle correlation functions extracted from Au+Au collisions at RHIC indicate R_O \approx R_S, naively implying a short emission duration. Several authors have suggested that source opacity could account for this observation, even with a sizable emission duration. However, the high-energy eikonal approximation used in that work can't be justified for low momentum pions measured to extract radii, and causes R_O \ne R_S at K_T=0, violating a basic symmetry. The effects of opacity and the related attractive real potential, which we find important, are included by solving quantum mechanical wave equations for pions in a dense medium using a relativistic, complex, energy-dependent optical potential. When implemented using a boost invariant pion source function, including transverse flow, we find that at K_T = 0, R_O = R_S, and that at larger momenta R_O \approx R_S with long emission times.