The transition temperature for a dilute, homogeneous, three-dimensional Bose gas has the expansion T c = T 0 {1+c 1 an 1/3 +[c ′ 2 ln(an 1/3 )+c ′′ 2 ]a 2 n 2/3 +O(a 3 n)}, where a is the scattering length, n the number density, and T 0 the ideal gas result. The first-order coefficient c 1 depends on non-perturbative physics. In this paper, we show that the coefficient c ′ 2 can be computed perturbatively. We also show that the remaining second-order coefficient c ′′ 2 depends on nonperturbative physics but can be related, by a perturbative calculation, to quantities that have previously been measured using lattice simulations of three-dimensional O(2) scalar field theory. Making use of those simulation results, we find T c ≃ T 0 {1 + (1.32 ± 0.02) an 1/3 + [19.7518 ln(an 1/3 ) + (75.7 ± 0.4)]a 2 n 2/3 + O(a 3 n)}. in the dilute (or, equivalently, weak-interaction) limit, where c 1 is a numerical constant, a is the scattering length, which parameterizes the low energy 2-particle scattering crosssection, and n is the density of the homogeneous gas. We will assume that the interactions are repulsive (a > 0). A clean argument for (1.1) may be found in Ref. [1], which also shows how the problem of calculating the constant c 1 can be reduced to a problem in threedimensional O(2) field theory. Recent numerical simulations of that theory have obtained the results c 1 = 1.29 ± 0.05 [2] and c 1 = 1.32 ± 0.02 [3,4].In this paper, we shall extend the result for T c (n) to second order in a for a homogeneous Bose gas. This is also the relationship between T c and the central number density for a

We discuss the Yano-Koonin-Podgoretskii (YKP) parametrization of the twoparticle correlation function for azimuthally symmetric expanding sources.We derive model-independent expressions for the YKP fit parameters and discuss their physical interpretation. We use them to evaluate the YKP fit parameters and their momentum dependence for a simple model for the emission function and propose new strategies for extracting the source lifetime.Longitudinal expansion of the source can be seen directly in the rapidity dependence of the Yano-Koonin velocity.PACS numbers: 25.75. Gz, 25.75.Ld, 12.38.Mh Typeset using REVT E X 1

We introduce a new scenario for heavy ion collisions that could solve the lingering problems associated with the so-called HBT puzzle. We postulate that the system starts expansion as the perfect quark-gluon fluid but close to freeze-out it splits into clusters, due to a sharp rise of bulk viscosity in the vicinity of the hadronization transition. We then argue that the characteristic cluster size is determined by the viscosity coefficient and the expansion rate. Typically it is much smaller and at most weakly dependent of the total system volume (hence reaction energy and multiplicity). These clusters maintain the pre-existing outward-going flow, as a spray of droplets, but develop no flow of their own, and hadronize by evaporation. We provide an ansatz for converting the hydrodynamic output into clusters. 25.75.Dw, 25.75.Nq

For some time, the theoretical result for the transition temperature of a dilute three-dimensional Bose gas in an arbitrarily wide harmonic trap has been known to first order in the interaction strength. We extend that result to second order. The first-order result for a gas trapped in a harmonic potential can be computed in mean field theory (in contrast to the first order result for a uniform gas, which cannot). We show that, at second order, perturbation theory suffices for relating the transition temperature to the chemical potential at the transition, but the chemical potential is non-perturbative at the desired order. The necessary information about the chemical potential can be extracted, however, from recent lattice simulations of uniform Bose gases.

have recently used the large-N approximation to calculate the effect of interactions on the transition temperature of dilute Bose gases. We extend their calculation to next-to-leading order in 1/N and find a relatively small correction of Ϫ26% to the leading order result. This suggests that the large-N approximation works surprisingly well in this application.

Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb-Pb and pi-p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distribution f=1/[exp(E/T)-1] at T ~ 120 MeV, modified for radial expansion. pi-p data are also consistent with f, but at T ~ 180 MeV and without radial flow.Comment: 15 pages LaTeX, including 6 postscript figure

The Yano-Koonin-Podgoretskiȋ (YKP) parametrisation of Hanbury Brown-Twiss (HBT) two-particle correlation functions opens new strategies for extracting the emission duration and testing the longitudinal expansion in heavy-ion collisions. Based on the recently derived model-independent expressions, we present a detailed parameter study of the YKP parameters for a finite, hydrodynamically expanding source model of heavy-ion collisions. For the class of models studied here, we show that the three YKP radius parameters have an interpretation as longitudinal extension, transverse extension and emission duration of the source in the YKP frame. This frame is specified by the fourth fit parameter, the Yano-Koonin velocity which describes to a good approximation the velocity of the fluid element with highest emissivity and allows to test for the longitudinal expansion of the source. Deviations from this interpretation of the YKP parameters are discussed quantitatively.PACS numbers: 25.75. Gz,25.75.Ld,12.38.Mh Typeset using REVT E X

We argue that strong final state rescattering among the secondary particles created in relativistic heavy ion collisions is essential to understand the measured Bose-Einstein correlations. The recently suggested "random walk models" which contain only initial state scattering are unable to reproduce the measured magnitude and K ⊥ -dependence of R ⊥ in Pb+Pb collisions and the increase of R l with increasing size of the collision system. 25.75.Gz An important aspect of understanding ultrarelativistic heavy ion collisions is the clear identification of genuine collective nuclear effects which cannot be explained in terms of a simple superposition of nucleon-nucleon collisions. An integral part of our task to look for new physics must therefore be the careful construction of models for nucleus-nucleus collisions ("A-B collisions") based on a superposition of individual nucleon-nucleon (N -N ) collisions in order to establish where they fail.Recently there have been some renewed attempts to construct such models. In the "Random Walk Model" (RWM) of [1] the single-particle transverse mass spectra measured in A-B collision have been calculated by extrapolating those from pA collisions. The LEXUS model of [2] goes even further, by simulating A-B collisions as a simple folding of independent N -N collisions.Here we demonstrate that, while these models have had some success in describing measured single-particle spectra, they fail to reproduce crucial features of the observed two-particle Bose-Einstein correlations. This is shown to be due to their lack of final state rescattering.The idea behind the RWM was to provide an alternative interpretation of the measured single-particle m ⊥ spectra, opposite in spirit to the popular hydrodynamical parametrizations [3]. The latter are based on the assumption of a locally thermalized hadron resonance gas which undergoes longitudinal and transverse hydrodynamic expansion. The transverse expansion is interpreted as a genuine nuclear collective effect with no analogue in N -N collisions; it is identified through the characteristic flattening it causes in the transverse mass spectra, especially at small M ⊥ < 2m 0 where the inverse slope parameter is found to increase linearly with the rest mass m 0 of the produced hadrons [3,4].The RWM, on the other hand, starts from the observation that such a flattening, relative to N -N collisions, happens even in pA collisions where hydrodynamic transverse expansion is not expected to occur. In the RWM an incident nucleon undergoes multiple collisions in the nuclear target, leading to a random walk pattern in the transverse momentum plane. When it collides inelastically it creates a little "fireball", identical to those formed in elementary inelastic pp collisions, but moving with a transverse rapidity ρ which is Gaussian distributed. In A-B collisions the same mechanism works for both projectile and target nucleons. The width of the ρ distribution is fixed in pA collisions and then extrapolated to A-B collisions using geometric consideration...