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Paul Chung is a research scientist in the Chemistry Department at the University of Stony Brook working on the PHENIX experiment.

3D Source Imaging of the Expanding Fireball

By Paul Chung

The PHENIX Collaboration at RHIC has performed a model-independent extraction of the three-dimensional (3D) source function for mid-rapidity pion pairs, with transverse momentum p_T between 0.2 and 0.36 GeV, produced in semi-central relativistic collisions of Au beams at a centre-of-mass energy of 200 GeV/nucleon. A model calculation comparison of the source function suggests a dynamical picture in which the pion source expands for a proper duration of  ~  9 fm/c before fizzling out and emitting pions over a much shorter proper emission duration of  ~  2 fm/c.

Pion interferometric studies have long held the promise of offering access to the size and lifetime information of the tremendously hot nuclear source formed in relativistic heavy ion collisions. These studies exploit the correlation, due to Coulomb interaction and Bose-Einstein quantum statistical interference (also known as Hanbury-Brown Twiss) effect, of pion pairs in which the two particles have a relative momentum less than 50 MeV in the centre-of-mass frame of the pair. This 3D pion correlation function is directly related to the 3D shape and lifetime of the source emitting the pions. Hence, source shape and lifetime information first involves the experimental measurement of the 3D correlation function for pion pairs with subsequent source function extraction. The source function gives the probability density of pion pair separations (i.e separation distance between the two pions in each pair) and is the physical quantity directly accessible by experimental measurements.

However, the 3D correlation function measurement and a precise source shape determination require an abundance of high quality data and a state-of-the-art implementation of the source function extraction technique, both of which have been achieved only recently. The current procedure, first proposed by Danielewicz and Pratt, reduces the three-dimensional problem into a set of one-dimensional (1D) problems, each involving a single correlation and source moment. Each 1D problem is solved using an inversion technique, developed by Brown and Danielewicz, to image the source moment from the corresponding correlation moment. Finally, the set of source moments is combined to yield the 3D source function. The overall 3D source imaging technique is very powerful in that the 3D source determination is model-independent i.e. no initial assumption of the 3D source shape is required or made.

Profiles of the extracted source function in the three directions of the Cartesian system of coordinates are shown in Figure 1 (a)-(c). They are imaged from the corresponding correlation function profiles shown in Figure 1 (d)-(f). To infer quantitative information about the breakup dynamics of the pion source necessitates comparison with model calculations. The model best suited for this purpose is the Therminator model of Kisiel et al. It describes the emission from a thermal source of transverse dimension ρ_max which lives for a time τ₀ before breaking up and emitting pions during a time duration of δτ. A crucial ingredient in Therminator is the inclusion of all known resonance decays.

Fig.1: Source function profiles S(r_x), S(r_y) and S(r_z) (left panels) and their associated correlation profiles C(q_x), C(q_y) and C(q_z) (right panels) for mid-rapidity, low p_T pion pairs. The bands indicate statistical and systematic errors.

Figure 2 (a)-(c) show the comparison between source image and calculated source function profiles from Therminator under various combinations of resonance decay and emission durations. The comparison indicates that a non-zero emission duration of δτ = 2 fm/c is required together with a source lifetime of  ~  9 fm/c in order to describe the pion source image. Decay curves for pion pair relative formation times are shown in Figure 2 (d) for the three model assumptions indicated. The fit to the data is found for the longest lifetime shown.

Fig.2: Source function comparison between Therminator calculation and source image for (a) S(r_x), (b) S(r_y) and (c) S(r_z) for mid-rapidty, low p_T pion pairs. Panel (d) compares decay curves for pion pair relative formation times from Therminator events with various assumptions for emission duration and resonance emission.

Hence, the picture which emerges from the data in the context of the Therminator model is consistent with an expanding fireball which hadronizes and emits particles over a short but non-zero emission duration of  ~  2 fm/c.

More information can be found in arXiv:0712.4372 to appear in Physical Review Letters.

The Relativistic Heavy Ion Collider at Brookhaven National Laboratory is a world-class scientific research facility primarily funded by the U.S. Department of Energy Office of Science. Hundreds of physicists from around the world use RHIC to study what the universe may have looked like in the first few moments after its creation. What physicists learn from these collisions may help us understand more about why the physical world works the way it does, from the smallest subatomic particles, to the largest stars.