HBT correlators - current formalism vs. Wigner function formulation

Abstract

We clarify the relationship between the current formalism developed by Gyulassy, Kaufmann and Wilson and the Wigner function formulation suggested by Pratt for the 2-particle correlator in Hanbury-Brown Twiss interferometry. When applied to a hydrodynamical description of the source with a sharp freeze-out hypersurface, our results remove a slight error in the prescription given by Makhlin and Sinyukov which has led to confusion in the literature.It is widely accepted that if the nuclear matter created in ultra-relativistic heavyion collisions attains a high enough energy density, it will undergo a phase transition into a quark-gluon plasma. For this reason, it is of great interest to determine the energy densities actually attained in these collisions. The total interaction energy of a given reaction can be directly measured by particle calorimeters and spectrometers.Although there is no analogous direct measurement for the size of the reaction region, Hanbury-Brown Twiss interferometry [1] provides an indirect measurement in termsof the correlations between produced particles.Ten years ago, Pratt [2] used the covariant current formulation of Gyulassy, Kaufmann and Wilson [3] to show that the correlations between two particles could be expressed in terms of one-particle pseudo-Wigner functions. Although Pratt's derivation was non-relativistic, it provided a valuable link between the experimental data and many semi-classical event generators whose output came in the form of one-particle * Work supported by BMFT, DFG, and GSI

Interferometric signatures of the temperature dependence of the specific shear viscosity in heavy-ion collisions

“…On the freeze-out surface for each event, the pion emission function is defined by the Cooper-Frye integral [23][24][25] …”

TWO-PARTICLECORRELATIONS INRELATIVISTICHEAVY-IONCOLLISIONS

“…Several approaches to derive this connection [12] are worked out in the literature, parametrizing the source as a covariant superposition of classical currents [5,[13][14][15][16][17][18] or using a superposition of nonrelativistic wave packets [9,10]. One finds the simple relations (with the upper (lower) sign for bosons (fermions))…”

Extracting source parameters from Gaussian fits to two-particle correlations

“…For the two-particle correlation function, we use the well-established theoretical approximation [8,11,12] …”