Two-particle correlations in the wave function and covariant current approaches
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ELEMENTARY PARTICLES AND FIELDS Theory
Two-Particle Correlations in the Wave Function and Covariant Current Approaches* D. Anchishkin1)** and U. Heinz2)*** Received March 26, 2008
Abstract—We consider two-particle correlations which appear in relativistic nuclear collisions owing to the quantum statistics of identical particles in the frame of two formalisms: wave-function and current parametrizations. The first one is based on solution of the Cauchy problem, whereas the second one is a so-called current parametrization of the source of secondary particles. We argue that these two parametrizations of the source coincide when the wave-function at freeze-out times is put into a specific correspondence with a current. Then, the single-particle Wigner density evaluated in both approaches gives the same result. PACS numbers: 25.75.-q, 25.75.Gz, 12.38.Mh DOI: 10.1134/S1063778808090202
1. INTRODUCTION The models and approaches which are used to describe the processes occurring in the reaction region in relativistic heavy-ion collisions are examined by comparison of provided predictions with experimental data on single-, two-, and many-particle momentum spectra, which contain information about the source at the early stage (photons, dileptons) and at the stage of so-called freeze-out (hadron spectra). Two-particle correlations or the Hanbury–Brown–Twiss interferometry (HBT) encapsulates information about the space–time structure and dynamics of the emitting source [1–7]. Usually, consideration of the correlations which occur in relativistic heavy-ion collisions assumes that (i) the particles are emitted independently (or the source is completely chaotic), and (ii) finite-multiplicity corrections can be neglected. Both approximations are expected to be good for high-energy nuclear collisions with large multiplicities. Then, correlations reflect (a) the effects from symmetrization (antisymmetrization) of the amplitude to detect identical particles with certain momenta and (b) the effects which are generated by the finalstate interactions (FSI) of the detected particles between themselves and with the source. At first sight,
one can regard the FSI as a contamination of “pure” particle correlations. But it should be noted that the FSI depend on the structure of the emitting source and thus provide as well information about source dynamics [8]. Several surprising questions motivated by new experimental data appeared recently in the HBT. For instance, the experimental measurements on two-pion correlations [9–12] give the ratio of Rout /Rside ≈ 1, which is much smaller than that predicted theoretically (the so-called RHIC HBT puzzle). This raises the question to what extent some of the model predictions are consistent with experimental measurements [13, 14], or maybe the observed discrepancies are due to such an “apples-with-oranges” comparison. All this drew attention and inspired a more detailed discussion of the theoretical background of the HBT. In the present paper, we are going along this line, and we would like to clarify a ques
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