Bose-Einstein correlations for Lévy stable source distributions

Abstract

The peak of the two-particle Bose-Einstein correlation functions has a very interesting structure. It is often believed to have a multivariate Gaussian form. We show here that for the class of stable distributions, characterized by the index of stability 0 < α ≤ 2, the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of α = 2. We give examples for the Bose-Einstein correlation functions for univariate as well as multivariate stable distributions, and check the model against two-particle correlation data.

Inter-string Bose-Einstein Correlations in Hadronic Z Decays using the L3 Detector at LEP

“…(1.1), ρ 2 is a function of the two fourmomenta. However, BEC are large only when p 1 ≈ p 2 , and it has been found that the correlation function can be adequately parametrized as a function of the four-momentum difference Q, 24) which has the clear advantage of reducing ρ from a six-dimensional function to a one-dimensional one. Hence, two-particle BEC are investigated here using the function…”

“…There have been many discussions (see e.g. [24]) on alternatives to the Gaussian parametrization. However, many of these require model assumptions.…”

Lévy Analysis of HBT Correlation Functions in s N N = 62 GeV and 39 GeV Au + Au Collisions at PHENIX

“…In previous years, Gaussian-type sources were usually utilized to describe the correlation functions, but the latest results from the PHENIX experiment showed that we can and have to go beyond the Gaussian approximation [6,7]. In an expanding medium, on the basis of the generalized central limit theorem and the anomalous diffusion we can expect the appearance of Lévy-type sources [8,9]. The symmetric Lévy distribution is the generalization of the Gaussian distribution and it is defined by the following expression:…”

“…In case of α < 2 the Lévy distribution exhibits a power-law behavior. Neglecting the final-state interactions and assuming that the source is a spherically symmetric three-dimensional Lévy distribution, furthermore using the framework of the core-halo model, the two-particle correlation function takes the following simple form (Q is a one-dimensional relative momentum variable, see details in [9] and in Section 2):…”

PHENIX Results on L\'evy Analysis of Bose--Einstein Correlation Functions

“…One of the best tools to gain information about the particle-emitting source is the measurement of Bose-Einstein or HBT correlations of identical bosons. In our latest measurements, we utilize Lévy-type sources [4,5] to describe the measured correlation functions. In case of a second order QCD phase-transition, one of the source parameters, the index of stability α is related to one of the critical exponents (the so-called correlation exponent η).…”