Stable Bose-Einstein correlations

The shape of Bose-Einstein (or HBT) correlation functions is determined for the case when particles are emitted from a stable source, obtained after convolutions of large number of elementary random processes. The two-particle correlation function is shown to have a {\it stretched exponential} shape, characterized by the L\'evy index of stability $0 < \alpha \le 2$ and the scale parameter $R$. The normal, Gaussian shape corresponds to a particular case, when $\alpha = 2$ is selected. The asymmetry parameter of the stable source, $\beta$ is shown to be proportional to the angle, measured by the normalized three-particle cumulant correlations.Comment: 7 pages, no figures, invited talk of T. Csorgo at the 2nd Warsaw Meeting on Particle Correlations and Resonances in HIC, see http://hirg.if.pw.edu.pl/en/meeting/oct2003/talks/csorgo/Csorgo.pp

Bose-Einstein or HBT correlations and the anomalous dimension of QCD

Bose-Einstein (or HBT) correlation functions are evaluated for the fractal structure of QCD jets. These correlation functions have a stretched exponential (or Levy-stable) form. The anomalous dimension of QCD determines the Levy index of stability, thus the running coupling constant of QCD becomes measurable with the help of two-particle Bose-Einstein correlation functions. These considerations are tested on NA22 and UA1 two-pion correlation data.Comment: 8 pages, 5 figures, presented by T. Csorgo at the XXXIV International Symposium on Multiparticle Dynamics, Sonoma County, California, USA, July 2004, to appear in Acta Physica Polonica

Bose-Einstein or HBT correlation signature of a second order QCD phase transition

For particles emerging from a second order QCD phase transition, we show that a recently introduced shape parameter of the Bose-Einstein correlation function, the Levy index of stability equals to the correlation exponent - one of the critical exponents that characterize the behavior of the matter in the vicinity of the second order phase transition point. Hence the shape of the Bose-Einstein / HBT correlation functions, when measured as a function of bombarding energy and centrality in various heavy ion reactions, can be utilized to locate experimentally the second order phase transition and the critical end point of the first order phase transition line in QCD.Comment: 8 pages, talk given by T. Csorgo at the Workshop on Particle Correlations and Femtoscopy 2005, Kromeriz, Czech Republic, August 200

A Bose-Einstein Model of Particle Multiplicity Distributions

A model of particle production is developed based on a parallel with a theory of Bose-Einstein condensation and similarities with other critical phenomena such as critical opalescence. The role of a power law critical exponent tau and Levy index alpha are studied. Various features of this model are developed and compared with other commonly used models of particle production which are shown to differ by having different values for tau, alpha. While void scaling is a feature of this model, hierarchical structure is not a general property of it. The value of the exponent tau=2 is a transition point associated with void and hierarchical scaling features. An exponent gamma is introduced to describe enhanced fluctuations near a critical point. Experimentally determined properties of the void scaling function can be used to determine tau.Comment: Accepted for publication in Nucl. Phys.

Analytic Solution of the Pion-Laser Model

Brooding over bosons, wave packets and Bose - Einstein correlations, we find that a generalization of the pion-laser model for the case of overlapping wave-packets is analytically solvable with complete n-particle symmetrization. The effective radius parameter of the two-particle correlation function is reduced for low values and enlargened for high values of the mean momentum in the rare gas limiting case, as compared to the case when multi-particle symmetrization effects are neglected. These results explicitly depend on the multiplicity, providing a theoretical basis for event-by-event analysis of high energy heavy ion reactions.Comment: LaTeX, ReVTeX 3.1, 7 pages, uses 1 eps figure and epsfig.sty (shortened version

Model independent shape analysis of correlations in 1, 2 or 3 dimensions

A generic, model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT or GGLP), statistical, dynamical or other short-range correlation functions. The method is based on a data-motivated choice for the zero-th order approximation for the shape of the correlation function, and on a systematic determination of the correction terms with the help of complete orthonormal set of functions. The Edgeworth expansion is obtained for approximately Gaussian, the Laguerre expansion for approximately exponential correlation functions. Multi-dimensional expansions are also introduced and discussed.Comment: Latex, 15 pages, uses epsfig.sty elsart.sty, misprints correcte

Quality evaluation of fresh and bloomed filled chocolates in House of Quality

C