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

Scaling Laws in Hierarchical Clustering Models with Poisson Superposition

Properties of cumulant- and combinant ratios are studied for multihadron final states composed of Poisson distributed clusters. The application of these quantities to ``detect'' clusters is discussed. For the scaling laws which hold in hierarchical clustering models (void scaling, combinant scaling) a generalization is provided. It is shown that testing hierarchical models is meaningful only for phase-space volumes not larger than the characteristic correlation length introduced by Poisson superposition. Violation of the scaling laws due to QCD effects is predicted.Comment: 14 pages, Plain TeX, no figure

H-function extension of the NBD: further applications

The H-function extension of the Negative Binomial Distribution is investigated for scaling exponents mu<0. Its analytic form is derived via a convolution property of the H-function. Applications are provided using multihadron and galaxy count data for P(n).Comment: 6 pages REVTeX, 3 figure

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