Alexandre GAVRILIK
Bogolyubov Institute for Theoretical Physics,
14-b Metrologichna Str.,
Kyiv 03143,
UKRAINE
E-mail: omgavr@bitp.kiev.ua

Combined analysis of two- and three-particle correlations in q,p-Bose gas model

Abstract:
Multimode system of $q$-deformed oscillators and the model of ideal gas of $q$-bosons proved to be useful in effective description  [1, 2] of the observed non-Bose type behaviour of the "strength" (intercept) $\lambda^{(2)}\equiv C^{(2)}(K,K)-1$ of two-particle correlation function $C^{(2)}(p_1,p_2)$ of
identical pions emitted and registered in experiments on relativistic heavy-ion collisions.

Three-particle (and higher-order) correlation functions of pions (or kaons) are as well important, as they carry additional useful information on geometry and
dynamics of the emitting sources in such experiments.

Main results of the approach based on the $q$-Bose gas model were further extended [3]: the intercepts of $n$-particle correlation functions were obtained for the
$q$-Bose gas model; general formulas were derived  for the intercepts of $n$-particle correlators within two-parameter ($qp$-) generalization of the model.

Our goal is to present, both for the $q$-Bose gas model and its two-parameter (or $qp$-) extension, the combined analysis of two- and three-pion correlation functions intercepts, and to make a comparison with the existing data on pion correlations from the recent STAR/RHIC experiments.

Important peculiar dependences of $C^{(2)}(p,p)$ and its 3-particle analogue $C^{(3)}(p,p,p)$ on mean momenta of particles (pions, kaons) are studied in detail.

The developed approach implies complete chaoticity of sources, unlike other approaches which assume some (portion of) coherence of sources.

1. D.V. Anchishkin, A.M. Gavrilik and N.Z. Iorgov, Two-particle correlations in the $q$-Bose gas model, Europ. Phys. Journ.  A7 (2000), 229; nucl-th/9906034.
2. D.V. Anchishkin, A.M. Gavrilik and S. Panitkin, Intercept parameter $\lambda$ of two-pion (-kaon) correlation functions in the $q$-boson model: character of its  $p_T$-dependence, Ukrain. J. Phys. 49 (2004), 935; hep-ph/0112262.
3. L.V. Adamska and A.M. Gavrilik, Multi-particle correlations in $qp$-Bose gas model, J. Phys. A 37 (2004), 4787; hep-ph/0312390.