Combined Analysis of Two- and Three-Particle Correlations in q,p-Bose Gas Model

Abstract

Abstract. q-deformed oscillators and the q-Bose gas model enable effective description of the observed non-Bose type behavior of the intercept ("strength") λ (2) ≡ C (2) (K, K) − 1 of two-particle correlation function C (2) (p 1 , p 2 ) of identical pions produced in heavy-ion collisions. Three-and n-particle correlation functions of pions (or kaons) encode more information on the nature of the emitting sources in such experiments. And so, the q-Bose gas model was further developed: the intercepts of n-th order correlators of q-bosons and the n-particle correlation intercepts within the q,p-Bose gas model have been obtained, the result useful for quantum optics, too. Here we present the combined analysis of two-and three-pion correlation intercepts for the q-Bose gas model and its q,p-extension, and confront with empirical data (from CERN SPS and STAR/RHIC) on pion correlations. Similar to explicit dependence of λ (2) on mean momenta of particles (pions, kaons) found earlier, here we explore the peculiar behavior, versus mean momentum, of the 3-particle correlation intercept λ (3) (K). The whole approach implies complete chaoticity of sources, unlike other joint descriptions of two-and three-pion correlations using two phenomenological parameters (e.g., core-halo fraction plus partial coherence of sources).

Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels

“…It would be of interest to analyze possible peculiarities of applying, along the lines similar to those in [16,17,18], the respective versions of q-Bose gas model based on the above constructed novel, nonstandard q-oscillators, in order to examine their efficiency for description of the nonBose type features shown by the data on pion correlations collected in experiments on relativistic heavy ion collisions. Certainly, other applications of the exotic deformed oscillators treated in this paper are worth of detailed study.…”

“…Having chosen two pairs of energy levels, in particular, those given in (10), we applied different cases of quadratic relation p = f (q): parabolic, hyperbolic and elliptic ones, to the two-parametric q,poscillator. On the other hand, with the specified parabolic dependence we treated and obtained the cases of p-oscillator such that the pairs of energy levels (16) or (17) exhibit the two-fold double degeneracy.…”

“…Table 4. Values of the parameters in equation (9) corresponding to p = p 0 and equation (16). Figure 3.…”

Geometric Aspects and Some Uses of Deformed Models of Thermostatistics

“…These include: description of the properties of phonon spectrum in 4 He [8]; physics of excitons [9]; usage of nonstandard statistics and DBGMs in the physics of black holes and dark matter [10][11][12][13][14]; attempts to explain the observed non-Bose features of pions shown by π π-correlations in the RHIC/STAR experiments (see, e.g., [15]). The latter line of application was initiated in [16][17][18], and the approach was further developed in [19][20][21][22][23], with main attention on explicit two-and n-particle distributions and respective correlations (intercepts).…”

The symmetric Tamm–Dancoffq-oscillator: the representation, quasi-Fibonacci nature, accidental degeneracy and coherent states

“…In models of quantum field theory or particle theory, the involved Bose-like deformed oscillators (implying unusual statistics of particles and requiring modified commutation relations) can provide better description of real quantum processes, in particular with participation of pions, see [1], [2]. The use of bosonic deformed oscillators for treating phonons can significantly improve [3] matching between theory and experiment concerning the unstable phonon spectrum in 4 He.…”