Higher order femtoscopy measured to examine the heat exchanger characterization of the fluid debris produced in the collisions and investigated a remarkable suppression in the bosons interferences measurement. The analogous suppression can be analyzed to explore the coherence of boson thermal particle production sources at unprecedented energies. We illustrate the particles emissions from radiated sources with statistical coherence which induce the thermal particles interferences to probe the peculiarity of the heated sources as well as the distinctions about the heat exchangers in the collisions at higher temperature. We perspicacious that the bosons seem to the pertinent aspirant of heat exchanger, and the normalized three particles correlators evaluate the existence of such hybrid phases significantly. The key point of this research is that we analyze the three particles correlations with their normalized correlations by difference equations to determine the characteristics of heat exchanger and its applications. With such distinctive and efficient approach, we observe a significant difference in the correlation functions at higher temperature and momenta regimes.

Femtoscopy is a unique tool to investigate the space-time geometry of the matter created in ultra-relativistic collisions. If the probability density distribution of hadron emission is parametrized, then the dependence of its parameters on particle momentum, collision energy, and collision geometry can be given. In recent years, several measurements came to light that indicated the adequacy of assuming a Lévy-stable shape for the mentioned distribution. In parallel, several new phenomenological developments appeared, aiding the interpretation of the experimental results, or providing tools for the measurements. In this paper we review and discuss some of these advances, phenomenological and experimental.

In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in $\sqrt{S_{NN}}$= 200 GeV Au+Au collisions, in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a statistically acceptable description of the measured correlation functions, with three physical parameters: correlation strength parameter λ , Lévy index α and Lévy scale parameter R. The transverse mass dependence of these Lévy parameters is then investigated. Their physical interpretation is also discussed, and the appearance of a new scaling variable is observed.