Abstract

The dynamics of QCD matter is often described using effective mean field (MF) models based on Boltzmann–Gibbs (BG) extensive statistics. However, such matter is normally produced in small packets and in violent collisions where the usual conditions justifying the use of BG statistics are not fulfilled and the systems produced are not extensive. This can be accounted for either by enriching the original dynamics or by replacing the BG statistics by its nonextensive counterpart described by a nonextensivity parameter q ≠ 1 (for q → 1 , one returns to the extensive situation). In this work, we investigate the interplay between the effects of dynamics and nonextensivity. Since the complexity of the nonextensive MF models prevents their simple visualization, we instead use some simple quasi-particle description of QCD matter in which the interaction is modeled phenomenologically by some effective fugacities, z. Embedding such a model in a nonextensive environment allows for a well-defined separation of the dynamics (represented by z) and the nonextensivity (represented by q) and a better understanding of their relationship.

Highlights

  • Dense hadronic matter is usually described using relativistic mean field (MF) theory models (like, for example, the Walecka model for nucleons [1,2,3] or the Nambu–Jona-Lasinio model (NJL)for quarks [4,5,6,7])

  • We will continue to use this model and call it the z-quasi-particle models (QPM). This choice is motivated by the fact that in z-QPM, the masses of quasi-particles are not modified by the interaction (they do not depend on the fugacities z(i) ), which allows us to avoid the problems encountered in other approaches

  • To match the pressures in the z-QPM and in the lattice QCD simulations. Note that this procedure assumes that the trace anomaly in the z-QPM (Equation (15) with q = 1) is the same as that resulting from the QCD lattice data [32]

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Summary

Introduction

Dense hadronic matter is usually described using relativistic mean field (MF) theory models (like, for example, the Walecka model for nucleons [1,2,3] or the Nambu–Jona-Lasinio model (NJL). In which the interacting particles (quarks and gluons) are replaced by free quasi-particles They can be formulated in a number of ways, the most popular approaches being: the model encoding the interaction in the effective masses [28,29], the model using the Polyakov loop concept [30,31], and the model based on the Landau theory of Fermi liquids where the effects of the interaction are modeled by some temperature-dependent factors called effective fugacities, z(i) ( T ), which distort the original. We will continue to use this model and call it the z-QPM (note that there are quite a number of other works on the QPM, cf., for example, [38,39,40,41,42]) This choice is motivated by the fact that in z-QPM, the masses of quasi-particles are not modified by the interaction (they do not depend on the fugacities z(i) ), which allows us to avoid the problems encountered in other approaches.

A Short Reminder of the z-QPM
Formulation of the qz-QPM
Results
Summary and Conclusions
Full Text
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