Spinodal instability in the quark-gluon plasma

Abstract

We investigate the onset of spinodal decomposition in a relativistic fluid of quarks coupled to a nonequilibrium chiral condensate. Studying small fluctuations around equilibrium, we identify the role played by sound and chiral waves in the generation of unstable modes.The hadronization of the quark-gluon plasma (QGP) possibly produced in the early universe or in high-energy heavy-ion collisions may proceed in a number of different ways, depending on the nature of the QCD phase transition. In the heavy-ion case, some results from CERN-SPS and BNL-RHIC suggest what has been called sudden hadronization [1] or explosive behavior [2,3]. From the theoretical side, this phenomenon has been associated associated with deep supercooling of the QGP followed by spinodal decomposition, and also to rapid changes in the effective potential of QCD near the critical temperature, such as predicted, for instance, by the Polyakov loop model [4]. Clearly, an understanding of the interplay between the typical space and time scales of the expanding plasma is welcome. Some attempts in this direction can be found in Refs. [5,6,7,8,9,10,11,12,13].In this paper, we discuss the onset of spinodal instability in an expanding plasma. As a phenomenological model to mimic the case of the QGP, we use a relativistic plasma of quarks coupled to a chiral field. The later is not necessarily in thermal equilibrium with the quark fluid. Although we derive a phenomenological nonequilibrium chiral hydrodynamics from a variational principle, we do not focus on the numerical solution of the resulting hydrodynamic transport equations.To model the mechanism of chiral symmetry breaking present in QCD, we adopt a simple low-energy effective chiral model: the linear σ-model coupled to quarks [14], which in turn comprise the hydrodynamic degrees of freedom of the system. Similar approaches, relying on low-energy effective models for QCD and making use of a number of techniques to treat the expanding plasma, can be found in the literature [5,6,7,8,9]. The gas of quarks provides a thermal bath in which the long-wavelength modes of the chiral field evolve. The latter plays the role of an order parameter in a Landau-Ginzburg description of the chiral phase transition [8,9].Let us consider a chiral field φ = (σ, π), where σ is a scalar field and π i are pseudoscalar fields playing the role of the pions, coupled to two flavors of quarks according to the Lagrangian:Here q = (u, d) is the constituent-quark field and µ q = µ/3 is the quark chemical potential. The interaction between the quarks and the chiral field is given by In what follows, we treat the gas of quarks as a heat bath for the chiral field, with temperature T and baryon-chemical potential µ. Integrating over the fermionic degrees of freedom and using a classical approximation for the chiral field, we can write the thermodynamic potential aswhere G E is the fermionic Euclidean propagator and V is the (infinite) volume of the system. The determinant that results from the functional integration over the qua...

Topics on hydrodynamic model of nucleus-nucleus collisions

“…In this sense, it is very important to develop transport theoretical investigations [75,76] related to hydro description. Another interesting type of phenomena related to the hydrodynamical model is the ocurrence of instabilities associated to the phase transition and surface tension (finite-size effects), such as spinodal instabilities [77]. Some studies in this direction is in progress.…”

Finite-size effects on nucleation in a first-order phase transition

“…Moreover, one would be able to control the behavior of domains and study, for instance, scaling properties [12]. It is also interesting to study the hydrodynamics of nuclear matter at chiral limit as a phenomenological description of the chiral transition in an expanding quark-gluon plasma [34][35][36][37]. Results in this direction will be presented elsewhere.…”

Two-particle correlations at high-energy nuclear collisions, peripheral-tube model revisited

“…On the other hand, in our code, it is possible to determine the number of participant nucleons in each event, which is closely related to the experimental centrality. In specific cases, they may give rise to nontrivial effects [43] due to the fluctuations. In the calculations presented below, however, we still utilize the impact parameter to determine the centrality class.…”