First-order chiral phase transition in high-energy collisions: Can nucleation prevent spinodal decomposition?

We consider an approximation procedure to evaluate the finite-temperature one-loop fermionic density in the presence of a chiral background field which systematically incorporates effects from inhomogeneities in the chiral field through a derivative expansion. Modifications in the effective potential and their consequences for the bubble nucleation process are discussed. Keywords: Chiral symmetry breakingThe mechanism of chiral symmetry breaking and the study of the dynamics of phase conversion after a temperaturedriven chiral transition can be done conveniently within lowenergy effective models [1][2][3][4][5][6][7][8][9]. In particular, to study the mechanisms of bubble nucleation and spinodal decomposition in a hot expanding plasma [10], it is common to adopt the linear σ-model coupled to quarks [11]. The gas of quarks provides a thermal bath in which the long-wavelength modes of the chiral field evolve, and the latter plays the role of an order parameter in a Landau-Ginzburg approach to the description of the chiral phase transition. The standard procedure is then integrating over the fermionic degrees of freedom, using a classical approximation for the chiral field, to obtain a formal expression for the thermodynamic potential from which one can obtain all the physical quantities of interest.To compute correlation functions and thermodynamic quantities, one has to evaluate the fermionic determinant that results from the functional integration over the quark fields within some approximation scheme. Usually one performs a standard one-loop calculation assuming a homogeneous and static background field [12]. Nevertheless, for a system that is in the process of phase conversion after a chiral transition, one expects inhomogeneities in the chiral field configuration due to fluctuations to play a major role in driving the system to the true ground state. In fact, for high-energy heavy ion collisions, hydrodynamical studies have shown that significant density inhomogeneities may develop dynamically when the chiral transition to the broken symmetry phase takes place [6], and inhomogeneities generated during the late stages of the nonequilibrium evolution of the order parameter might leave imprints on the final spatial distributions and even on the integrated, inclusive abundances [13].In this paper we briefly describe an approximation procedure to evaluate the finite-temperature fermionic density in the presence of a chiral background field, which systematically incorporates effects from inhomogeneities in the bosonic field through a gradient expansion. (For details, see Ref. [14].) The method is valid for the case in which the chiral field varies smoothly, and allows one to extract information from its long-wavelength behavior, incorporating corrections order by order in the derivatives of the field. For simplicity, we ignore corrections coming from bosonic fluctuations in what follows. Those would result in a bosonic determinant correction to the effective potential [15]. To focus on the effect of an inhomogeneou...

Section: Abstract: Chiral Symmetry Breakingmentioning

confidence: 99%

“…This kind of effective potential is commonly used as the coarse-grained thermodynamic potential in a phenomenological description of the chiral transition for an expanding quarkgluon plasma [3][4][5][6].…”

Section: Now We Expandmentioning

confidence: 99%

Nucleation in the chiral transition with an inhomogeneous background

Taketani¹,

Fraga²

2007

“…The effective potential, U e f f (φ, T ), for the chiral condensate φ( x,t) can be obtained, for instance, from an effective chiral model as described in Ref. [4].…”

Section: Chiral Transition Early-time Dynamicsmentioning

confidence: 99%

“…Results from CERN-SPS and BNL-RHIC feature an explosive behavior in the hadronization process and seem to favor a very fast spinodal decomposition as the mechanism of phase conversion. Effective chiral field theory models for QCD also point to an explosive spinodal decomposition scenario [3,4].…”

Section: Introductionmentioning

confidence: 99%

Non-local effects at the onset of the chiral transition

Palhares¹,

Fraga²,

Kodama³

et al. 2007

Inspired by analytic results obtained for a systematic expansion of the memory kernel in dissipative quantum mechanics, we propose a phenomenological procedure to incorporate non-markovian corrections to the Langevin dynamics of an order parameter in field theory systematically. In this note, we restrict our analysis to the onset of the evolution. As an example, we consider the process of phase conversion in the chiral transition.

“…On the other hand, for small chemical potential, far from the region where the σ-field is critical, the relevant scale might be set by the correlation length for Polyakov loops, which is of comparable magnitude [16]. Classical nucleation theory for strong firstorder phase transitions predicts even larger "bubbles" [17] but is unlikely to apply to small, rapidly expanding systems encountered in heavy-ion collisions [5,18]. Another (classical) model for the formation of small droplets in rapidly expanding QCD matter has been introduced in [19].…”

Section: Introductionmentioning

confidence: 99%

The role of local and global strangeness neutrality at the inhomogeneous freeze-out in relativistic heavy ion collisions

Zschiesche¹,

Portugal²

2007

The decoupling surface in relativistic heavy-ion collisions may not be homogeneous. Rather, inhomogeneities should form when a rapid transition from high to low entropy density occurs. We analyze the hadron "chemistry" from high-energy heavy-ion reactions for the presence of such density inhomogeneities. We show that due to the non-linear dependence of the particle densities on the temperature and baryon-chemical potential such inhomogeneities should be visible even in the integrated, inclusive abundances. We analyze experimental data from Pb+Pb collisions at CERN-SPS and Au+Au collisions at BNL-RHIC to determine the amplitude of inhomogeneities and the role of local and global strangeness neutrality.