Finite-size constraints on nucleation of hadrons in a quark-gluon plasma

Abstract

We discuss finite-size effects on homogeneous nucleation in first-order phase transitions. We study their implications for cosmological phase transitions and to the hadronization of a quark-gluon plasma generated in high-energy heavy ion collisions.Finite-size scaling has achieved an immense success in the study of equilibrium critical phenomena. On the other hand, systematic studies of finite size effects in the case of metastable decays and other nonequilibrium processes are rare [1,2]. In this paper, we discuss finite size effects on the dynamics of homogeneous nucleation in a first-order temperature-driven transition (For more details, see [3]). In particular, we consider the case of cosmological phase transitions in the early universe [4], and that of a quark-gluon plasma (QGP) decay into hadronic matter in a high-energy heavy ion collision [5,6]. The former might provide sensible mechanisms to explain the baryon number asymmetry in the universe and primordial nucleosynthesis [7,8], whereas the latter is expected to be observed [9] at BNL Relativistic Heavy Ion Collider (RHIC). The length and time scales involved in each of these cases differ by several orders of magnitude.In the usual description of homogeneous nucleation [1], there are two ways in which the finite size of the system can affect the formation and evolution of bubbles and, consequently, the dynamics of phase conversion. Firstly, one has to consider the effects on the nucleation rate and the early stage growth of the bubbles. As will be shown below, this correction comes about through an intrinsic uncertainty in the determination of the supercooling undergone by the system. For the cases considered here, it brings only minor modifications to a description which assumes an infinite system. The second and, in general, most important finite-size effect is its influence on the domain coarsening process, or late-stage growth of the bubbles. The relevant length scales here are the typical size of the system, the radius of the critical bubble and the correlation length.In a continuum description of a first-order phase transition, it is common to consider a coarse-grained free energy, F , of the Landau-Ginzburg form with temperaturedependent coefficients [1]. (In the case of QCD, such a free energy can be obtained, for instance, from the oneloop effective potential of a linear sigma model coupled to quarks [10,11].) The nucleation rate can be expressed as Γ = P e −F b /T , where F b is the free energy of a critical bubble, with radius R c , and the prefactor P measures statistical and dynamical fluctuations about the saddle point of the Euclidean action in functional space. It is convenient to write the prefactor P as a product of the bubble's growth rate and a factor proportional to the ratio of the determinant of the fluctuation operator around the bubble configuration relative to that around the homogeneous metastable state [12]. For the relativistic case, in the thin-wall limit, we have [13]:Here, η and ξ are respectively the shear viscosity and ...

Finite size effects on pion spectra in relativistic heavy-ion collisions

“…Although not commonly considered, it is certainly true that small size effects are important in the description of statistical systems. For example, finite size effects have influence on the late-stage growth of nucleated bubbles during a first order phase transition [8]. Also, in the statistical hadronization model, the states used for the description are in general different to the observed asymptotic ones but such difference is not an issue unless the volume of the system is small, typically of order O(10 fm) 3 [9].…”

Proton and pion transverse spectra at the BNL Relativistic Heavy Ion Collider from radial flow and finite size effects

“…Although not commonly considered, small size effects are important in the description of a variety of phenomena associated with statistical systems such as the latestage growth of nucleated bubbles during a first order phase transition [10] and the statistical hadronization model [11]. Finite size effects are also known to influ-ence the interpretation of the correlation lengths in Hanbury Brown-Twiss analysis in the context of relativistic heavy-ion collisions [12,13].…”