Hadronic Bubbles Research Articles

Quark-hadron phase transitions in the viscous early universe

Based on hot big bang theory, the cosmological matter is conjectured to undergo QCD phase transition(s) to hadrons, when the universe was about $1-10 \mu$s old. In the present work, we study the quark-hadron phase transition, by taking into account the effect of the bulk viscosity. We analyze the evolution of the quantities relevant for the physical description of the early universe, namely, the energy density $\rho$, temperature $T$, Hubble parameter $H$ and scale factor $a$ before, during and after the phase transition. To study the cosmological dynamics and the time evolution we use both analytical and numerical methods. By assuming that the phase transition may be described by an effective nucleation theory (prompt {\it first-order} phase transition), we also consider the case where the universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles. The numerical estimation of the cosmological parameters, $a$ and $H$ for instance, makes it clear that the time evolution varies from phase to phase. As the QCD era turns to be fairly accessible in the high-energy experiments and the lattice QCD simulations, the QCD equation of state is very well defined. In light of this, we introduce a systematic study of the {\it cross-over} quark-hadron phase transition and an estimation for the time evolution of Hubble parameter.

Effect of an extrinsic curvature on a quark–hadron phase transition

The last phase transition predicted by the standard model of particle physics took place at the QCD scale T ∼ 200 MeV when the universe was about t ∼ 10−5 s old and the Hubble radius was around 10 km. In this paper, we consider the quark–hadron phase transition in the context of braneworld cosmology where our universe is a 3-brane embedded in an m-dimensional bulk and localization of matter on the brane is achieved by means of a confining potential. We study the behavior of the physical quantities relevant to the description of the early universe such as the energy density, temperature and scale factor, before, during and after the phase transition and investigate the effects of an extrinsic curvature on the cosmological phase transition. We show that the braneworld effects reduce the effective temperature of the quark–gluon plasma and of the hadronic fluid. Finally, we discuss the case where the universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles.

Quark–hadron phase transitions in brane-world cosmologies

When the universe was about 10 μs old, a first order cosmological quark–hadron phase transition occurred at a critical temperature of around 200 MeV. In this work, we study the quark–hadron phase transition in the context of brane-world cosmologies, in which our Universe is a three-brane embedded in a five-dimensional bulk, and within an effective model of QCD. We analyze the evolution of the physical quantities, relevant for the physical description of the early universe, namely, the energy density, temperature and scale factor, before, during, and after the phase transition. To study the cosmological dynamics and evolution we use both analytical and numerical methods. In particular, due to the high energy density in the early Universe, we consider in detail the specific brane world model case of neglecting the terms linearly proportional to the energy density with respect to the quadratic terms. A small brane tension and a high value of the dark radiation term tend to decrease the effective temperature of the quark–gluon plasma and of the hadronic fluid, respectively, and to significantly accelerate the transition to a pure hadronic phase. By assuming that the phase transition may be described by an effective nucleation theory, we also consider the case where the Universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles.

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

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. Very general arguments allow us to show that the finite size of the early universe has virtually no relevance in the process of nucleation and in the growth of cosmological bubbles during the primordial quark–hadron and the electroweak phase transitions. In the case of high-energy heavy ion collisions, finite-size effects play an important role in the late-stage growth of hadronic bubbles.

EFFECTS OF CURVATURE AND INTERACTIONS ON THE DYNAMICS OF THE DECONFINEMENT PHASE TRANSITION

We study the dynamics of first-order confinement-deconfinement phase transition through nucleation of hadronic bubbles in an expanding quark–gluon plasma in the context of heavy ion collisions for interacting quark and hadron gas and by incorporating the effects of curvature energy. We find that the interactions reduce the delay in the phase transition whereas the curvature energy has a mixed behavior. In contrast to the case of early Universe phase transition, here lower values of surface tension increase the supercooling and slow down the hadronization process. Higher values of bag pressure tend to speed up the transition. Another interesting feature is the start of the hadronization process as soon as the QGP is created.

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

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. Very general arguments allow us to show that the finite size of the early universe has virtually no relevance in the process of nucleation and in the growth of cosmological bubbles during the primordial quark–hadron and the electroweak phase transitions. In the case of high-energy heavy ion collisions, finite-size effects play an important role in the late-stage growth of hadronic bubbles.

Dynamical growth of the hadron bubbles during the quark-hadron phase transition

The rate of dynamical growth of the hadron bubbles in a supercooled baryon free quark-gluon plasma is evaluated by solving the equations of relativistic fluid dynamics in all regions. For a nonviscous plasma, this dynamical growth rate is found to depend only on the range of correlation $\ensuremath{\xi}$ of order parameter fluctuation, and the radius R of the critical hadron bubble, the two length scales relevant for the description of the critical phenomena. Further, it is shown that the dynamical prefactor acquires an additive component when the medium becomes viscous. Interestingly, under certain reasonable assumptions for the velocity of the sound in the medium around the saddle configuration, the viscous and the nonviscous parts of the prefactor are found to be similiar to the results obtained by Csernai and Kapusta and Ruggeri and Friedman (for the case of zero viscosity), respectively.

Inhomogeneous nucleation in a quark-hadron phase transition

The effect of subcritical hadron bubbles on a first-order quark-hadron phase transition is studied. These subcritical hadron bubbles are created due to thermal fluctuations, and can introduce a finite amount of phase mixing (quark phase mixed with hadron phase) even at and above the critical temperature. For reasonable choices of surface tension and correlation length, as obtained from the lattice QCD calculations, we show that the amount of phase mixing at the critical temperature remains below the percolation threshold. Thus, as the system cools below the critical temperature, the transition proceeds through the nucleation of critical-size hadron bubbles from a metastable quark-gluon phase (QGP), within an inhomogeneous background populated by an equilibrium distribution of subcritical hadron bubbles. The inhomogeneity of the medium results in a substantial reduction of the nucleation barrier for critical bubbles. Using the corrected nucleation barrier, we estimate the amount of supercooling for different parameters controlling the phase transition, and briefly discuss its implications to cosmology and heavy-ion collisions.

Erratum: Supercooling in viscous hydrodynamics for QCD phase transition [Phys. Rev. C59, 914 (1999)

First order quark hadron phase transition is considered in scaling hydrodynamics including the Csernai-Kapusta model of nucleation of hadronic bubbles leading to supercooling. The effect of viscosity on the entropy production is studied in ideal as well as in viscous hydrodynamics with and without supercooling. It is found that the excess entropy produced due to supercooling depends weakly on viscosity.

Does the quark-gluon plasma contain stable hadronic bubbles?

We calculate the thermodynamic potential of bubbles of hadrons embedded in quark-gluon plasma, and of droplets of quark-gluon plasma embedded in hadron phase. This is a generalization of our previous results to the case of non-zero chemical potentials. As in the zero chemical potential case, we find that a quark-gluon plasma in thermodynamic equilibrium may contain stable bubbles of hadrons of radius $R \simeq 1$ fm. The calculations are performed within the MIT Bag model, using an improved multiple reflection expansion. The results are of relevance for neutron star phenomenology and for ultrarelativistic heavy ion collisions.

Dynamical viscosity of nucleating bubbles

We study the viscosity corrections to the growth rate of nucleating bubbles in a first order phase transition in scalar field theory. We obtain the non-equilibrium equation of motion of the coordinate that describes small departures from the critical bubble and extract the growth rate consistently in weak coupling and in the thin wall limit. Viscosity effects arise from the interaction of this coordinate with the stable quantum and thermal fluctuations around a critical bubble. In the case of 1+1 dimensions we provide an estimate for the growth rate that depends on the details of the free energy functional. In 3+1 dimensions we recognize robust features that are a direct consequence of the thin wall approximation and give the leading viscosity corrections.These are long-wavelength hydrodynamic fluctuations that describe surface waves, quasi-Goldstone modes which are related to ripples on interfaces in phase ordered Ising-like systems. We discuss the applicability of our results to describe the growth rate of hadron bubbles in a quark-hadron first order transition.

Effect of thermal fluctuations on the first order quark-hadron phase transition

We study the effects of thermal fluctuations on the dynamics of the quark-hadron phase transition assuming the phase transition to be of first order. These fluctuations give rise to a sizable fraction (up to 0.5) of the total volume occupied by the hadronic phase in the form of subcritical bubbles for temperatures near and below the critical temperature ${(T}_{c}).$ This suggests that the phase transition will not proceed through homogeneous bubble nucleation. We also discuss the possibility, if any, of percolation of subcritical hadron bubbles and its role in the phase transition.

Free energy of bubbles and droplets in the quark-hadron phase transition

Using the MIT bag model, we calculate the free energy of droplets of quark-gluon plasma in a bulk hadronic medium, and of hadronic bubbles in a bulk quark-gluon plasma, under the assumption of vanishing chemical potentials. We investigate the validity of the multiple reflection expansion approximation, and we advise a novel procedure for calculating finite-size corrections to the free energy of hadronic bubbles in a bulk quark-gluon plasma. While our results agree largely with earlier calculations, we show that the usual multiple reflection expansion should be used with caution, and we propose a modification of the multiple reflection expansion, which makes this approximation agree nicely with direct numerical calculations. The results should be of relevance in connection with the cosmological quark-hadron transition as well as for ultrarelativistic heavy ion collisions.

Supercooling in viscous hydrodynamics for QCD phase transition

First order quark hadron phase transition is considered in scaling hydrodynamics including the Csernai-Kapusta model of nucleation of hadronic bubbles leading to supercooling. The effect of viscosity on the entropy production is studied in ideal as well as in viscous hydrodynamics with and without supercooling. It is found that the excess entropy produced due to supercooling depends weakly on viscosity.

Quark-hadron phase transition in models with chiral symmetry

We calculate the hadron bubble nucleation rate in the quark plasma after the quark-hadron phase transition within chiral models of QCD. The model parameters are constrained by the phenomenology of low energy hadron physics. It is found that for some of the values of the parameters in the ranges allowed by these constraints the bubble nucleation rate is strongly suppressed, resulting in a high degree of supercooling, indicating the possibility of forming large quark star-like objects.

AN UPPER LIMIT ON MASS DENSITY OF QUARK NUGGETS FROM THE MICROLENSING EVENT STATISTICS

We calculate the spectrum of separations between nucleation sites of hadron bubbles formed during the first-order cosmic QCD phase transition considered within the Lee–Wick model, an effective QCD model. On the basis of the separation spectrum, we construct a naive model mass spectrum of quark nuggets. Using this mass spectrum and the microlensing event statistics of the MACHO group, we place an upper limit on the mass density of quark nuggets in the galactic halo.

Surface tension in the QCD phase transition in the dual Ginzburg-Landau theory

We study the surface tensions in the mixed phase of QCD at the quenched level using the dual Ginzburg-Landau theory, where the QCD-monopole condensate is the order parameter on the confinement. First, we consider the thermal mixed phase, and derive the analytical expressions for the surface tension, the boundary thickness in terms of the shape of the effective potential, and the latent heat. We study also the properties of the spherical hadron bubble in the quark-gluon-plasma phase at finite temperature. Second, we study the surface tension in the mixed phase with the external color-electric field at zero temperature. In the type-II dual superconductor, the individual flux tubes with unit color flux are stable. On the other hand, the flux tubes tend to melt into a huge tube, which is energetically favored, in the type-I case.

Dynamical growth rate of hadron bubbles in a baryon-free quark-gluon plasma.

We evaluate the factor $\kappa$ appearing in Langer's expression for the nucleation rate extended to the case of hadron bubbles forming in zero baryon number cooled quark-gluon plasma. We consider both the absence and presence of viscosity and show that viscous effects introduce only small changes in the value of $\kappa$

Hydrodynamics of the cosmological quark-hadron transition in the presence of long-range energy and momentum transfer.

Two previous papers in this series have presented a study of the growth of hadronic bubbles during the cosmological quark-hadron transition, treating the material within each phase as a single perfect fluid. Here, we extend the analysis to include the effects of long-range energy and momentum transfer by weakly and electromagnetically interacting particles. After a short review of the formalism adopted, we discuss the numerical strategies used in the computer code which has been constructed in order to solve this system of equations. Results for the growth of single hadronic bubbles are also presented.

Large scale inhomogeneities from the QCD phase transition.

We examine the first-order cosmological QCD phase transition for a large class of parameter values, previously considered unlikely. We find that the hadron bubbles can nucleate at very large distance scales, they can grow as detonations as well as deflagrations, and that the phase transition may be completed without reheating to the critical temperature. For a subset of the parameter values studied, the inhomogeneities generated at the QCD phase transition might have a noticeable effect on nucleosynthesis.