Chiral Phase Transition In QCD Research Articles

Random matrix model for chiral symmetry breaking.

We formulate a random matrix model which mimics the chiral phase transition in QCD with two light flavors. Two critical exponents are calculated. We obtain the mean field values $\beta = \frac 12 $ and $\delta = 3$. We also find that the chiral phase transition can be characterized by the dynamics of the smallest eigenvalue of the Dirac operator. This suggests an alternative order parameter which may be of relevance for lattice QCD simulations.

The chiral phase transition in a random matrix model with molecular correlations

The chiral phase transition of QCD is analyzed in a model combining random matrix elements of the Dirac operator with specially chosen non-random ones. The special form of the latter is motivated by the assumption that the fermionic quasi-zero modes associated with instanton and anti-instanton configurations determine the chiral properties of QCD. Our results show that the degree of correlation between these modes plays the decisive role. To reduce the value of the chiral condensate by more than a factor of 2 about 95 percent of the instantons and anti-instantons must form so-called molecules. This conclusion agrees with numerical results of the Stony Brook group.

Intermittency in the N-component φ4 theory

The effective 3D action of the N-component φ 4 theory is adapted to the space-time hyperbolas of the critical multiparticle system, produced in relativistic ion collisions. In a systematic treatment of the ordered phase at T = T c , a strong intermittency pattern, with a minimal scale in rapidity, naturally emerges. The connection of the solution to chiral QCD phase transition is emphasized and its phenomenological implications are discussed.

Chiral phase transition and instanton-anti-instanton molecules.

We explore the idea that the chiral phase transition in QCD can be described as a transition from a disordered instanton liquid to a strongly correlated phase of polarized instanton anti-instanton molecules. We find a number of non perturbative effects caused by the presence of instantons above T_c, among them the fact that instantons contribute to the euquation of state. We also study how instantons affect the propagation of light quarks at high temperature and determine the spacelike screening masses for mesons and baryons. We derive the corresponding effective interaction and find that the interaction in the scalar-pseudoscalar channel is attractive and four times stronger than the one in the vector-axial-vector channel, in agreement with recent lattice QCD simulations.

QCD AND ASYMPTOTIC FREEDOM: PERSPECTIVES AND PROSPECTS

QCD is now a mature theory, and it is possible to begin to view its place in the conceptual universe of physics with an appropriate perspective. There is a certain irony in the achievements of QCD. For the problems which initially drove its development — specifically, the desire to understand in detail the force that holds atomic nuclei together, and later the desire to calculate the spectrum of hadrons and their interactions — only limited insight has been achieved. However, I shall argue that QCD is actually more special and important a theory than one had any right to anticipate. In many ways, the importance of the solution transcends that of the original motivating problems. After elaborating on these quasiphilosophical remarks, I discuss two current frontiers of physics that illustrate the continuing vitality of the ideas. The recent wealth of beautiful precision experiments measuring the parameters of the standard model have made it possible to consider the unification of couplings in unprecedented quantitative detail. One central result emerging from these developments is a tantalizing hint of virtual supersymmetry. The possibility of phase transitions in matter at temperatures of order ~102 MeV, governed by QCD dynamics, is of interest from several points of view. Besides having a certain intrinsic grandeur, the question “Does the nature of matter change qualitatively, as it is radically heated?” is important for cosmology, relevant to planned high-energy heavy-ion collision experiments, and provides a promising arena for numerical simulations of QCD. Recent numerical work seems to be consistent with expectations suggested by renormalization group analysis of the potential universality classes of the QCD chiral phase transition; specifically, that the transition is second-order for two species of massless quarks but first order otherwise. There is an interesting possibility of long-range correlations in heavy ion collisions due to the creation of large regions of the misaligned chiral condensate. Finally, at the end, there is a brief discussion on the relation between scaling violations and running of the coupling. Some statements made later in the conference seemed to indicate that the relationship between these concepts is commonly misunderstood, so I’m smuggling this bit in even though it wasn’t part of the original talk.

APPLICATION OF THE RENORMALIZATION GROUP TO A SECOND-ORDER QCD PHASE TRANSITION

An earlier suggestion that the chiral phase transition in QCD for two flavors of massless quarks might be a second-order transition has gained credibility as a result of recent numerical simulations. One can test this hypothesis, and draw very specific quantitative consequences from it, using universality and renormalization group ideas. This hypothetical second order phase transition is in the universality class of a four component isotropic Heisenberg antiferromagnet—a model which has been investigated intensely by condensed matter physicists. Existing calculations can be adapted to yield predictions for critical exponents governing the QCD transition. The perturbation due to small equal quark masses maps onto an external staggered magnetic field; that due to unequal quark masses is effective only in second order and generates a quadratic anisotropy. Several other potential applications of the renormalization group to related questions are suggested, including a model of the tricritical point which arises with finite strange quark mass, and a model for the dynamic critical behavior.

On the order of the phase transition in three-dimensionalSU( N)⊗SU( N) and U( N)⊗U( N) Heisenberg models and finite temperature QCD

The finite temperature QCD chiral phase transition for massless SU(2), SU(3), U(2), and U(3) flavor groups is studied using the chiral Heisenberg model. A variety of numerical techniques, including metastability analysis, reduced cumulant of the energy, and finite size scaling were employed to determine the order of the finite temperature chiral phase transition for these flavor symmetries. The SU(2) Heisenberg model had a second order transition while the SU(3), U(2) and U(3) models were first order transitions.

The chiral phase transition in QCD: Critical exponents and their flavour dependence

Abstract We discuss the strong flavour dependence of the critical temperature as well as the order of the phase transition found in Monte Carlo simulations of QCD. Analytical and numerical studies of strong coupling QCD show that the lattice U ( f ) × U ( f ) symmetry may lead to modifications of the order of the phase transition on the lattice, which in the continuum limit is expected to be controlled by the global SU ( n f ) × SU ( n f ) chiral symmetry.

Finite-size study of the finite-temperature chiral phase transition in QCD with light quarks

Finite-size tests were carried out for the finite-temperature chiral phase transition in QCD on a lattice with 4 times slices usign the Kogut-Susskind quark action at the quark mass of 0.025 ( N f = 4 and 2) and 0.0125 ( N f = 2) in lattice units. For N f = 4, all the evidence supports a supports a first-order transition. for N f = 2, however, the data up to a 12 3 spatial lattice do not yield finite-size signatures for a first-order transition of these quark masses.

Chiral phase transition in QCD for finite temperature and density

The chiral phase diagram in the plane of chemical potential and temperature, as derived by studying the effective potential for the fermion sector of QCD with three flavours (in the chiral limit), shows the existence of a tricritical point. In the case of continuous transitions, the critical exponents both for the fermion condensate and for the pion decay constant are the classical ones.

Ambiguities in chiral-symmetry breaking using the effective potential approach

Using a form of the effective potential for composite operators with a variational approach we show that it is possible to get different directions of the chiral phase transition in QCD. Which one occurs depends on the way the Schwinger-Dyson equation for the fermion self-energy is used in the 2-loop term of the effective potential. We must choose the 2-loop term which agrees with phenomenology in each form of the effective potential.

Finite-size test for the finite-temperature chiral phase transition in lattice QCD.

A finite-size test was carried out for the finite-temperature chiral phase transition in QCD for flavor number ${\mathit{N}}_{\mathit{f}}$=4 and 2 on a lattice with four time slices using the Kogut-Susskind quark action at quark mass of 0.025 in lattice units. All the evidence supports a first-order transition for ${\mathit{N}}_{\mathit{f}}$=4. For ${\mathit{N}}_{\mathit{f}}$=2, however, the data on spatial lattice up to ${12}^{3}$ fail to yield convincing finite-size signatures for a first-order transition at this quark mass.

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.

The chiral phase transition in QCD

The Chiral Phase Transition in QCD is studied analytically by looking at truncations of the Schwinger-Dyson equation for the quark self-mass. We find that the usual implementation of the gluon propagator at non-zero temperature is far too simple. When the gluons are given the correct qualitative non-zero temperature behaviour, the calculation of the critical temperature changes significantly.

A model for the chiral phase transition in QCD

We study the temperature dependence of chiral symmetry breaking in Coulomb gauge QCD with massless quarks and an instantaneous approximation for the gluon interaction. The latter is modelled with a simple temperature dependent running coupling constant, which takes into account the known theoretical constraints on the QCD gluon propagator. The ensuing gap equation for the quark-antiquark condensate is solved numerically. We find the predictions of the model to come out quite reasonably, considering the simplicity of our model interaction. The results strongly suggest that the chiral symmetry restoration transition is second order.

On the order of the finite temperature chiral phase transition in QCD

A differential renormalisation group equation is derived for the effective potential of the chiral order parameter of a theory with N f light flavors. Its solution for N f = 3 provides further support to the first-order nature of the finite temperature restoration of chiral symmetry in QCD.