Chiral Phase Transition In QCD Research Articles

Signal of the pion string at high-energy collisions

We study the possible signals of a pion string associated with the QCD chiral phase transition in LHC Pb-Pb collision at energy $\sqrt{s}=5.5\phantom{\rule{0.3em}{0ex}}\text{TeV}$. In terms of the Kibble-Zurek mechanism we discuss the production and evolution of the pion string. The pion string is not topologically stable; it decays into neutral pions and sigma mesons that in turn decay into pions. Our results show that all the neutral pions from the pion string are distributed at the low momentum and the ratio of neutral to charged pions from the pion string violates the isospin symmetry. For the momentum spectra of the total pions, the signal from the sigma particle decay from the pion string will be affected by the large decay width of the sigma significantly.

On the chiral phase transition in hadronic matter

A qualitative analysis of the chiral phase transition in QCD with two massless quarks and non--zero baryon density is performed. It is assumed that at zero baryonic density, \rho=0, the temperature phase transition is of the second order. Due to a specific power dependence of baryon masses on the chiral condensate the phase transition becomes of the first order at the temperature T=T_{ph}(\rho) for \rho>0. At temperatures T_{cont}(\rho) > T > T_{ph}(\rho) there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature T = T_{cont}(\rho) the system experiences a continuous transition to the pure chirally symmetric phase.

Magnetic wall from chiral phase transition and CMBR correlations

Possible cosmic microwave background radiation (CMBR) correlations are estimated for a model in which a Hubble-size magnetic wall is formed during the QCD chiral phase transition. Measurable polarization correlations are found for l values greater than about 1000. It is also found that metric perturbations from the wall could give rise to observable CMBR correlations for large l.

Large scale magnetogenesis from a nonequilibrium phase transition in the radiation dominated era

We study the generation of large scale primordial magnetic fields by a cosmological phase transition during the radiation dominated era. The setting is a theory of N charged scalar fields coupled to an Abelian gauge field, that undergoes a phase transition at a critical temperature much larger than the electroweak scale. The dynamics after the transition features two distinct stages: a spinodal regime dominated by linear long-wavelength instabilities, and a scaling stage in which the nonlinearities and back reaction of the scalar fields are dominant. This second stage describes the growth of horizon sized domains. We implement a recently introduced formulation to obtain the spectrum of magnetic fields that includes the dissipative effects of the plasma. We find that large scale magnetogenesis is very efficient during the scaling regime. The ratio between the energy density on scales larger than L and that in the background radiation $r(L,T)={\ensuremath{\rho}}_{B}(L,T)/{\ensuremath{\rho}}_{\mathrm{cmb}}(T)$ is $r(L,T)\ensuremath{\sim}{10}^{\ensuremath{-}34}$ at the electroweak scale and $r(L,T)\ensuremath{\sim}{10}^{\ensuremath{-}14}$ at the QCD scale for $L\ensuremath{\sim}1\mathrm{Mpc}.$ The resulting spectrum is insensitive to the magnetic diffusion length. We conjecture that a similar mechanism could be operative after the QCD chiral phase transition.

Pion Propagation near the QCD Chiral Phase Transition

We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that, when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition.

New critical matrix models and generalized universality

We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus defining a new class of multicritical matrix models. The corresponding microscopic scaling law is given and possible applications to the chiral phase transition in QCD are discussed. For generic coupling constants off-criticality we prove that all microscopic correlation functions at the origin of the spectrum remain in the known Bessel universality class. An arbitrary number of Dirac mass terms can be included and the corresponding massive universality is maintained as well. We also investigate the critical behavior at the edge of the spectrum: there, in contrast to the behavior at the origin, we find the same critical exponents as derived from matrix models with a polynomial action.

RELAXING NEAR THE CRITICAL POINT

I present an analysis of the relaxation rate for long-wavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point. Our motivation is to model the non-equilibrium dynamics of critical fluctuations near the chiral phase transition in QCD. In the next-to-leading order in the large N expansion we find a critical slowing down regime, i.e. an increasing of the relaxation time of long wavelengths fluctuations. This result suggests, for near critical systems, relevant deviations from thermal equilibrium for the distribution functions of low-energy particles and could have important phenomenological consequences in Heavy Ions Collision and in the Early Universe Cosmology.

Current quark mass effects on the chiral phase transition of QCD in the improved ladder approximation

Current quark mass effects on the chiral phase transition of QCD is studied in the improved ladder approximation. An infrared behavior of the gluon propagator is modified in terms of an effective running coupling. The analysis is based on a composite operator formalism and a variational approach. We use the Schwinger-Dyson equation to give a ``normalization condition'' for the Cornwall-Jackiw-Tomboulis effective potential and to isolate the ultraviolet divergence which appears in an expression for the quark-antiquark condensate. We study the current quark mass effects on the order parameter at zero temperature and density. We then calculate the effective potential at finite temperature and density and investigate the current quark mass effects on the chiral phase transition. We find a smooth crossover for $T>0$, $\mu=0$ and a first-order phase transition for $\mu>0$, T=0. Critical exponents are also studied and our model gives the classical mean-field values. We also study the temperature dependence of masses of scalar and pseudoscalar bosons. A critical end point in the $T$-$\mu$ plane is found at $T \sim 100$ MeV, $\mu \sim 300$ MeV.

NONLINEAR SIGMA MODEL APPROACH FOR PHASE DISORDER TRANSITIONS IN CHIRAL GROSS–NEVEU, NAMBU–JONA-LASINIO MODELS AND STRONG-COUPLING SUPERCONDUCTORS

We briefly review the nonlinear sigma model approach for the subject of increasing interest: "two-step" phase transitions in the Gross–Neveu and the modified Nambu–Jona-Lasinio models at low N and condensation from pseudogap phase in strong-coupling superconductors. Recent success in describing of "Bose-type" superconductors that possess two characteristic temperatures and a pseudogap above Tc is the development approximately comparable with the BCS theory. One can expect that it should have influence on high-energy physics, similar to impact of the BCS theory on this subject. Although first generalizations of this concept to particle physics were made recently, these results were not systematized. In this review we summarize this development and discuss similarities and differences of the appearance of the pseudogap phase in superconductors and the Gross–Neveu and Nambu–Jona-Lasinio-like models. We discuss its possible relevance for chiral phase transition in QCD and color superconductors. This paper is organized in three parts. In the first part, we briefly review the separation of temperatures of pair formation and pair condensation in strong-coupling and low carrier density superconductors (i.e. the formation of the pseudogap phase). The second part is a review of nonlinear sigma model approach to an analogous phenomenon in the chiral Gross–Neveu model at small N. In the third part we discuss the modified Nambu–Jona-Lasinio model where the chiral phase transition is accompanied by a formation of a phase analogous to the pseudogap phase.

The chiral phase transition at high baryon density from nonperturbative flow equations

We investigate the QCD chiral phase transition at high baryon number density within the linear quark meson model for two flavors. The method we employ is based on an exact renormalization group equation for the free energy. Truncated nonperturbative flow equations are derived at nonzero chemical potential and temperature. Whereas the renormalization group flow leads to spontaneous chiral symmetry breaking in vacuum, we find a chiral symmetry restoring first order transition at high density. Combined with previous investigations at nonzero temperature, the result implies the presence of a tricritical point with long--range correlations in the phase diagram.

Chiral Phase Transition of QCD at Finite Temperature and Density from Schwinger-Dyson Equation

Chiral Phase Transition of QCD at Finite Temperature and Density from Schwinger-Dyson Equation

Ginzburg criterion for the chiral transition

This report is based on the work done together with J.B. Kogut and C.G. Strouthos. We study a Yukawa theory with spontaneous chiral symmetry breaking and with a large number N of fermions near the finite temperature phase transition. Critical properties in such a system can be described by the mean field theory very close to the transition point. We show that the width of the window of non-trivial scaling is suppressed by a certain power of 1/N. Our Monte Carlo simulations confirm these analytical results. We discuss implications for the chiral phase transition in QCD.

QCD phase transition in multiparticle environment

Chiral QCD phase transition is examined in the environment of relativistic nuclear collisions. The effective potential, at T = T c , of the O(4) universality class is used in order to formulate the Statistical Mechanics of primordial hadrons (masseless pions and sigmas) produced in heavy ion collisions. Critical fluctuations in rapidity space are revealed and their universal properties identified. A Monte Carlo simulation of the corresponding events (critical events) shows that the predictions of the theory are accessible to experimental observation.

Chiral phase transition of QCD at finite temperature and density from the Schwinger-Dyson equation

We study the chiral phase transition of QCD at finite temperature and density by numerically solving Schwinger-Dyson equation for the quark propagator with the improved ladder approximation in the Landau gauge. Using the solution we calculate a pion decay constant from a generalized version of Pagels-Stokar formula. Chiral phase transition point is determined by analyzing an effective potential for the quark propagator. We find solutions for which chiral symmetry is broken while the value of the effective potential is larger than that for the chiral symmetric vacuum. These solutions correspond to meta-stable states, and the chiral symmetric vacuum is energetically favored. We present a phase diagram on the general temperature--chemical potential plane, and show that phase transitions are of first order in wide range.

Critical region of the finite temperature chiral transition

We study a Yukawa theory with spontaneous chiral symmetry breaking and with a large number $N$ of fermions near the finite temperature phase transition. Critical properties in such a system can be described by the mean field theory very close to the transition point. We show that the width of the region where non-trivial critical behavior sets in is suppressed by a certain power of $1/N.$ Our Monte Carlo simulations confirm these analytical results. We discuss implications for the chiral phase transition in QCD.

Critical events and intermittency in nuclear collisions

The structure of events in relativistic heavy ion collisions (RHIC), associated with chiral QCD phase transition, is investigated. In particular the density fluctuations of pions, emitted from the excited vacuum (at T≈ T c ), are studied and classified in terms of intermittency patterns in rapidity space. For this purpose a Monte Carlo simulation of critical events in the central region is presented, on the basis of the O(4) theory of chiral phase transition. The universal character of these events is revealed and the predictions of the theory are discussed in connection with event by event measurements in current and future experiments with relativistic heavy ions.

On the QCD phase transition at finite baryon density

We investigate the QCD chiral phase transition at finite chemical potential μ, using the renormalization group (RG) to characterize the infrared behavior of sigma models constrained by the flavor and spacetime symmetries. The results are similar to those obtained from RG analysis of the finite temperature transition at zero baryon density. When there are more than two massless flavors of quarks, a first order transition is predicted for the entire phase boundary. In the two flavor case, a boundary with first and second order regions separated by a tricritical point seems most likely. We discuss the real-world case with two light quarks and an intermediate mass strange quark. Improved lattice data on the temperature transition will strongly constrain the possibilities for the phase boundary.

Chiral QCD phase transition in nuclear collisions

The characteristic aspects of multiparticle states generated at $T = T_c$ , as a result of chiral QCD phase transition, are studied in the framework of the O(4) $\phi^4$ theory. Predictions concerning critical events, in connection with current and future experiments with ultrarelativistic heavy ions, are presented.

Chiral phase transition of QCD at finite temperature and density from the Schwinger-Dyson equation

Chiral phase transition of QCD at finite temperature and density from the Schwinger-Dyson equation

Chiral QCD phase transition in nuclear collisions

Chiral QCD phase transition in nuclear collisions