No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.     

Chiral symmetry breaking and pion properties at finite temperatures

Spontaneous and explicit chiral symmetry breaking is analyzed in Coulomb gauge QCD at finite temperatures, using an instantaneous approximation for the quark interaction and incorporating confinement through a running coupling constant. The thermodynamics of the quarks is treated approximatively by assuming that the momentum-dependent constituent quark mass sets the scale for thermodynamic fluctuations of colour singlet excitations. We investigate the class of a temperature independent and a temperature dependent interaction between quarks. In the chiral limit both temperature independent and a smooth temperature dependent interaction yields a second order chiral phase transition with critical exponents close to the values for a BCS super-conductor. For explicit chiral symmetry breaking we find a nearly constant pion mass below the transition temperature, but a strongly overdamped mode above. For a first order deconfining transition in the gluonic sector also the quark sector shows a first order chiral phase transition. The relevance of our results for relativistic heavy ion collisions is briefly discussed.     

QCD with two colors at finite baryon density at next-to-leading order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau–Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Pion condensation in heavy ion collisions

We calculate the pion spectrum in dense nuclear matter for finite temperatures. The critical temperatureT _c(ρ) that marks the beginning of a second order phase transition due to pion condensation is given in a phase diagram. We show that in heavy ion collisions, pion condensation should occur, leading to an enhancement in the formation of nuclear shock waves.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

Effective potential of the O(N) linear sigma-model at finite temperature

We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation, which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed. Received: 21 June 2000 / Accepted: 13 September 2000     

Phase transitions in nucleonic matter and neutron-star cooling

A new scenario for neutron-star cooling is suggested by the correspondence between pion condensation, induced by critical spin-isospin fluctuations, and the metal-insulator phase transition in a 2D electron gas. Above the threshold density for pion condensation, the neutron single-particle spectrum acquires an insulating gap that quenches neutron contributions to neutrino production. In the liquid phase just below the transition, the fluctuations play dual roles by (i) creating a multisheeted neutron Fermi surface that extends to low momenta and activates the normally forbidden direct Urca cooling mechanism, and (ii) amplifying the nodeless P-wave neutron superfluid gap while suppressing S-wave pairing. Lighter stars without a pion-condensed core undergo slow cooling, whereas enhanced cooling occurs in heavier stars via direct Urca emission from a thin shell of the interior.     

Inelastic shadowing effects in multiple scattering

The projectile-nucleon scattering amplitudes used as input into multiple scattering theories of projectile-nucleus scattering naturally include the effects of coupling to inelastic (i.e., production) channels. We employ a multichannel separable potential to describe the projectile-nucleon interaction and show that within the fixed nucleon framework we can obtain the nuclear elastic scattering amplitude. This includes terms outside the conventional formalisms, corresponding to intermediate propagation in the inelastic channels both above and below inelastic threshold. We refer to this as inelastic shadowing. In a two-channel approximation, we show that knowledge of the projectile-nucleon elastic scattering phase shifts plus specification of the inelastic threshold energy are sufficient to determine the off-shell coupled-channel transition matrix, implying that the nuclear amplitude can be calculated within this model without any detailed information about the inelastic channels. We study this solution quantitatively for some model problems and for pion scattering, with the general result that inelastic shadowing can be significant whenever the elementary interaction has important channel coupling. For pion scattering in the energy regime characterized by strongly absorptive resonances, we find, for example, that the effect of inelastic shadowing is much more important than that due to two-nucleon correlations.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Pion and σ-meson Properties in a Strong Magnetic Field

With the Nambu-Jona-Lasinio (NJL) model we calculate the properties of pion and σ-meson at finite temperature and finite magnetic field. The obtained temperature and magnetic field strength dependence of the constituent quark mass M, the pion and σ-meson masses and the neutral pion decay constant indicates that, in the simple four fermion interaction model, there exists the magnetic catalysis effect. It also shows that the Gell-Mann-Oakes-Renner relation is violated obviously with the increasing of the temperature, and the effect of the magnetic field becomes pronounced only around the critical temperature. The deviation of the critical temperatures obtained with different criteria indicates that the chiral phase transition driven by the temperature in the magnetic field strength region we have considered is in fact a crossover.     

Pion dispersion relation in hot pion matter

We study the modification of the pion propagation properties when it is embedded in hot pionic matter. We calculate the real part and the imaginary part of the pion self-energy in a scheme, analogous to the Brückner-Hartree-Fock approximation used in nuclear physics, which allows to incorporate in a fully consistent way unitarity and Bose correlations at finite temperature. We discuss the consequences of the medium effects on the pion transverse momentum spectrum measured in ultrarelativistic heavy ion collisions and the so-called soft pion puzzle.     

核物质中内介质等效手征Lagrange量和π介子质量

在核物质中从手征等效Lagrange量得到的π介子有效质量是单值的,并且与π介子场的离壳扩展无关,例如PCAC选择.同位旋对称核物质中的有效π介子质量随增加的核密度有些上升,因此有效类时π介子衰变常数和密度相关的夸克凝聚渐渐下降.另外研究了内介质Gell–Mann–Oakes–Renner关系和其它内介质同一性.最后讨论了同位旋对称、各向同性和均匀的核物质中关于介子传播的等效Lagrange量的几个限制.     

Off-center displacements and hydrostatic pressure induced phase transition in perovskites

Pressure has a profound effect on the paraelectric and ferroelectric properties of perovskite crystals. In this paper we theoretically investigate the effect of pressure on the cubic-to-tetragonal phase transition and on the soft mode dynamics of some classical perovskite crystals: BaTiO(3), PbTiO(3), and KNbO(3). We use a model consisting of three subsystems: electrons, phonons, and off-center displacements treated as spins. Experiments show that pressure has a large effect on the tunneling and hopping of the off-center displacements, that in turn strongly affect the pressure dependence of the transition temperature and the soft mode frequency. This model, with a very small number of adjustable parameters, accounts quantitatively for the experimentally measured nonlinear pressure dependence of the cubic-to-tetragonal phase transition temperature, up to the critical pressure where the transition temperature is zero. It also accounts quantitatively for the pressure dependence of the soft mode frequency, which is finite at the phase transition in spite of the fact that the phase transition at elevated pressures is second order, and for the pressure dependence of the electronic gap energy.     

The Effects of the Pion String at Heavy ion Collisions

We study the possible signals of the pion string associated with the QCD chiral phase transition in LHC Pb–Pb collision at energy s=5.5 TeV.We follow the Kibble–Zurek mechanism to discuss the production and evolution of the pion string.We will show that if the QCD chiral phase transition really takes place in the LHC Pb-Pb collision process and the phase transition is in the second order,the pion string will be inevitably produced and subsequently decay.The main effect of this phenomenon is that there is a generation of a large number of pions in the final state produced by the decay of the pion string, and these pions are mostly distributed in a low momentum region with p～143MeV; also there are lots of neutral pions distributed in a low momentum region with the mean momentum at p～21MeV.     

Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a 5% change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.     

Lowering Critical Temperature in the Extended Quark Sigma Model at Finite Temperature

A phase transition, a critical temperature, and meson masses are studied in the extended quark sigma model, in which the effective mesonic potential is extended to include eighth-order mesonic interactions. The second derivative of the effective mesonic potential is applied to calculate the effective sigma and pion masses as functions of temperature. We find that the critical temperature assumes a lower value in comparison with that of original quark sigma model. A comparison with recent calculations of lattice QCD is introduced. The behavior of the phase transition remains unchanged when the higher-order mesonic interactions are included. We find that the spontaneous symmetry-breaking condition is necessary to satisfy the Goldstone theorem at low temperatures.     

Pion decay constant at finite temperature

The values of the pion decay constant, and of the bilinear fermionic condensate, for temperatures from zero up to the critical temperature for chiral phase transition, are calculated using our composite operator approach to finite temperature QCD. For small temperatures our results agree with those found with other approaches. Near the critical temperature we recover the universal behaviour typical of second order phase transition. We have assumed that effects responsible for deconfinement do not strongly perturb our chiral approach for two and possibly three flavours.     

Crack propagation as a free boundary problem

A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force, and a tip splitting instability above a critical driving force.     

Bulk viscosity of low-temperature strongly interacting matter

We study the bulk viscosity of a pion gas in unitarized Chiral Perturbation Theory at low and moderate temperatures, below any phase transition to a quark-gluon plasma phase.We argue that inelastic processes are irrelevant and exponentially suppressed at low temperatures. Since the system falls out of chemical equilibrium upon expansion, a pion chemical potential must be introduced, so we extend the existing theories that include it. We control the zero modes of the collision operator and Landau?s conditions of fit when solving the Boltzmann equation with the elastic collision kernel.The dependence of the bulk viscosity with temperature is reminiscent of the findings of Fernández-Fraile and Gómez Nicola (2009) [1], while the numerical value is closer to that of Davesne (1996) [2]. In the zero-temperature limit we correctly recover the vanishing viscosity associated to a non-relativistic monoatomic gas.