QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

Cooper pairs? magnetic moment in MCFL color superconductivity

We investigate the effect of the alignment of the magnetic moments of Cooper pairs of charged quarks that form at high density in three-flavor quark matter. The high-density phase of this matter in the presence of a magnetic field is known to be the Magnetic Color-Flavor-Locked (MCFL) phase of color superconductivity. We derive the Fierz identities of the theory and show how the explicit breaking of the rotational symmetry by the uniform magnetic field opens new channels of interactions and allows the formation of a new diquark condensate. The new order parameter is a spin-1 condensate proportional to the component in the field direction of the average magnetic moment of the pairs of charged quarks. The magnitude of the spin-1 condensate becomes comparable to the larger of the two scalar gaps in the region of large fields. The existence of the spin-1 condensate is unavoidable, as in the presence of a magnetic field there is no solution of the gap equations with nonzero scalar gaps and zero magnetic moment condensate. This is consistent with the fact that the extra condensate does not break any symmetry that has not already been broken by the known MCFL gaps. The spin-1 condensate enhances the condensation energy of pairs formed by charged quarks and the magnetization of the system. We discuss the possible consequences of the new order parameter on the issue of the chromomagnetic instability that appears in color superconductivity at moderate density.     

Nuclear matter properties in the relativistic random phase approximation

Nuclear matter properties at zero temperature are studied in terms of the relativistic σ-ω model, including the random phase approximation (RPA) contribution. At normal density, the medium polarization adds about −35 MeV of binding energy to the mean field result. The scalar and vector effective interaction strengths are fitted to the nuclear matter saturation conditions under various approximations for the energy functional including the RPA term. The effective mass and bulk modulus are calculated with these parameters. The relative importance of different contributions to the binding energy is analyzed.     

Single-particle potential in a relativistic Hartree-Fock mean field approximation

A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.     

Strange goings on in dense nucleonic matter

It has been suggested that charged pions form a Bose-Einstein condensate in baryonic matter at zero temperature and about twice nuclear density. In this letter it is shown that at somewhat higher densities one finds a charged kaon condensate, driven to a large extent by the “stgma term” interaction with baryons. Using the SU(3) × SU(3) chiral lagrangian to model meson-baryon interactions it is found that baryonic matter acquires a strangeness-per-baryon ratio approaching one at several times nuclear density. The relevance of kaon condensation as a route to strange matter and its role in neutron stars are discussed.     

Pion condensation in neutron star matter: (II). Nuclear forces and stability

This paper presents several stable models of charged-pion condensed neutron star matter. The non-relativistic limit of the chirally symmetric Weinberg Lagrangian is used to describe interactions of the condensed pion field with the nucleons, as well as the pi-pi interactions of the condensed field. In the absence of nucleon-nucleon interactions, matter in this model is unstable, tending to ever-increasing baryon density and condensate wave vector. The connection of this model of condensation with the σ-model is shown.A general framework for including nuclear forces is then laid out. Results are given for a simple model in which the nuclear forces are assumed to produce an interaction energy V(ρ) dependent only on the total baryon density, independent of the degree of pion condensation, and also to produce a constant G-matrix element g in the nucleon-nucleon charge exchange channel. In the absence of condensation the equation of state reduces to that of interacting normal matter. We also consider effects of beta equilibrium and form factors in the p-wave pion-nucleon interaction. The condensed models are stable. Depending on the choice of parameters the models exhibit first- or second-order pion condensation phase transitions, or both.     

核子质量、 半径及夸克凝聚的核物质密度依赖性

简要介绍核物质中核子的质量、 半径及夸克凝聚的密度依赖关系基于QCD模型和QCD有效场论研究的现状, 并具体介绍整体色对称模型（GCM）的研究结果. GCM研究表明, 在小于临界密度的情况下, 核物质中核子的质量随核物质密度的增大而减小, 核子的半径和夸克凝聚随核物质密度的增大而增大. 当达到临界密度时, 核子质量减小为零, 核子半径变为无限大, 夸克凝聚突变为零, 进而提出一个核物质中手征对称性恢复的新机制. The status of the investigations on the nucleon mass, nucleon radius and quark condensate in the framework of QCD inspired models and QCD effective field theories is briefly reviewed. The results in the global color symmetry model (GCM) are described a little detailedly. The calculated results indicate that, before the maximal density is reached, the mass of a nucleon in nuclear matter decreases, the radius of a nucleon and the quark condensate increase very slowly, with the increase of the nuclear matter density. As the maximal nuclear matter density is reached, the mass of the nucleon vanishes gradually. The radius becomes infinite and the quark condensate vanishes suddenly. A new mechanism for the chiral symmetry restoration in nuclear matter is proposed.     

How deep is the antinucleon optical potential at FAIR energies

The key question in the interaction of antinucleons in the nuclear medium concerns the deepness of the antinucleon-nucleus optical potential. In this work we study this task in the framework of the non-linear derivative (NLD) model which describes consistently bulk properties of nuclear matter and Dirac phenomenology of nucleon-nucleus interactions. We apply the NLD model to antinucleon interactions in nuclear matter and find a strong decrease of the vector and scalar self-energies in energy and density and thus a strong suppression of the optical potential at zero momentum and, in particular, at FAIR energies. This is in agreement with available empirical information and, therefore, resolves the issue concerning the incompatibility of G-parity arguments in relativistic mean-field (RMF) models. We conclude the relevance of our results for the future activities at FAIR.     

Pion condensation at finite temperature: (I). Mean field theory

The pion-condensed state of neutron-rich matter at finite temperature is calculated within the framework of a simple σ-model, treating the pion field as a mean field. At high densities the matter is condensed with a spatially non-uniform condensate. However, we find the unexpected result that as the density is lowered, at any finite temperature, pure neutron matter always makes a transition to a state with a spatially uniform condensate. Pure neutron matter, within mean field theory, is condensed at all non-zero temperatures and densities. Matter with a small proton fraction at zero temperature has a qualitatively similar phase diagram, except that it is normal when both the temperature and density are sufficiently low.     

Pion condensation in a relativistic field theory consistent with bulk properties of nuclear matter

Pion condensation has not previously been investigated in a theory that accounts for the known bulk properties of nuclear matter, its saturation energy and density and compressibility. We have formulated and solved self-consistently, in the mean field approximation, a relativistic field theory that possesses a condensate solution and reproduces the correct bulk properties of nuclear matter. The theory is solved in its relativistically covariant form for a general class of space-time dependent pion condensates. Self-consistency and compatibility with bulk properties of nuclear matter turn out to be very stringent conditions on the existence and energy of the condensate, but they do allow a weak condensate energy to develop. The spin-isospin density oscillations, on the other hand, can be large. It is encouraging, as concerns the possible existence of new phases of nuclear matter, that this is so, unlike the Lee-Wick density isomer, that appears to be incompatible with nuclear matter properties.     

Hot nuclear matter with dilatons

We study hot nuclear matter in a model based on nucleon interactions deriving from the exchange of scalar and vector mesons. The main new feature of our work is the treatment of the scale breaking of quantum chromodynamics through the introduction of a dilaton field. Although the dilaton effects are quite small quantitatively, they affect the high-temperature phase transition appreciably. We find that inclusion of the dilaton leads to a metastable high-density state at zero pressure, similar to that found by Glendenning who considered instead the admixture of higher baryon resonances.     

Density waves in quark matter within the Nambu-Jona-Lasinio model in an external magnetic field

The possibility of forming static dual scalar and pseudo-scalar density wave condensates in dense quark matter is considered for the Nambu-Jona-Lasinio model in an external magnetic field. Within a mean-field approximation, the effective potential of the theory is obtained and its extrema are numerically studied and a phase diagram of the system is constructed. It is shown that the presence of a magnetic field favors the formation of spatially inhomogeneous condensate configurations at low temperatures.     

Isovector Scalar Field Effects in Asymmetric Nuclear Matter

Density-dependent parametrization models of the nucleon-meson coupfing constants, including the isovector scalar δ-field, are applied to asymmetric nuclear matter. The nuclear equation of state （EOS） and the neutron star properties are studied in a relativistic Lagrangian density, using the relativistic mean field （RMF） hadron theory. It is known that the δ-field in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses, finally influences the stability of the neutron stars. We use density-dependent models of the nucleon-meson couplings to study the properties of neutron star matter and to reexamine the （~-field effects in asymmetric nuclear matter. Our calculation shows that the stability conditions of the neutron star matter can be improved in presence of the δ-meson in the density-dependent models of the coupling constants. The EOS of nuclear matter strongly depends on the density dependence of the interactions.     

Acceleration Field of a Universe Modeled as a Mixture of Scalar and Matter Fields

A model of the Universe as a mixture of a scalar (inflaton or rolling tachyon from the string theory) and a matter field (classical particles) is analyzed. The particles are created at the expense of the gravitational energy through an irreversible process whereas the scalar field is supposed to interact only with itself and to be minimally coupled with the gravitational field. The irreversible processes of particle creation are related to the non-equilibrium pressure within the framework of the extended (causal or second-order) thermodynamic theory. The scalar field (inflaton or tachyon) is described by an exponential potential density added by a parameter which represents its asymptotic value and can be interpreted as the vacuum energy. This model can simulate three phases of the acceleration field of the Universe, namely, (a) an inflationary epoch with a positive acceleration followed by a decrease of the acceleration field towards zero, (b) a past decelerated period where the acceleration field decreases to a maximum negative value followed by an increase towards zero, and (c) a present accelerated epoch. For the energy densities there exist also three distinct epochs which begin with a scalar field dominated period followed by a matter field dominated epoch and coming back to a scalar field dominated phase.     

Dynamical symmetry breaking in models with the Yukawa interaction

The models with a massless fermion and a self-interacting massive scalar field with the Yukawa interaction are discussed. The chiral condensate and the fermion mass are calculated analytically through a one-loop approximation in (1 + 1)-dimensions. It is shown that the models have a phase transition as a function of the squared mass of the scalar field.     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Effective Masses of Pentaquark Θ+ in Nuclear Matter

The properties of baryons in nuclear matter are analysed in the relativistic mean-field theory(RMF). It is found that the scalar field σ meson affects the properties of baryon at high density. A density dependent scalar coupling gσN is determined according to the idea of quark-meson coupling model and extended to RMF. It is shown that gσN affects the property of nuclear matter weakly at low density, but strongly at high density. The relation between the scalar density ρ_S and the nuclear density ρ and the effective mass of the pentaquark Θ⁺ are studied with the density dependent coupling constant. The density dependent scalar coupling obviously affects the effective masses of baryons in nuclear matter, especially at high density.