Chiral Quark-meson Model Research Articles

Fluctuations and phases in baryonic matter

The phase structure of baryonic matter is investigated with focus on the role of fluctuations beyond the mean-field approximation. The prototype test case studied is the chiral nucleon-meson model, with added comments on the chiral quark-meson model. Applications to nuclear matter include the liquid-gas phase transition. Extensions to high baryon densities are performed for both nuclear and neutron matter. The role of vacuum fluctuations is systematically explored. It is pointed out that such fluctuations tend to stabilize the hadronic phase characterized by spontaneously broken chiral symmetry, shifting the chiral restoration transition to very high densities. This stabilization effect is shown to be further enhanced by additional dynamical fluctuations treated with functional renormalisation group methods.

Color superconductivity from the chiral quark–meson model

We study the two-flavor color superconductivity of low-temperature quark matter in the vicinity of chiral phase transition in the quark–meson model where the interactions between quarks are generated by pion and sigma exchanges. Starting from the Nambu–Gorkov propagator in real-time formulation we obtain finite temperature (real axis) Eliashberg-type equations for the quark self-energies (gap functions) in terms of the in-medium spectral function of mesons. Exact numerical solutions of the coupled nonlinear integral equations for the real and imaginary parts of the gap function are obtained in the zero temperature limit using a model input spectral function. We find that these components of the gap display a complicated structure with the real part being strongly suppressed above 2Δ0, where Δ0 is its on-shell value. We find Δ0≃40MeV close to the chiral phase transition.

Twin stars within the SU(3) chiral quark-meson model

We present new stable solutions of the Tolman Oppenheimer Volkoff equations for quark stars using a quark matter equation of state based on the SU(3) Quark-Meson model that exhibits the onset of the chiral phase transition. These new solutions appear as two stable branches in the mass-radius relation allowing for so called twin stars, i.e. two stable quark star solutions with the same mass, but distinctly different radii. We find solutions which are compatible with causality, the stability conditions of dense matter, the astrophysical constraints of the rotation of the millisecond pulsar PSR J1748-2446ad and the 2$M_{\odot}$ pulsar mass constraint.

Compact stars in a SU(3) quark-meson model

The recent observations of the massive pulsars PSR J1614-2230 and of PSR J0348+0432 with about two solar masses implies strong constraints on the properties of dense matter in the core of compact stars. Effective models of QCD aiming to describe neutron star matter can thereby be considerably constrained. In this context, a chiral quark-meson model based on a SU(3) linear $\sigma$-model with a vacuum pressure and vector meson exchange is discussed in this work. The impact of its various terms and parameters on the equation of state and the maximum mass of compact stars are delineated to check whether pure quark stars with two solar masses are feasible within this approach. Large vector meson coupling constant and a small vacuum pressure allow for maximum masses of two or more solar masses. However, pure quark stars made of absolutely stable strange quark matter, so called strange stars, turn out to be restricted to a quite small parameter range.

Renormalized vs. nonrenormalized chiral transition in a magnetic background

We study analytically the chiral phase transition for hot quark matter in presence of a strong magnetic background, focusing on the existence of a critical point at zero baryon chemical potential and nonzero magnetic field. We build up a Ginzburg-Landau effective potential for the chiral condensate at finite temperature, computing the coefficients of the expansion within a chiral quark-meson model. Our conclusion is that the existence of the critical point at finite $\bm B$ is very sensitive to the way the ultraviolet divergences of the model are treated. In particular, we find that after renormalization, no chiral critical point is present in the phase diagram. On the other hand, such a critical point there exists when the ultraviolet divergences are not removed by a proper renormalization of the thermodynamic potential.

Phase diagram in an external magnetic field beyond a mean-field approximation

The phase structure of the Polyakov loop-extended chiral quark-meson model is explored in a nonperturbative approach, beyond a mean-field approximation, in the presence of a magnetic field. We show that by including meson fluctuations one cannot resolve the qualitative discrepancy on the dependence of the crossover transition temperature in a nonzero magnetic field between effective model predictions and recent lattice results [1]. We compute the curvature of the crossover line in the $T\ensuremath{-}{\ensuremath{\mu}}_{B}$ plane at a nonzero magnetic field and show that the curvature increases with increasing magnetic field. On the basis of QCD inequalities, we also argue that, at least in the large ${N}_{c}$ limit, a chiral critical end point and, consequently, a change from crossover to a first-order chiral phase transition are excluded at zero baryon chemical potential and nonzero magnetic field.

Nuclear chiral dynamics and phases of QCD

This presentation starts with a brief review of our current picture of QCD phases, derived from lattice QCD thermodynamics and from models based on the symmetries and symmetry breaking patterns of QCD. Typical approaches widely used in this context are the PNJL and chiral quark-meson models. It is pointed out, however, that the modeling of the phase diagram in terms of quarks as quasiparticles misses important and well known nuclear physics constraints. In the hadronic phase of QCD governed by confinement and spontaneously broken chiral symmetry, in-medium chiral effective field theory is the appropriate framework, with pions and nucleons as active degrees of freedom. Nuclear chiral thermodynamics is outlined and the liquid–gas phase transition is described. The density and temperature dependence of the chiral condensate is deduced. As a consequence of two- and three-body correlations in the nuclear medium, no tendency towards a first-order chiral phase transition is found at least up to twice the baryon density of normal nuclear matter and up to temperatures of about 100 MeV. Isospin-asymmetric nuclear matter and neutron matter are also discussed. An outlook is given on new tightened constraints for the equation-of-state of cold and highly compressed matter as implied by a recently observed two-solar-mass neutron star.

Charge fluctuations in chiral models and the QCD phase transition

We consider the Polyakov loop-extended two-flavor chiral quark–meson model and discuss critical phenomena related to the spontaneous breaking of the chiral symmetry. The model is explored beyond the mean-field approximation in the framework of the functional renormalization group. We discuss properties of the net-quark number density fluctuations as well as their higher cumulants. We show that with the increasing net-quark number density, the higher order cumulants exhibit a strong sensitivity to the chiral crossover transition. We discuss their role as probes of the chiral phase transition in heavy-ion collisions at RHIC and LHC.

The effect of the Polyakov loop on the chiral phase transition

The Polyakov loop is included in the SU(2)_L x SU(2)_R chiral quark-meson model by considering the propagation of the constituent quarks, coupled to the (sigma,pi) meson multiplet, on the homogeneous background of a temporal gauge field, diagonal in color space. The model is solved at finite temperature and quark baryon chemical potential both in the chiral limit and for the physical value of the pion mass by using an expansion in the number of flavors N_f. Keeping the fermion propagator at its tree-level, a resummation on the pion propagator is constructed which resums infinitely many orders in 1/N_f, where O(1/N_f) represents the order at which the fermions start to contribute in the pion propagator. The influence of the Polyakov loop on the tricritical or the critical point in the mu_q-T phase diagram is studied for various forms of the Polyakov loop potential.

Vacuum fluctuations and the thermodynamics of chiral models

We consider the thermodynamics of chiral models in the mean-field approximation and discuss the relevance of the (frequently omitted) fermion vacuum loop. Within the chiral quark-meson model and its Polyakov loop extended version, we show that the fermion vacuum fluctuations can change the order of the phase transition in the chiral limit and strongly influence physical observables. We compute the temperature-dependent effective potential and baryon number susceptibilities in these models, with and without the vacuum term, and explore the cutoff and the pion mass dependence of the susceptibilities. Finally, in the renormalized model the divergent vacuum contribution is removed using the dimensional regularization.

Meson fluctuations and thermodynamics of the Polyakov-loop-extended quark-meson model

Thermodynamics and the phase structure of the Polyakov loop-extended two flavor chiral quark-meson model (PQM) are explored. The analysis of the PQM model is based on the functional renormalization group (FRG) method. An appropriate truncation of the effective action with quarks coupled to background gluonic fields is introduced. Within this scheme, we derive the renormalization group flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry breaking external field. The influence of fluctuations and of the background gluon field on the properties of net-quark number density fluctuations and their higher moments is explored. We study the dependence of the kurtosis of quark number fluctuations on the pion mass and show that, in the presence of a symmetry breaking term, the fluctuations lead to a smoothing of observables near the crossover transition.

The functional renormalization group and O(4) scaling

The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry-breaking external field. We perform a set of approximations to formulate and solve the FRG flow equation in the presence of fermionic degrees of freedom and test their influence on the O(4) critical properties expected in the quark-meson model. Within this scheme, the critical scaling behavior of the order parameter, its transverse and longitudinal susceptibilities as well as the correlation lengths near the chiral phase transition are computed for vanishing baryon density. We focus on the scaling properties of these observables at non-vanishing external field when approaching the critical point from the symmetric as well as from the broken phase. We confront our numerical results with the Widom–Griffiths form of the magnetic equation of state, obtained by a systematic ε expansion of the scaling function.

Manoj K Banerjee’s insights in intermediate energy nuclear physics

Professor Manoj Banerjee had a commanding arsenal of techniques to gain insight into the secrets of the nucleon. After a brief overview of some of his contributions in intermediate energy nuclear physics, we describe the chiral quark-meson model of the nucleon that he developed with Birse and Broniowski.

Analytic Determination of the T–ν Phase Diagram of the Chiral Quark Model

Using a gap equation for the pion mass a non-perturbative method is given for solving the chiral quark-meson model in the chiral limit at the lowest order in the fermion contributions encountered in a large-N fapproximation. The location of the tricritical point is analytically determined. A mean field potential is constructed from which critical exponents can be obtained.

Strangeness, charm, and bottom in a chiral quark-meson model

In this paper, we investigate an SU(3) extension of the chiral quark-meson model. The spectra of baryons with strangeness, charm, and bottom are considered within a “rigid oscillator” version of this model. The similarity between the quark sector of the Lagrangian in the model and the Wess-Zumino term in the Skyrme model is noted. The binding energies of baryonic systems with baryon numbers B=2 and 3 possessing strangeness or heavy flavor are also estimated. The results are in good qualitative agreement with those obtained previously in the chiral soliton (Skyrme) model.

Self-consistent approach to the Wigner-Seitz treatment of soliton matter

We propose a self-consistent approach to the treatment of nuclear matter as a crystal of solitons in the Wigner-Seitz approximation. Specifically, we use a Bloch-like boundary condition on the quarks at the edge of a spherical cell which allows the dispersion relation for a given radius to be calculated self-consistently along with the meson fields; in previous work some ansatz for the dispersion relation has always been an input. Results in all models are very sensitive to the form of the dispersion relation, and so our approach represents a significant advance. We apply the method to both the Friedberg-Lee model and the chiral quark-meson model of Birse and Banerjee. Only the latter shows short-range repulsion; in the former the transition to a quark plasma occurs at unrealistically low densities.

Nonlinear chiral models: Soliton solutions and spatio-temporal chaos

Nonlinear effective Lagrangian models with a chiral symmetry have been used to describe strong interactions at low energy, for a long time. The Skyrme model and the chiral quark-meson model are two such models, which have soliton solutions which can be identified with the baryons. We describe the various kinds of soliton states in these nonlinear models and discuss their physical significance and uses in this review. We also study these models from the view point of classical nonlinar dynamical systems. We consider fluctuations around theB=1 soliton solutions of these models (B, being the baryon number) and solve the spherically symmetric, time-dependent systems. Numerical studies indicate that the phase space around the Skyrme soliton solution exhibits spatio-temporal chaos. It is remarkable that topological solitons signifying stability/order and spatio-temporal chaos coexist in this model. In contrast with this, the soliton of the quark-meson model is stable even for large perturbations.

Effective action for the chiral quark-meson model.

The scale dependence of an effective average action for mesons and quarks is described by a nonperturbative flow equation. The running couplings lead to spontaneous chiral symmetry breaking. We argue that for strong Yukawa coupling between quarks and mesons the low momentum physics is essentially determined by infrared fixed points. This allows us to establish relations between various parameters related to the meson potential. The results for $f_\pi$ and $\VEV{\olpsi\psi}$ are not very sensitive to the poorly known details of the quark--meson effective action at scales where the mesonic bound states form. For realistic constituent quark masses we find $f_\pi$ around $100\MeV$.

Neutron electric dipole moment in chiral quark-meson models.

The neutron electric dipole moment is calculated in models of the quark structure of nucleons. The models studied incorporate chiral symmetry and the axial anomaly. The results are shown to satisfy the requirement of vanishing if either the strength of the anomaly or any current quark mass vanishes. In the cloudy-bag model both quark and pion-loop contributions to the dipole moment are found and these reinforce. In the color-dielectric model, which is consistent with partial conservation of the axial-vector current, there is only a pion-loop contribution.

Strange baryons in a chiral quark-meson model: (II). broken SU(3)

The chiral-quark meson model is used to study baryon properties with realistic breaking of SU(3). The symmetry breaking is assumed to be strong, so that a random phase approximation (RPA) can be used. In this the strange baryons are described as excitations built on the hedgehog soliton and have an excitation energy of 315 MeV. Other properties of strange baryons are obtained by an approximate spin-isospin projection from the RPA wave function. The magnetic moments agree reasonably well with experiment, but the deviations from the experimental values suggest that the method is valid for the case of rather stronger symmetry breaking than is realistic. The dependence of the RPA energy on the magnitude of the symmetry breaking is examined, and found to be strongly nonlinear for realistic values. This supports the idea that a large πN sigma commutator need not imply a large strange-quark content in the proton. For reasonable values of the scalar meson masses the strange-quark condensate is found to be less than 5% of the total, at the mean-field level. We also estimate the contribution to the condensate from RPA correlations. Within a one-mode approximation we find these to be very small, ∼2%.