Meson Mean Fields Research Articles

Kaon–baryon coupling schemes and kaon condensation in hyperon-mixed matter

Abstract The possible coexistence of kaon condensation and hyperons in highly dense matter [the (Y + K) phase] is investigated on the basis of the relativistic mean-field theory combined with the effective chiral Lagrangian. Two coupling schemes for the s-wave kaon–baryon interaction are compared regarding the onset density of kaon condensation in hyperon-mixed matter and the equation of state for the developed (Y + K) phase. One is the contact interaction scheme related to the nonlinear effective chiral Lagrangian. The other is the meson exchange scheme, where the interaction vertices between the kaon field and baryons are described by an exchange of mesons (σ, σ* mesons for scalar coupling, and ω, ρ, ϕ mesons for vector coupling). It is shown that in the meson exchange scheme, the contribution from the nonlinear scalar self-interaction gives rise to a repulsive effect for the kaon effective energy, pushing up the onset density of kaon condensation as compared with the contact interaction scheme. In general, the difference in kaon–baryon dynamics between the contact interaction scheme and the meson exchange scheme relies on the specific forms of the nonlinear self-interacting meson terms. They generate many-baryon forces through the equations of motion for the meson mean fields. However, they should have a definite effect on the ground state properties of nuclear matter only around the saturation density. It is shown that the nonlinear self-interacting term is not relevant to repulsive energy leading to stiffening of the equation of state at high densities, and that it cannot be compensated with a large attractive energy due to the appearance of the (Y + K) phase in the case of the contact interaction scheme. We also discuss what effects are necessary in the contact interaction scheme to make the equation of state with (Y + K) phase stiff enough to be consistent with recent observations of massive neutron stars.

Effects of three-baryon forces on kaon condensation in hyperon-mixed matter

Possibility of kaon-condensed phase in hyperon-mixed matter is considered on the basis of chiral symmetry for kaon-baryon and kaon-kaon interactions, being combined with the relativistic mean-field theory for two-body baryon interaction. In addition, universal three-baryon repulsive force in the string-junction model and phenomenological three-nucleon attractive force are introduced. It is shown that softening of the equation of state stemming from both kaon condensation and mixing of hyperons is compensated with the repulsive effect of the three-baryon force and the relativistic effect for two-body baryon-baryon interaction. The latter effect reflects the density-dependence of scalar and vector meson mean-fields, which is constrained by the contribution of the attractive three-nucleon force to the binding energy at saturation density. The kaon-condensed phase in hyperon-mixed matter becomes stiff enough to be consistent with recent observations of massive neutron stars.

A unified quark-nuclear matter equation of state from the cluster virial expansion within the generalized Beth\u2013Uhlenbeck approach

We consider a cluster expansion for strongly correlated quark matter where the clusters are baryons with spectral properties that are described within the generalized Beth–Uhlenbeck approach by a medium dependent phase shift. We employ a simple ansatz for the phase shift which describes an on-shell bound state with an effective mass and models the continuum by an anti-bound state located at the mass of the three-quark continuum threshold, so that the Levinson theorem is fulfilled by construction. The quark and baryon interactions are accounted for by the coupling to scalar and vector meson mean fields modelled by density functionals. At increasing density and temperature, due to the different medium-dependence of quark and baryon masses, the Mott dissociation of baryons occurs and its contributions to the thermodynamics vanish. It is demonstrated on this simple example that this unified approach to quark-hadron matter is capable of describing crossover as well as first order phase transition behaviour in the phase diagram with a critical endpoint. Changing the meson mean field, the case of a “crossover all over” in the phase diagram is also obtained.

Comprehensive study of mass modifications of light mesons in nuclear matter in the three-flavor extended linear σ model

We present a comprehensive study of mass modifications of scalar, pseudo-scalar, vector, and axial-vector mesons in nuclear matter using the three-flavor extended Linear Sigma Model (eLSM) and the two-flavor Parity Doublet Model (PDM). The meson masses in nuclear matter are determined by calculating the one-loop nucleon corrections to the meson mean fields. As a result, we find all spin-$0$ meson masses except those of the pion, kaon, and the lightest scalar-isoscalar mesons decrease at finite baryon density. For spin-$1$ mesons, masses of all axial-vector mesons decrease in medium, and the density dependences of the $\rho$ and $\omega$ meson masses strongly depend on the value of chiral invariant mass ($M_0$). Also, our results suggest $M_0\approx0.8\, {\rm GeV}$ is preferable.

Magnetic moments of the lowest-lying singly heavy baryons

A light baryon is viewed as Nc valence quarks bound by meson mean fields in the large Nc limit. In much the same way a singly heavy baryon is regarded as Nc−1 valence quarks bound by the same mean fields, which makes it possible to use the properties of light baryons to investigate those of the heavy baryons. A heavy quark being regarded as a static color source in the limit of the infinitely heavy quark mass, the magnetic moments of the heavy baryon are determined entirely by the chiral soliton consisting of a light-quark pair. The magnetic moments of the baryon sextet are obtained by using the parameters fixed in the light-baryon sector. In this mean-field approach, the numerical results of the magnetic moments of the baryon sextet with spin 3/2 are just 3/2 larger than those with spin 1/2. The magnetic moments of the bottom baryons are the same as those of the corresponding charmed baryons.

Equation of state of dense matter from a density dependent relativistic mean field model

We calculate the equation of state (EoS) of dense matter, using a relativistic mean field (RMF) model with a density dependent coupling that is a slightly modified form of the original NL3 interaction. For nonuniform nuclear matter we approximate the unit lattice as a spherical Wigner-Seitz cell, wherein the meson mean fields and nucleon Dirac wave functions are solved fully self-consistently. We also calculate uniform nuclear matter for a wide range of temperatures, densities, and proton fractions, and match them to non-uniform matter as the density decreases. The calculations took over 6,000 CPU days in Indiana University's supercomputer clusters. We tabulate the resulting EoS at over 107,000 grid points in the proton fraction range $Y_P$ = 0 to 0.56. For the temperature range $T$ = 0.16 to 15.8 MeV we cover the density range $n_B$ = 10$^{-4}$ to 1.6 fm$^{-3}$; and for the higher temperature range $T$ = 15.8 to 80 MeV we cover the larger density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$. In the future we plan to study low density, low temperature (T$<$15.8 MeV), nuclear matter using a Virial expansion, and we will match the low density and high density results to generate a complete EoS table for use in astrophysical simulations of supernova and neutron star mergers.

Multi-antikaonic nuclei in relativistic mean-field theory

Properties of multi-antikaonic nuclei (MKN), where several numbers of ${K}^{\ensuremath{-}}$ mesons are bound, are studied in the relativistic mean-field model, combined with chiral dynamics for the kaonic part of the thermodynamic potential. The density profiles for nucleons and ${K}^{\ensuremath{-}}$ mesons, the single particle energy of the ${K}^{\ensuremath{-}}$ mesons, and binding energy of the MKN are obtained. The effects of the $\overline{K}\text{\ensuremath{-}}\overline{K}$ interactions on these quantities are discussed in comparison with other meson ($\ensuremath{\sigma}$, $\ensuremath{\omega}$, and $\ensuremath{\rho}$)-exchange models. It is shown that the $\overline{K}\text{\ensuremath{-}}\overline{K}$ interactions originate from two contributions: One is the contact interaction between antikaons inherent in chiral symmetry, and the other is the one generated through coupling between the ${K}^{\ensuremath{-}}$ and meson mean fields. Both effects of the $\overline{K}\text{\ensuremath{-}}\overline{K}$ repulsive interactions become large on the ground state properties of the MKN as the number of the embedded ${K}^{\ensuremath{-}}$ mesons increases. A relation between the multi-antikaonic nuclei and kaon condensation in infinite and uniform matter is mentioned.

Charge and parity projected relativistic mean field model with pion for finite nuclei

We construct a new relativistic mean field model by explicitly introducing a \ensuremath{\pi}-meson mean field with charge number and parity projection. We call this model the charge and parity projected relativistic mean field (CPPRMF) model. We take the chiral \ensuremath{\sigma} model Lagrangian for the construction of finite nuclei. We apply this framework first for the $^{4}\mathrm{He}$ nucleus as a pilot case and study the role of the \ensuremath{\pi}-meson field on the structure of nuclei. We demonstrate that it is essential to solve the mean field equation with the variation introduced after the projection in order to take the pionic correlations into account explicitly. We study the ground-state properties of $^{4}\mathrm{He}$ by varying several parameters, such as the \ensuremath{\sigma}-meson mass and the \ensuremath{\omega}-meson coupling constant. We are able to construct a good ground state for $^{4}\mathrm{He}$. A depression appears in the central region of the density distribution, and the second maximum and the position of the dip in the form factor of $^{4}\mathrm{He}$ are naturally obtained in the CPPRMF model.

Relativistic Hartree States and Collective Tunneling Transition of a Nucleus

The study of relativistic Hartree theory for finite nuclei by the Nuclear Theory Group at the University of Tsukuba is reviewed. It is argued that negative energy nucleons should be taken into account in nuclear physics. When negative energy nucleons are taken into account in the relativistic mean-field approximation, the Dirac sea contributes to suppress the single-particle potential and to increase the nuclear radius. The fundamental mechanism of these effects of the Dirac sea is analyzed in the positive energy nucleon state sector picture of a nucleus by showing that N vacuum polarizations correct the meson exchange interactions between positive energy nucleons, suppressing the coupling constant and increasing the range of the σ-meson exchange interaction. The renormalized N vacuum polarization functions depend on the nuclear medium nucleon density. Therefore the vacuum polarizations create repulsive effective three-body interactions in the nucleus. The values of the three-body interaction energy obtained from the N vacuum polarizations are on the order of the three-body interaction energy extracted from the experimental nuclear energy data. As an extension of the nuclear mean-field theory, we formulate a collective tunneling transition from one nuclear mean-field state to another. We determine a Hamiltonian to describe this nuclear transition, in view of the quantum fluctuations of the meson fields needed to steer the transition. The structure of the meson mean fields in two nuclear mean-field states uniquely determines the Hamiltonian in terms of the meson fields needed to steer the nuclear transition from one mean-field state to another. The Hamiltonian, which recovers the symmetries of the nuclear system, yields nuclear eigenstates in terms of a linear combination of the two nuclear mean-field states with definite angular momentum.

NEUTRON STARS WITH PARAMETRIZED MESON COUPLINGS

We investigate static properties of nuclear and neutron star matter by using a relativistic mean field theory with parametrized couplings. With a suitable choice of mathematical parameters, the couplings allow one to reproduce results of current quantum hadrodynamics models. For other parametrizations, a better description of bulk properties of nuclear matter is obtained. The formalism is extended to include hyperon and lepton degrees of freedom, and an analysis on the effects of the phenomenological couplings in the fermion populations and mass of neutron stars is performed. The results show a strong similarity between the predictions of ZM-like models and those with exponential couplings. We have observed in particular an extreme sensibility of the predictions of these theories on the specific choice of the values of the binding energy of nuclear matter and saturation density. Additionally, the role of the very intense scalar meson mean field found in the interior of neutron stars in the screening of the nucleon mass is discussed.

Quark mean field model for nuclear matter and finite nuclei

We study nuclear matter and finite nuclei in terms of the quark mean field (QMF) model, in which we describe the nucleon using the constituent quark model. The meson mean fields, in particular the sigma meson, created by other nucleons act on quarks inside a nucleon and change the nucleon properties in nuclear medium. The QMF model predicts an increasing size of the nucleon as well as a reduction of the nucleon mass in the nuclear environment. The present model is applied to study the properties of finite nuclei after fixing all the parameters by the nuclear matter properties, and it is found to give satisfactory results on the nuclear properties.

The nucleus as a fluid of skyrmions: energy levels and nucleon properties in the medium

A model of a fluid of skyrmions coupled to a scalar and to the meson mean fields is developed. The central and spin-orbit potentials of a skyrmion generated by the fields predict correct energy levels in selected closed shell nuclei. The effect of the meson fields on the properties of skyrmions in nuclei is investigated.

Quark mean field model for nucleons in nuclei

We propose the quark mean field model for nucleons in nuclei, where the meson mean fields created by other nucleons act on quarks in a nucleon and change the nucleon properties in nuclei. We take the constituent quark model for the nucleon, which naturally allows the direct coupling of pions and in turn other mesons as $\ensuremath{\sigma}$ and $\ensuremath{\omega}$ mesons. We find very good nuclear matter properties with the use of the nonlinear self-energy terms in the meson Lagrangian. We expect the spin-orbit splitting in finite nuclei to be large due to the large reduction of the nucleon mass, which is in agreement with experiment. The nucleon size increases by about 7% at the normal matter density.

The role of nucleon structure in finite nuclei

The quark-meson coupling model, based on a mean field description of non-overlapping nucleon bags bound by the self-consistent exchange of $\sigma$, $\omega$ and $\rho$ mesons, is extended to investigate the properties of finite nuclei. Using the Born-Oppenheimer approximation to describe the interacting quark-meson system, we derive the effective equation of motion for the nucleon, as well as the self-consistent equations for the meson mean fields. The model is first applied to nuclear matter, after which we show some initial results for finite nuclei.

Probing vector meson properties in nuclei with photo-production of the neutral pion

The nuclear contribution to forward angle photo-production of the π 0-meson is calculated using an effective lagrangian derived from the triangle anomaly. This lagrangian mediates the interaction of a pion, a photon, and a vector meson mean field. The vector meson mass, m v, and the pion decay constant, f π , are assumed to have a density-dependence given by m v ∗ ( r)/m v = f π ∗( r)/f π = 1−λ( r)/ϱ NM) . The nuclear and Coulomb contributions to pion photo-production yield a cross-section which is sensitive to the properties of the vector meson in nuclear matter. In particular, both the overall strength of the vector meson mean field which is parameterized by g v and the density-dependence of the meson field which is parameterized by λ can be extracted.

Nuclear linear response to electroweak interactions in a relativistic theory for 16O.

The linear response of the $^{16}\mathrm{O}$ nucleus to an external electroweak current is studied in a relativistic model. The relativistic form for the nuclear linear response is applied using the random-phase approximation, Dirac-Hartree single-nucleon orbitals obtained along with Lorentz-vector and scalar self-consistent meson mean fields, and various particle-hole residual interactions. Form factors for inelastic electron scattering are combined into complexes and compared with experiments and previous nonrelativistic predictions. The agreement with electron scattering experiments is of similar quality for both nonrelativistic and relativistic theories with no obvious signature obtained motivating the superiority of a relativistic treatment. For weak interactions, the relativistic approach yields a considerable variation in predictions depending on the residual interaction adopted and whether pseudovector or pseudoscalar \ensuremath{\pi}NN coupling is assumed.

Modification of the mean field theory of super-dense matter

We further discussed the Modified Mean Field Theory proposed in [1,2]. We found that this model has a new solution ml = 2; adding ϱ-meson, we calculated the symmetric energy of nuclear matter a 4; with the new parameters we calculated the equations of state with and without the addition of ϱ-meson; we compared the two; we also compared with the results for ml = 4.3; we made a preliminary theoretical investigation of the form of the vector meson mean field using the two-body correlation function; lastly, using the structural equation of neutron star we calculated the maximum mass for the various equations of state. The results are: MMFT-2 (ml = 2): M max = 2.22M⊙ (without ϱ- meson) M max = 2.27M⊙ (with ϱ-meson) MMFT-1 (ml = 4.3): M max = 1.69M⊙ (without ϱ- meson) M max = 1.89M⊙ (with ϱ- meson)

Mean field model of nuclear matter

Phenomenological models of nuclear matter based on meson theory in the mean field approximation are investigated. In particular, the vector meson mean field function is studied in detail. It is shown that the low experimental compression modulus of nuclear matter places severe constraint on the form of the vector meson mean field function. Meson mean field functions taking into account nuclear correlation effects are discussed.

Meson exchange contributions in a relativistic description of nuclei and Λ- or ∑-hypernuclei

Using the meson mean field theory the central and spin-orbit potentials are determined and compared in the case of nuclei and Λ- or ∑-hypernuclei. The tensor-coupled term of the vector meson cancels the Thomas precession term of the spin-orbit potential in the case of the Λ-particle. In the case of the ∑-particle it is responsible for a contribution which adds to the precession part and yields a spin-orbit coupling of the same magnitude as for the nucleon.