Effective chiral meson lagrangian with Weinberg and KSFR relations from microscopic four-quark interactions

An effective chiral meson lagrangian is derived from a microscopic quark lagrangian. It contains a partial Higgs mechanism for ϱ-A₁ mass splitting reproducing Weinberg and KSFR relations, and includes quartic derivative “Skyrme” terms and the gauges Wess-Zumino term. The connection to previous approaches deriving the effective lagrangian exclusively from the chiral anomaly including “normal-parity” terms is established.     

Nuclear matter in the skyrme model

The applicability of the Skyrme model to the analysis of nuclear matter is discussed. Constraints on an ansatz that describes a cubic skyrmion crystal are presented. Properties of this ansatz are studied numerically. Results are used to discuss nuclear matter in the large-N limit and at N = 3.     

Nuclear mean field from chirally symmetric effective theory

The mean-field theory of the nuclear many-body problem proposed recently by Furnstahl, Serot, and Tang (FST) is discussed. The FST chiral Lagrangian is derived in terms of an effective field theory. This new approach allows one to construct in a controlled manner the universal nuclear Lagrangian consistent with symmetries of QCD. The FST Lagrangian is constructed by using power counting, i.e., the expansion in powers of the lowest lying hadronic fields and their derivatives. Terms in the Lagrangian are organized by applying Georgi’s naive dimensional analysis and “naturalness” condition. The relevant degrees of freedom are nucleons, pions, an isoscalar-vector field ω meson), an isoscalar-scalar field (σ meson), and an isovector-vector field (ρ meson). The chiral symmetry is realized nonlinearly using a standard WCCWZ procedure.     

Thermodynamic properties of superconducting nuclear matter

Phase diagrams of superconducting nuclear matter are calculated by solving a set of finite temperature gap equations, using several Skyrme effective interactions. Our results indicate that nuclear matter may have a superconducting phase in a small region with density near one half of the normal nuclear matter density and temperature k_BT ≲ 1.4 MeV. Our calculation is based on a finite temperature Green's function method with an abnormal pair cutoff approximation. The same approximation is employed in deriving the internal energy, entropy and chemical potential of superconducting nuclear matter. In this way, its equation of state is obtained, and compared with that of normal nuclear matter. The energy gap of superconducting nuclear matter is found to depend rather sensitively on both density and temperature. This dependence is analysed in terms of the Skyrme interaction parameters. The correlation effect on chemical potential is found to be important at high density, and its inclusion is essential in determining the equation of state of superconducting nuclear matter.     

Solitons bound to heavy mesons

We improve the bound state approach of the Skyrme model applied to the heavy baryons by adopting a static heavy meson picture where the soliton moves around the fixed heavy meson. This allows to take into account the center of mass corrections in a more consistent way. The bound state masses so obtained are comparable to the experimentally observed Λ _c and Λ _c ^* masses. A loosely bound state of a soliton with an antiflavored heavy meson is found, which leaves a possibility of the nonstrange pentaquark baryon(s).     

Characteristic predictions of topological soliton models

Characteristic predictions of the chiral soliton models (the Skyrme model and its extensions) are discussed. The chiral soliton model predictions of low-lying dibaryon states qualitatively agree with recent evidence for the existence of narrow dibaryons in reactions of the inelastic proton scattering on deuterons and the double photon radiation pp→ppγγ. The connection between magnetic moment operators and inertia tensors valid for arbitrary SU(2) skyrmion configurations allows us to estimate the electromagnetic decay width of some states of interest. Predictions of a different type are multibaryons with a nontrivial flavor (strangeness, charm, or bottom), which can be found, in particular, in high-energy heavy ion collisions. It is shown that the large-B multiskyrmions given by the rational map ansatz can be described within the domain-wall approximation or as a spherical bag with the energy and the baryon number density concentrated at the boundary.     

Topologically non-trivial chiral transformations

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu-Jona-Lasinio model the hidden gauge and massive Yang-Mills approaches to vector mesons are linked by a special chiral transformation which removes the chiral field from the scalar-pseudoscalar sector. The chirally rotated axial vector meson field (à _μ ) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu-Jona-Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important feature, which usually is generated by non-vanishing axial vector profiles, is thus maintained by the simplificationà _μ = 0.     

Mesonic wakes in nuclear matter,with application to meson production in nuclear collisions

The process of meson production by a source moving uniformly through infinite nuclear matter is studied in field theoretic models in which a source-meson coupling is assumed, and in which the only effect of the nuclear medium is to modify the propagator of the mesons. If the meson dispersion relation, ω(k), in the medium becomes space-like in some region of k, k > ω(k), there is, for relativistic source velocities, energy loss to the mesonic excitations. Models of the pion propagator in nuclear matter lead to such a space-like region. Rates of pion production are calculated in the lowest order of the pion-source coupling. Consideration of higher order terms leads to an interesting class of problems which we designate as those of “non-Abelian Cherenkov radiation.” Brief consideration is given to the excitation of nuclear collective modes and to the problems of treating meson production in finite nuclei.     

Mass splittings of nuclear isotopes in chiral solition approach

The differences in the masses of isotopes with atomic numbers between ～10 and ～30 can be described within the chiral soliton model in satisfactory agreement with data. The rescaling of the model is necessary for this purpose—a decrease in the Skyrme constant by ～30%, providing the “nuclear variant” of the model. The asymmetric term in the Weizsäcker-Bethe-Bacher mass formula for nuclei can be obtained as the isospin-dependent quantum correction to the nucleus energy. Some predictions of the binding energies of neutron-rich isotopes are made in this way from, e.g., ¹⁶Be, ¹⁹B to ³¹Ne or ³²Na. The neutron-rich nuclides with high values of isospin are unstable relative to decay owing to strong interactions. The SK4 (Skyrme) variant of the model, as well as the SK6 variant (sixth-order term in the derivatives of the chiral field in the Lagrangian as soliton stabilizer), is considered; the rational-map approximation is used to describe multi-Skyrmions.     

Influence of Self-Interaction ofσ Meson to the Equation of State of Nuclear Matter

In the relativistic σ-ωmodel, the influence of the parameters in self-interaction of a meson to the equation of state of normal nuclear matter, especially, to incompressibility, effective mass, and coupling constants, is studied in detail. We find that these parameters have an intense relationship to the property of nuclear matter. At the same time , we study the relation between the binding energy and pressure of relativestic △-resonance nuclear matter and temperature using using above results in the relativistic σ-ω-π model,and it is interesting to compare it to our prior work. In all these studies, the vacuum fluctuation on nucleon, △-isobar, and σmeson is considered.     

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU(2)_L × SU(2)_R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.     

Instability in relativistic mean-field theories of nuclear matter

We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly.     

Constant-cutoff approach to meson-hyperon couplings

The kaon coupling constants at hyperon-nucleon vertices and the pion coupling constants at hyperon-hyperon vertices are calculated in the framework of the constant-cutoff approach to the CHK bound-state model of hyperons, where the postive-parity hyperons such as Λ, Σ, and ∑^*=∑(1385) are theP-wave bound states of an antikaon and theSU(2) Skyrme soliton, while Λ^* is theS-wave bound state. Meson coupling constants are defined as matrix elements of the meson-source terms between two single-baryon states following the method developed for resolving the Yukawa coupling problem in theSU(2) Skyrme soliton model. The magnitudes of the meson coupling constants are found to be close to those obtained using the complete Skyrme model and the phenomenological values.     

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

Effective chiral hadron lagrangian with anomalies and skyrme terms from quark flavour dynamics

By bosonization of an extended Nambu-Jona-Lasinio type of quark model with explicit breaking of chiral U(n) × U(n) symmetry we derive a effective low-energy lagrangian of composite scalar, pseudoscalar, vector and axial-vector mesons. This lagrangian contains the gauged Wess-Zumino term as well as higher order derivative terms of the Skyrme type, the coefficients of which agree with recent phenomenological estimates. In particular, the value predicted for the strength of the standard fourth-order Skyrme term is in satisfactory agreement with the results obtained by fitting the nucleon and delta masses. Our effective chiral lagrangian reproduces the wealth of the results of successful phenomenological lagrangians as, e.g. soft-pion theorems, Goldberger-Treiman relations, PCAC, the KSFR relation, the (approximate) Weinberg relation, etc. Moreover, the predicted mass spectra and decay constants of composite mesons are in qualitative agreement with the experimental findings. Furthermore, when electroweak interactions are included the lagrangian contains vector (axial-vector) dominance based on field-current identities.     

Bound state approach for strange dibaryons in the skyrme model

The bound state approach to strange dibaryons in the Skyrme model is extended to baryon number n > 1. Kaon bound states are obtained in a (variational) axially symmetric SU (2) skyrmion background field. Collective quantization of isospin and spatial zero modes leads to dibaryon quantum states. These are classified in flavor multiplets.     

Flavored exotic multibaryons and hypernuclei in topological soliton models

The energies of baryon states with positive strangeness, or anticharm (antibeauty), are estimated in the chiral soliton approach, in the “rigid oscillator” version of the bound-state soliton model proposed by Klebanov and Westerberg. Positive strangeness states can appear as relatively narrow nuclear levels (Θ-hypernuclei), and the states with heavy antiflavors can be bound with respect to strong interactions in the original Skyrme variant of the model (SK4 variant). The binding energies of antiflavored states are also estimated in the variant of the model with a sixth-order term in chiral derivatives added to the Lagrangian to stabilize solitons (SK6 variant). This variant is less attractive, and nuclear states with anticharm and antibeauty can be unstable relative to strong interactions. The chances of obtaining bound hypernuclei with heavy antiflavors increase within the “nuclear variant” of the model with a rescaled model parameter (the Skyrme constant e or e′ decreased by a out 30%), which is expected to be valid for baryon numbers greater than B ～ 10. The rational map approximation is used to describe multiskyrmions with a baryon number of up to about 30 and to calculate the quantities necessary for their quantization (moments of inertia, sigma term, etc.).     

A Modified Pion-Rho-Omega Mesonic Lagrangian in Nuclear Matter

We present an in-medium modified effective Lagrangian which describes the pion, rho- and omega mesons and the corresponding soliton properties in nuclear matter. We discuss possible modifications of ρ- and ω-meson properties in nuclear matter. In particular, the masses of vector mesons are shown to decrease about 30% at normal nuclear matter density within the present approach.     

The Fourth-Order Symmetry Energy of Finite Nuclei

The fourth-order symmetry energy E_sym,4(A) of heavy nuclei is investigated based on the Skyrme energy density functional in combination with a local density approximation. Unlike some previous works, in our method, the interferences from the other energy terms are removed since it is completely isolated from the rest of energy terms. The calculated E_sym,4(A) is much less than that extracted from nuclear masses. The underlying reason for the big difference is discussed. The Brueckner theory also gives a small fourth-order symmetry energy coefficient of nuclear matter, which is also different from recent conclusions with another methods.