Skyrme Model Research Articles

Antineutrino Opacity in Neutron Stars in Models Constrained by Recent Terrestrial Experiments and Astrophysical Observations

Inthe present paper, we investigate neutral current (NC) antineutrino scattering with the constituents of neutron star (NS) matter at zero temperature. The modeling of standard matter in NS is constructed within the framework of both extended relativistic mean-field (E-RMF) and nonrelativistic Korea-IBS-Daegu-SKKU energy density functional (KIDS-EDF) models. In the E-RMF model, we use a new parameter, G3(M), which was constrained by the recent PREX II experiment measurement of neutron distribution in 208Pb, while the KIDS-EDF models are constrained by terrestrial experiments, gravitational-wave signals, and astrophysical observations. Using both realistic and well-constrained matter models, we then calculate the antineutrino differential cross-section (ADCS) and antineutrino mean free path (AMFP) for the interaction between antineutrinos and neutron star (NS) matter constituents using linear response theory. It is found that the AMFP for the KIDS0 and KIDSA models are smaller compared to the SLy4 model and the E-RMF model with the G3(M) parameter. The AMFP result of the Skyrme model with the SLy4 parameter set is found to have a prediction almost similar to that of the E-RMF model with the G3(M) parameter. Contributions of each nucleon to the total AMFP are also presented for the G3(M) model.

Nuclear mass radius and pressure in the Skyrme model

We compute the mass radius, scalar radius, tensor radius, baryon number radius, and mechanical radius of nuclei with baryon number B=1,2,3,4,5,6,7,8, 32, 108 in the Skyrme model. The relations between these radii and the nuclear gravitational form factors are investigated. We also compute the ‘pressure’ distribution and find that it is negative in the core region for all the nuclei with B>1. This suggests that the way mechanical stability is achieved in nuclei is qualitatively different than in the nucleon. Published by the American Physical Society 2024

Mass and isospin breaking effects in the Skyrme model and in holographic QCD

We discuss how the quark masses and their mass splitting affect the baryons in the Skyrme model as well as the Witten-Sakai-Sugimoto (WSS) model. In both cases, baryons are described by solitonic objects, i.e., Skyrmions and instantons, respectively. After the quantization of their zero modes, the nucleons become quantum states of a rotor. We show how the quark mass affects the moment of inertia and we provide a semianalytic approach valid in the small-mass limit. Additionally, we show how the two lightest quarks’ mass splitting affects the moments of inertia of the Skyrmion and induces an isospin breaking effect. This effect turns out not to be enough to split the degeneracy in the neutron-proton multiplet, but it splits some of the states in the Δ multiplet. Unlike the basic Skyrme model, the WSS model already includes vector mesons and another mechanism to transfer isospin breaking from quark masses to the solitons is known. We compute the splitting of the moment of inertia in the small-mass limit in the WSS model and combine the two effects on the spectrum of baryons, in particular the Δ’s. Published by the American Physical Society 2024

Baby skyrmion crystals stabilized by vector mesons

In this letter we study soliton crystals in the (2+1)-dimensional analogue model of the (3+1)-dimensional Adkins–Nappi model of nuclear physics. The baby ω-Skyrme model studied here is an O(3) nonlinear σ model coupled to a massive vector meson, the ω-meson. Using recently developed methods in the (3+1)-dimensional ω-Skyrme model we are able to construct soliton crystals in this (2+1)-dimensional baby ω-Skyrme model. The resulting crystals form a hexagonal lattice structure and are qualitatively and quantitatively similar to crystals observed in the standard baby Skyrme model.

Skyrmion crystals stabilized by ω-mesons

We investigate the ground state crystalline structure of nuclear matter in the ω-meson variant of the Skyrme model. After minimizing energy with respect to variations of both the Skyrme field and the period lattice, we find four distinct periodic solutions which are similar to those found in the standard Skyrme model. We use these crystals to calculate coefficients in the Bethe-Weizsäcker semi-empirical mass formula and the compression modulus of infinite nuclear matter, and find a significant improvement as compared with other variants of the Skyrme model.

Nonlinear rigid-body quantization of Skyrmions

We consider rigid-body quantization of the Skyrmion in the most general four-derivative generalization of the Skyrme model with a potential giving pions a mass, as well as in a class of higher-order Skyrme models. We quantize the spin and isospin zero modes following the results of Pottinger and Rathske. Although one could hope that a one-parameter family of theories could provide a smaller spin contribution to the energy at some point in theory space—which would be welcome for Bogomol’nyi-Prasad-Sommerfield-type models, we find that the standard Skyrme model limit, with two time derivatives, gives rise to the smallest spin contribution to the energy. We speculate whether this tuning of the spin energy could be useful in the larger picture of quantizing vibrational and light massive modes of the Skyrmions. Finally, we establish a topological energy bound for the Pottinger-Rathske model with potential terms as well as new bounds for higher-order Skyrme models, with and without a potential. Published by the American Physical Society 2024

Ordered Patterns of (3+1)-Dimensional Hadronic Gauged Solitons in the Low-Energy Limit of Quantum Chromodynamics at a Finite Baryon Density, Their Magnetic Fields and Novel BPS Bounds

In this paper, we will review two analytical approaches to the construction of non-homogeneous Baryonic condensates in the low-energy limit of QCD in (3+1) dimensions. In both cases, the minimal coupling with the Maxwell U(1) gauge field can be taken explicitly into account. The first approach (which is related to the generalization of the usual spherical hedgehog ansatz to situations without spherical symmetry at a finite Baryon density) allows for the construction of ordered arrays of Baryonic tubes and layers. When the minimal coupling of the Pions to the U(1) Maxwell gauge field is taken into account, one can show that the electromagnetic field generated by these inhomogeneous Baryonic condensates is of a force-free type (in which the electric and magnetic components have the same size). Thus, it is natural to wonder whether it is also possible to analytically describe magnetized hadronic condensates (namely, Hadronic distributions generating only a magnetic field). The idea of the second approach is to construct a novel BPS bound in the low-energy limit of QCD using the theory of the Hamilton–Jacobi equation. Such an approach allows us to derive a new topological bound which (unlike the usual one in the Skyrme model in terms of the Baryonic charge) can actually be saturated. The nicest example of this phenomenon is a BPS magnetized Baryonic layer. However, the topological charge appearing naturally in the BPS bound is a non-linear function of the Baryonic charge. Such an approach allows us to derive important physical quantities (which would be very difficult to compute with other methods), such as how much one should increase the magnetic flux in order to increase the Baryonic charge by one unit. The novel results of this work include an analysis of the extension of the Hamilton–Jacobi approach to the case in which Skyrme coupling is not negligible. We also discuss some relevant properties of the Dirac operator for quarks coupled to magnetized BPS layers.

"Polymerization" of Bimerons in Quasi-Two-Dimensional Chiral Magnets with Easy-Plane Anisotropy.

We re-examine the internal structure of bimerons, which are stabilized in easy-plane chiral magnets and represent coupled states of two merons with the same topological charge |1/2| but with opposite vorticity and the polarity. We find that, in addition to the vortices and antivortices, bimerons feature circular regions which are located behind the anti-vortices and bear the rotational sense opposite to the rotational sense chosen by the Dzyaloshinskii-Moriya interaction. In an attempt to eliminate these wrong-twist regions with an excess of positive energy density, bimerons assemble into chains, and as such exhibit an attracting interaction potential. As an alternative to chains, we demonstrate the existence of ring-shaped bimeron clusters of several varieties. In some rings, bimeron dipoles are oriented along the circle and swirl clockwise and/or counterclockwise (dubbed "roundabouts"). Moreover, a central meron encircled by the outer bimerons may possess either positive or negative polarity. In other rings, the bimeron dipoles point towards the center of a ring and consequently couple to the central meron (dubbed "crossings"). We point out that the ringlike solutions for baryons obtained within the Skyrme model of pions, although driven by the same tendency of the energy reduction, yield only one type of bimeron rings. The conditions of stability applied to the described bimeron rings are additionally extended to bimeron networks when bimerons fill the whole space of two-dimensional samples and exhibit combinations of rings and chains dispersed with different spatial density (dubbed bimeron "polymers"). In particular, bimeron crystals with hexagonal and the square bimeron orderings are possible when the sides of the unit cells represent chains of bimerons joined in intersections with three or four bimerons, respectively; otherwise, bimeron networks represent disordered bimeron structures. Moreover, we scrutinize the inter-transformations between hexagonal Skyrmion lattices and disordered bimeron polymers occuring via nucleation and mutual annihilation of merons within the cell boundaries. Our theory provides clear directions for experimental studies of bimeron orderings in different condensed-matter systems with quasi-two-dimensional geometries.

Pearcey integrals, Stokes lines and exact baryonic layers in the low energy limit of QCD

The first analytic solutions representing baryonic layers living at finite baryon density within a constant magnetic field in the gauged Skyrme model are constructed. A remarkable feature of these configurations is that, if the Skyrme term is neglected, then these baryonic layers in the constant magnetic background cannot be found analytically and their energies grow very fast with the magnetic field. On the other hand, if the Skyrme term is taken into account, the field equations can be solved analytically and the corresponding solutions have a smooth limit for large magnetic fields. Thus, the Skyrme term discloses the universal character of these configurations living at finite Baryon density in a constant magnetic field. The classical gran-canonical partition function of these configurations can be expressed explicitly in terms of the Pearcey integral. This fact allows us to determine analytically the Stokes lines of the partition function and the corresponding dependence on the baryonic chemical potential as well as on the external magnetic field. In this way, we can determine various critical curves in the (μB−Bext) plane which separates different physical behaviors. These families of inhomogeneous baryonic condensates can be also dressed with chiral conformal excitations of the solutions representing modulations of the layers themselves. Some physical consequences are analyzed.

Approximation of BPS Skyrme model using modified Lagrangian Skyrmion

One of the nuclear atomic models represented by Skyrmion was the Skyrme model. This model was a modified nonlinear sigma model with a Skyrme field where the classical solution use generalized sixth order terms and potential terms. The binding energy that will be studied in the Skyrme SU(2) model is to generalize the second order nonlinear sigma model terms with sixth order derivative terms. The Lagrangian will be obtained for these two terms to find the BPS (Bogomolny Prasad Sommerfield) solution for the profile function numerically. The result of numerical calculation will be used to calculate static energy and rotational energy, where the characteristic of the nucleus can be observed from these two energies. Furthermore, the value of the coupling constant in the Lagrangian Skyrmion will be calculated from the static energy and rotational energy obtained previously. These values are expected to help in the application of Skyrme model for many research physics field.

The role of the Callan–Witten anomaly density as a Chern–Simons term in Skyrme model *

We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan–Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy M electric charge Qe and angular momentum J can be both positive and negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.

A baby–Skyrme model with anisotropic DM interaction: Compact skyrmions revisited

We consider a baby–Skyrme model with Dzyaloshinskii–Moriya interaction (DMI) and two types of potential terms. The model has a close connection with the vacuum functional of fermions coupled with O(3) nonlinear n-fields and with a constant SU(2) gauge background. The energy functional is derived from the heat-kernel expansion for the fermion determinant. The model possesses normal skyrmions with topological charge Q=1. The restricted version of the model also includes both the weak-compacton case (at the boundary, not continuously differentiable) and genuine-compacton case (continuously differentiable). The model consists of only the Skyrme term, and the DMI provides soliton solutions that are known as skyrmions without any potential. The BPS equation in the supersymmetric soliton models implies that the impurity coupling is closely related to the DMI. Therefore, the effect of an exponentially localized DMI is also studied in the present model.

Nudged Elastic Bands and Lightly Bound Skyrmions

It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5\leq B\leq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.

Skyrme crystals with massive pions

The crystalline structure of nuclear matter is investigated in the standard Skyrme model with massive pions. A semi-analytic method is developed to determine local minima of the static energy functional with respect to variations of both the field and the period lattice of the crystal. Four distinct Skyrme crystals are found. Two of these were already known–the cubic lattice of half-skyrmions and the α-particle crystal–but two are new. These new solutions have lower energy per baryon number and less symmetry, being periodic with respect to trigonal but not cubic period lattices. Minimal energy crystals are also constructed under the constraint of constant baryon density, and it is shown that the two new non-cubic crystals tend to chain and multi-wall solutions at low densities.

Strong Necessary Conditions and the Cauchy Problem

Some exact solutions of boundary or initial conditions formulated for Bogomolny equations (derived by using the strong necessary conditions and associated with some ordinary equation and some partial differential equations) have been found. The solution obtained for the restricted baby Skyrme model, as well the density of energy for this solution, are localized. Moreover, it turns out that the densities of the ungauged Hamiltonian and the gauged Hamiltonian are correspondingly, non-zero and zero for the found solution of the Cauchy problem associated with the Bogomolny equation of the restricted baby Skyrme model. Hence, a degeneracy of the Hamiltonian for this model has been established. As such, one can see the breaking of some symmetry.

Gravitational form factors of nuclei in the Skyrme model

Gravitational form factors of nuclei in the Skyrme model

Baby skyrmion in two-component holographic superfluids

In the two-component Ginzburg-Landau theory of superfluidity, a pair of fractional vortices form a composite type of topological defect, usually referred to as a baby skyrmion. In this paper, we initiate the construction of such a baby skyrmion in the holographic model of two-component superfluids. As a result, two types of baby skyrmion configurations are found, where the monopole-type of one is constructed directly by solving the static equations of motion while the dipole-type of one is obtained by resorting to the time evolution method. In addition, we find that the existence of these two types of baby skyrmion depends on the inter-component coupling, reminiscent of the situation in the baby skyrmion model.

Multishell solution in the Skyrme model

Multishell solution in the Skyrme model

A Skyrme Model with Novel Chiral Symmetry Breaking

An extension of the Skyrme model is presented in which derivative terms are added that break chiral symmetry to isospin symmetry. The theory contains just one new parameter and it reduces to the standard Skyrme model when this symmetry breaking parameter vanishes. The same Faddeev-Bogomolny energy bound applies for all parameter values, but the parameter can be tuned so that the energy of the single Skyrmion is much closer to the bound than in the standard Skyrme model. Applying the rational map approximation to multi-Skyrmions suggests that, for a suitable value of the symmetry breaking parameter, binding energies in this theory may be significantly more realistic than in the standard Skyrme model.

Multi-skyrmion states in the Skyrme model with a false vacuum potential* *Y. L. M. was supported in part by the National Science Foundation of China (11875147, 12147103).

We study multi-skyrmion states using the Skyrme model with a false vacuum potential up to baryon number using the product ansatz. It is found that both the false and true vacuum potentials can result in a cluster structure for the multi-skyrmion states. We also analyze the effect of explicit chiral breaking on the masses and contour surfaces of the baryon number density of the multi-skyrmion states.