Recently, within the space of generalized Skyrme models, a BPS submodel was identified which reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is expected to be more accurate on theoretical grounds, the resulting binding energies are already in excellent agreement with their physical values. This result provides further strong evidence for the viability of the BPS Skyrme model as a distinguished starting point and lowest order approximation for the detailed quantitative investigation of nuclear and hadron physics.

One of the outstanding problems in modern nuclear physics is to determine the properties of nuclei from the fundamental theory of the strong force, quantum chromodynamics (QCD). Skyrmions offer a novel approach to this problem by considering nuclei as solitons of a low energy effective field theory obtained from QCD. Unfortunately, the standard theory of Skyrmions has been plagued by two significant problems, in that it yields nuclear binding energies that are an order of magnitude larger than experimental nuclear data, and it predicts intrinsic shapes for nuclei that fail to match the clustering structure of light nuclei. Here we show that extending the standard theory of Skyrmions, by including the next lightest subatomic meson particles traditionally neglected, dramatically improves both these aspects. We find Skyrmion clustering that now agrees with the expected structure of light nuclei, with binding energies that are much closer to nuclear data.QCD is the fundamental theory of the strong nuclear force and describes how quarks are confined to form protons and neutrons, together with the binding of these nucleons to form atomic nuclei. However, the complexity of the non-perturbative regime means that extracting the properties of nuclei directly from QCD is not within reach of current computational capabilities. Traditional methods of nuclear physics have confirmed that protons and neutrons are excellent effective degrees of freedom at the nuclear energy scale, but establishing a link to the more fundamental theory will not only provide a more complete understanding of nuclear physics but will also allow predictions for experimentally unknown nuclei and for matter under extreme conditions, for example in the interior of neutron stars.Skyrmions are named after the British physicist Tony Skyrme, who introduced the standard version of the model almost sixty years ago [1] as a nonlinear field theory of the lightest subatomic meson particles, called pions. This theory has topological soliton [2] solutions, that is, twisted localized particle-like excitations of the pion fields, that are now known as Skyrmions. The number of twists in the pion fields corresponds to the number of Skyrmions and Skyrme proposed that this be identified with baryon number: which is equal to the mass number A, that counts the number of nucleons in a nucleus. This proposal was verified twenty years later [3] by demonstrating that the model may be regarded as a low energy effective field theory of QCD in the limit of a large number of quark colours. Skyrmions therefore provide an intermediate approach to nuclei, between the currently intractable fundamental theory of quarks, and the accuracy of more conventional nuclear physics methods based directly on protons and neutrons.Skyrmions in the standard version of the model are displayed in Fig.1a, for nucleon numbers A = 1 to A = 8, by plotting baryon density isosurfaces that reveal the intrinsic shapes of the nuclei predicted by these Skyrmions [4]. Although Skyrmions have had some success in...

The BPS Skyrme model has been demonstrated already to provide a physically intriguing and quantitatively reliable description of nuclear matter. Indeed, the model has both the symmetries and the energy-momentum tensor of a perfect fluid, and thus represents a field theoretic realization of the "liquid droplet" model of nuclear matter. In addition, the classical soliton solutions together with some obvious corrections (spin-isospin quantization, Coulomb energy, proton-neutron mass difference) provide an accurate modeling of nuclear binding energies for heavier nuclei. These results lead to the rather natural proposal to try to describe also neutron stars by the BPS Skyrme model coupled to gravity. We find that the resulting self-gravitating BPS Skyrmions provide excellent results as well as some new perspectives for the description of bulk properties of neutron stars when the parameter values of the model are extracted from nuclear physics. Specifically, the maximum possible mass of a neutron star before black-hole formation sets in is a few solar masses, the precise value depending on the precise values of the model parameters, and the resulting neutron star radius is of the order of 10 km.Comment: 15 pages, 4 figures, Latex, 2 figures added, discussion extended and improved, references added; published versio

One problem in the application of the Skyrme model to nuclear physics is that it predicts too large a value for the compression modulus of nuclear matter. Here we investigate the thermodynamics of the BPS Skyrme model at zero temperature and calculate its equation of state. Among other results, we find that classically (i.e. without taking into account quantum corrections) the compressibility of BPS skyrmions is, in fact, infinite, corresponding to a zero compression modulus. This suggests that the inclusion of the BPS submodel into the Skyrme model lagrangian may significantly reduce this too large value, providing further evidence for the claim that the BPS Skyrme model may play an important role in the description of nuclei and nuclear matter.

We analyze the vector meson formulation of the BPS Skyrme model in (3+1) dimensions, where the term of sixth power in first derivatives characteristic for the original, integrable BPS Skyrme model (the topological or baryon current squared)is replaced by a coupling between the vector meson ω µ and the baryon current. We find that the model remains integrable in the sense of generalized integrability and almost solvable (reducible to a set of two first order ODEs) for any value of the baryon charge. Further, we analyze the appearance of topological solitons for two one-parameter families of one vacuum potentials: the old Skyrme potentials and the so-called BPS potentials. Depending on the value of the parameters we find several qualitatively different possibilities. In the massless case we have a parameter region with no skyrmions, a unique compact skyrmion with a discontinuous first derivative at the boundary (equivalently, with a source term located at the boundary, which screens the topological charge), and Coulomb-like localized solitons. For the massive vector meson, besides the no-skyrmion region and a unique C-compact soliton, we find exponentially as well as power-like localized skyrmions. Further, we find (for a specific potential) BPS solutions, i.e., skyrmions saturating a Bogomolny bound (both for the massless and massive vector mesons) which are unstable for higher values of the baryon charge. The properties of the model are finally compared with its baby version in (2+1) dimensions, and with the original BPS Skyrme model, contributing to a better understanding of the latter.