BPS Skyrme modelsexact methods in hadronic and nuclear phenomenology

Resumo

The Skyrme model is an effective theory for the description of nucleons, nuclei and pions, where the primary degrees of freedom are mesons and the hadrons and nuclei appear as topological solutions of such model. Furthermore, the number of baryons is identified with the topological charge of the solitons. The Skyrme model allow us to study hadrons and nuclei starting from a field theory instead of the more common nuclear models based on methods of the quantum mechanics with a finite number of degrees of freedom. The highly non-linear character of such field theory makes it very suitable to the description of complex phenomena of strong interaction and very present in several applications. In fact, using the Skyrme model, a lot of nucleus properties can be understood from a qualitative point of view, like their masses, or their spectra (corresponding to excitations of the spin and isospin of the Skyrmions). On the other hand, the quantitative precision of the standard Skyrme model do not exceed a 10-30%. The main reason for this limitation is the lack of BPS solutions in the standard Skyrme model, what implies binding energies too high and internuclear forces too strong, among other problems. To deal with this limitations, some generalizations of the Skyrme model have been studied with the same content of fields but adding new terms to the Lagrangian. Among these generalized Skyrme theories, an integrable theory with an infinite number of exact solutions (topological solitons) saturating a Bogomolny bound has been found out recently. This is the BPS Skyrme model. Due to its integrability, this model has the symmetries of an incompressible fluid. This and the BPS property make the model phenomenological suitable for nucleus description. For instance, because of the BPS property, binding energies of classical solitons are zero, and low binding energies of real nuclei are obtained by quantum corrections and by small contributions from additional terms in the Lagrangian. Soliton radii also grow with the cube root of the baryonic charge, as in real nuclei. With the purpose of studying in detail the BPS Skyrme model and its application to hadronic and nuclear physics, the following research lines has been developed: 1. The analyse of the thermodynamics of the BPS Skyrme model at zero temperature with the introduction of an external pressure and the calculation of the energy-momentum tensor. Moreover, two important thermodynamical quantities like the compressibility and the baryon chemical potential were studied. 2. The introduction of the quantization of the collective coordinates (spin and isospin), as in the the standard Skyrme model. Moreover, the electrostatic energy (Coulomb term) and a little explicit breaking of the isospin were added. The Coulomb term is really important for heavy nuclei, whereas isospin symmetry breaking will split the protons and neutrons. 3. The coupling of the BPS Skyrme model to gravity to describe neutron stars in good agreement with the observational constraints concerning mass and radius. Here, two distinct approaches were followed (exact and mean-field calculations) finding that, although for global properties there are not too much difference, it is not the case of local ones, where the difference is pronounced. 4. The study of the influence of several different potentials in the researches mentioned above, because the specific shape of the potential is not important for the mathematical properties. Finally, it is worth commenting that, although the BSP model gives the dominant contributions to many nuclear matter properties, some evidences have been found that an extension to a near-BPS model is needed for a complete description of strong interactions.