Generalized Skyrme model with the loosely bound potential

Abstract

We study a generalization of the loosely bound Skyrme model which consists of the Skyrme model with a sixth-order derivative term -motivated by its fluid-like properties -and the secondorder loosely bound potential -motivated by lowering the classical binding energies of highercharged Skyrmions. We use the rational map approximation for the Skyrmion of topological charge B = 4, calculate the binding energy of the latter and estimate the systematic error in using this approximation. In the parameter space that we can explore within the rational map approximation, we find classical binding energies as low as 1.8% and once taking into account the contribution from spin-isospin quantization we obtain binding energies as low as 5.3%. We also calculate the contribution from the sixth-order derivative term to the electric charge density and axial coupling.

Oscillons in a perturbed signum-Gordon model

“…Although the structure of static Skyrmions is fairly well understood both numerically and analytically (especially in the minimal Skyrme model [20,21], the loosely bound Skyrme models [11][12][13][14][15]22] and the BPS Skyrme model [4,5]), the time dependent solutions are much more difficult to obtain and to analyse. On the other hand, time-dependent configurations are needed in many physical applications of Skyrmions -especially in the (vibrational) quantization procedure.…”

“…Recently two important steps have been made allowing us to treat the model as an efficient tool in the quantitative description of nuclear matter. First of all, some attemps have been made [4][5][6][7][8][9][10][11][12][13][14][15], to improve the long standing issue of unphysically large binding energies of nucleons in nuclei as predicted by the standard Skyrme model. This has involved modifying the original Skyrme model by bringing it closer to a near BPS model.…”

Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential

“…These modifications are mainly motivated by the fact that there is a large disagreement between the experimental data for binding energies of hadrons and predictions of the Skyrme model, considered as an effective low energy theory of hadrons, the binding energy of nuclei do not exceed 1% of their masses while the binding energies of Skyrmions are on the level of 10%. It was noticed that a combination of the a sextic in derivatives of the pion field term and/or the higher-order potential may significantly reduce the binding energy of the solitons [21,22]. On the other hand, various symmetry breaking potentials were considered in the Skyrme model to construct half-Skyrmions [24][25][26][27][28] or various vortex strings [23].…”

Effect of the Coulomb energy on Skyrmions

“…Motivated by this puzzle, a series of alterations to the classical Lagrangian have been proposed. For example, one may include vector mesons in the Lagrangian or add a new potential energy term which unbinds the Skyrmion [25][26][27]. A Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrme model has solutions which saturate the Bogomol'nyi bound and thus they fix the binding energy problem in theory [28,29].…”