No abstract

We analyze the existence of localized finite energy topological excitations on top of the perturbative pion vacuum within the Skyrme model at finite isospin chemical potential and finite pion mass. We show that there is a critical isospin chemical potential $\mu_I^c$ above which such solutions cease to exist. We find that $\mu_I^c$ is closely related to the value of the pion mass. In particular for vanishing pion mass we obtain $\mu_I^c=0$ in contradiction with some results recently reported in the literature. We also find that below $\mui^c$ the skyrmion mass and baryon radius show, at least for the case of the hedgehog ansatz, only a mild dependence on the isospin chemical potential.Comment: 8 pages, 2 figure

We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate analytical solutions.We show that Padé approximants are well suited to continue analytically the asymptotic representation obtained in terms of a power series expansion near the origin, obtaining explicit approximate solutions for the Skyrme equations. We improve the approximations by applying the 2-point Padé approximant procedure whereby the exact behaviour at spatial infinity is incorporated. An even better convergence to the exact solution is obtained by introducing a modified form for the approximants. The new representations share the same analytical properties with the exact solution at both small and large values of the radial variable r.

The semiclassical description of Skyrmions at small isospin chemical potential µI is carefully analyzed. We show that when the calculation of the energy of a nucleon is performed using the straightforward generalization of the vacuum sector techniques (µI = 0), together with the "natural" assumption µI = O(N 0 c ), the proton and neutron masses are nonlinear in µI in the regime |µI | < mπ. Although these nonlinearities turn out to be numerically quite small, such a result fails to strictly agree with the very robust prediction that for those values of µI the energy excitations above the vacuum are linear in µI . The resolution of this paradox is achieved by studying the realization of the large Nc limit of QCD in the Skyrme model at finite µI . This is done in a simplified context devoid of the technical complications present in the Skyrme model but which fully displays the general scaling behavior with Nc. The analysis shows that the paradoxical result appears as a symptom of using the semi-classical approach beyond its regime of validity and that, at a formal level, the standard methods for dealing with the Skyrme model are only strictly justified for states of high isospin I ∼ Nc.