Skyrme model and Isospin Chemical Potential

Abstract

We discuss the stability of the Skyrmion solution in the presence of a finite isospin chemical potential $μ$. Solving numerically the mass of the Skyrmion as function of $μ$, we find a critical value $μ_c=222.8$ MeV where the Skyrmion mass vanishes. We compare the exact numerical treatment with an analytical discussion based on a special shape for the profile of the Skyrmion due to Atiyah and Manton. The extension of this ansatz for finite $μ$ works quite well for $μ<121$ MeV. Then, for small values of $μ$, where the analytical approach is valid, we consider the possibility of having an angular deformation for the Skyrmionic profile, which is possible for finite values of $μ$. This is however, a small effect. Finally we introduce finite temperature corrections, which strength the instability induced by the chemical potential, finding the dependence of the critical temperature on $μ$.