Skyrmion semiclassical quantization in the presence of an isospin chemical potential

Abstract

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.

Isospin asymmetry in holographic baryonic matter

“…The difference between a system of protons and neutrons and a gas of such deformed classical solutions was also discussed in the context of the Skyrme model in Ref. [72], where it was argued that the classical solutions are more accurate approximations for larger rather than smaller isospin asymmetries (the symmetry energy, where the discrepancy of our results to real-world nuclear matter is most obvious, is a derivative evaluated at vanishing isospin asymmetry). Analogous considerations hold in our context since, as shown in Ref.…”

Skyrmions confined as beads on a vortex ring

“…Although such chemical potential at the classical level, has been discussed in the literature [24][25][26][27], Ref. [28] pointed out that due to a subtlety in the large-N c counting of µ, one should not include the effects of the chemical potential at the classical level if one wishes to study the proton or neutron, because the large-N c nature of the model will pick out the largest spin state of the nucleon; hence not the proton or neutron. Therefore, if one does not include the effect of the chemical potential at the classical level, there is no presence of the potential that we use to construct vortex strings.…”

Isospin asymmetry in holographic baryonic matter

“…The difference between a system of protons and neutrons and a gas of such deformed classical solutions was also discussed in the context of the Skyrme model in Ref. [70], where it was argued that the classical solutions are more accurate approximations for larger rather than smaller isospin asymmetries (the symmetry energy, where the discrepancy of our results to real-world nuclear matter is most obvious, is a derivative evaluated at vanishing isospin asymmetry). Analogous considerations hold in our context since, as shown in Ref.…”