On Skyrmion semiclassical quantization in the presence of an isospin chemical potential

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dc.creatorCohen, Thomas D.
dc.creatorPonciano, Juan A.
dc.creatorScoccola, Norberto N.
dc.date2008-04-30
dc.date.accessioned2026-07-07T11:50:23Z
dc.date.available2026-07-07T11:50:23Z
dc.descriptionThe semiclassical description of Skyrmions at small isospin chemical potential $μ_I$ 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 ($μ_I=0$), together with the "natural" assumption $μ_I = {\cal O} (N_c^0)$, the proton and neutron masses are nonlinear in $μ_I$ in the regime $|μ_I| < m_π$. 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 $\mui$ the energy excitations above the vacuum are linear in $μ_I$. The resolution of this paradox is achieved by studying the realization of the large $N_c$ limit of $QCD$ in the Skyrme model at finite $\mui$. 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 $N_c$. 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 $I \sim N_c$.
dc.description12 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0804.4711
dc.identifierhttp://arxiv.org/abs/0804.4711
dc.identifierPhys.Rev.D78:034040,2008
dc.identifierdoi:10.1103/PhysRevD.78.034040
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/203548
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectNuclear Theory
dc.titleOn Skyrmion semiclassical quantization in the presence of an isospin chemical potential
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