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

Abstract

The semiclassical description of Skyrmions at small isospin chemical potential ${\mu }_I$ 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 (${\mu }_I=0$), together with the "natural" assumption ${\mu }_I=\mathcal{O}(N_c^0)$, the proton and neutron masses are nonlinear in ${\mu }_I$ in the regime $|{\mu }_I|<m_{\pi }$. 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 ${\mu }_I$. 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 $I\sim N_c$.

arXiv comment12 pages, 4 figures

References in corpus (13)

• QCD at finite isospin density
• Lattice QCD at finite isospin density at zero and finite temperature
• Imaginary chemical potential and finite fermion density on the lattice
• Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
• The role of the Delta isobar in chiral perturbation theory and hedgehog soliton models
• Baryon Isovector Electric Properties and the Large N_c and Chiral Limits
• Phases of QCD with nonvanishing isopin density
• Skyrme model and Isospin Chemical Potential
• Skyrmions in the presence of isospin chemical potential
• Interplay of the Chiral and Large N_c Limits in pi N Scattering
• Electromagnetic Properties of the Delta in the Large N and Chiral Limits
• Skyrmions, Hadrons and isospin chemical potential
• Topological Field Configurations in the Presence of Isospin Chemical Potential

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• Cosmological Constant, Dark Matter, and Electroweak Phase Transition
• Isospin asymmetry in holographic baryonic matter
• Baryon chemical potential and in-medium properties of BPS skyrmions
• Skyrmions confined as beads on a vortex ring
• Experimental and Theoretical Evidence for Extended Particle Models