Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-04-30
Phys.Rev.D78:034040,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
12 pages, 4 figures
Scientific paper
10.1103/PhysRevD.78.034040
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 $\mu_I = {\cal O} (N_c^0)$, 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 $I \sim N_c$.
Cohen Thomas D. .
Ponciano Juan A.
Scoccola Norberto N.
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