The Skyrmion Model and the Dynamical Breakdown of Chiral Symmetry

Abstract

A scalar field, $\eta({\bf r})$, is coupled to the skyrmion. Its classical value in the vacuum ("condensate") reduces to the pion decay constant, $f_{\pi}$, being thus proportional to the chiral condensate $<\bar{q} q>$. A quadratic coupling of the scalar field to the pion kinetic Lagrangian term, reminiscent from the linear sigma model, is considered. Its mass is an additional free parameter in the model associated to the lightest scalar isoscalar meson. Solutions for the two resulting coupled differential equations are found in several cases. The nucleon, as a topological soliton, ``digs a hole'' in the vacuum making the value of the scalar condensate to be close to zero inside the skyrmion. Some of the observables, as for example the baryon masses, may have their values closer to the experimental ones. Derrick's stability analysis is applied to the model.