Anomalous thresholds and the realization of chiral symmetry

Abstract

We follow the work of some other authors in a study of chiral-symmetry breaking based on the linear $\ensuremath{\sigma}$ model in the semiclassical approximation. By this procedure the masses of the mesons are known in terms of the symmetry-breaking parameters. Therefore, in those terms, we can analyze the system for the possible occurrence of anomalous thresholds corresponding to the bound-state properties of the scalar mesons. We find that when the critical parameter in the symmetric Lagrangian is such that a Goldstone symmetry limit can occur, then the anomalous threshold does not manifest itself by emerging to the physical sheet when mass continuation is performed; instead, the anomalous singularity stays out on the physical sheet and never disappears from it. Conversely, the system has an anomalous threshold with familiar emerging behavior when the critical parameter admits only the normal symmetry limit.