Classical pion fields in the presence of source

TL;DR

This paper investigates classical pion fields influenced by external sources within the nonlinear sigma-model, revealing multiple solutions, quasistationary states, and their potential decay via soft pion emission.

Contribution

It introduces a detailed analysis of classical pion field solutions in the presence of sources, including the existence of multiple solutions and quasistationary states, in both massless and finite pion mass cases.

Findings

Multiple classical solutions exist for small sources in the massless case.

No stable solutions for large nuclei, but quasistationary states can form.

Long-lived states decay by emitting very soft pions.

Abstract

Classical pion field similar to Disoriented Chiral Condensate (DCC) is considered in the presence of the external source. This field is similar to DCC in the sense that its isotopic orientation is specified with a single vector at the whole space. We study the classical field solutions in the nonlinear sigma-model both in the chiral limit with massless pion and for the finite pion mass. In both cases the field resembles the Coulomb field of charged particle however the nonlinear pion interactions lead to the existence of several solutions. In the massless case and for the very small size of the source there is the lot of classical solutions with finite discrete energies. In the more realistic situation of large nucleus (heavy ion) there are no stable solutions of the above type, but there is the possibility for the formation of the quasistationary states. They can live for a long time slowly decaying through the emission of very soft pions. The structure and the energies of these solutions is investigated numerically.