Constrained instanton approximation of Skyrmions with massive pions

TL;DR

This paper introduces a method using constrained instantons in an SU(2) Yang-Mills-Higgs theory to approximate Skyrmions with massive pions, capturing their exponential decay at large distances.

Contribution

It proposes a novel approximation technique for Skyrmions with massive pions using constrained instantons and the Atiyah-Manton construction.

Findings

Constrained instantons decay exponentially, matching massive pion Skyrmions.

The method accurately approximates Skyrmion solutions with pion mass.

The approach improves understanding of Skyrmion behavior with massive pions.

Abstract

We present the idea of using the holonomy along a line of a constrained instanton solution (an approximate solution of the Euclidean equations of motion subject to a constraint) of an $\rm SU(2)$ Yang-Mills-Higgs theory to approximate the Skyrmion solution in a chiral model with massive pions. The fact that the gauge field acquires a nonzero mass due to the Higgs mechanism implies that a constrained instanton decays exponentially far from its center, and so does the Skyrmion configuration that it generates via the Atiyah-Manton construction. This is precisely the desired behavior at large distances for the true Skyrmion solutions when the pion mass is included.