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

Constrained instanton approximation of Skyrmions with massive pions