Constrained instanton approximation of Skyrmions with massive pions
arXiv:2209.06607 · doi:10.1016/j.physletb.2022.137532
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 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.
arXiv comment11 pages, 2 figures. Typos corrected, especially in eqs. 36 and 37. Version accepted for publication in Phys. Lett. B
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