Topological stabilization via Higgs and <i>Z</i> -boson mediated repulsions in electroweak monopole-antimonopole pairs

We identify two distinct repulsive mechanisms in the Cho-Maison monopole-antimonopole pair (MAP) configuration. Our results show that the Higgs-mediated repulsion exhibits a nonmonotonic dependence on both topological charge and Higgs self-coupling, confirming its topological origin while revealing a mass-controlled range transition that deviates from the exponential form of a Yukawa potential. Simultaneously, the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Z</a:mi> </a:math> -boson field generates localized repulsive cores of radius <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>R</c:mi> <c:mi>c</c:mi> </c:msub> <c:mo>≈</c:mo> <c:mn>0.8</c:mn> <c:msubsup> <c:mi>m</c:mi> <c:mi>W</c:mi> <c:mrow> <c:mo>−</c:mo> <c:mn>1</c:mn> </c:mrow> </c:msubsup> </c:math> , consistent with the weak interaction scale. The collaborative effect of these mechanisms—operating in different physics regimes—counteracts the magnetic attraction, establishing a stabilization paradigm for the Cho-Maison MAP that extends naturally to other topological solitons in the Standard Model.