Topological Stabilization via Higgs and $Z$-Boson Mediated Repulsions in Electroweak Monopole-Antimonopole Pairs

Abstract

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 non-monotonic 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 $Z$-boson field generates localized repulsive cores of radius $R_c\approx0.8\,m_W^{-1}$, 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 and various systems described by effective field theories.