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

Abstract: We demonstrate dual repulsive mechanisms stabilizing Cho-Maison monopole-antimonopole pairs (MAPs) through stress-energy tensor analysis. Higgs-mediated repulsion exhibits non-monotonic dependence on topological charge and Higgs self-coupling, confirming its topological origin while revealing a mass-controlled range transition beyond Yukawa suppression. Simultaneously, $Z$-boson field generates localized repulsive cores of radius $R_c\approx 0.8$ $m_W^{-1}$, which aligns with weak interaction scales. Neutral charge distribution confirms $Z$-boson exchange as the physical mechanism. These competing effects -- operating at topological and electroweak scales -- establish a stabilization mechanism for Cho-Maison MAPs that extends to other topological solitons in the Standard Model.