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

Dan Zhu, Xurong Chen, Khai-Ming Wong

TL;DR

This work analyzes electroweak monopole-antimonopole pairs (MAPs) in the Cho-Maison construction within the Weinberg–Salam framework and benchmarks them against SU(2) MAPs. It identifies two distinct repulsive channels—Higgs-mediated repulsion with non-monotonic, multi-scale dependence on topological charge and Higgs mass, and Z-boson–mediated short-range repulsion—that counterbalance long-range magnetic attraction, yielding a finite pole separation. Through stress-energy tensor analysis and neutral charge density calculations, the study demonstrates how these repulsions stabilize MAP configurations and suggests a universal stabilization mechanism for topological solitons in the Standard Model and related effective theories. The findings have potential implications for electroweak vortex rings and other non-perturbative solitons across high-energy and condensed-mmatter-inspired systems.

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.

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

TL;DR

This work analyzes electroweak monopole-antimonopole pairs (MAPs) in the Cho-Maison construction within the Weinberg–Salam framework and benchmarks them against SU(2) MAPs. It identifies two distinct repulsive channels—Higgs-mediated repulsion with non-monotonic, multi-scale dependence on topological charge and Higgs mass, and Z-boson–mediated short-range repulsion—that counterbalance long-range magnetic attraction, yielding a finite pole separation. Through stress-energy tensor analysis and neutral charge density calculations, the study demonstrates how these repulsions stabilize MAP configurations and suggests a universal stabilization mechanism for topological solitons in the Standard Model and related effective theories. The findings have potential implications for electroweak vortex rings and other non-perturbative solitons across high-energy and condensed-mmatter-inspired systems.

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 -boson field generates localized repulsive cores of radius , 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.

Paper Structure

This paper contains 12 sections, 21 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Frameworks
  3. The Weinberg-Salam Model
  4. The Yang-Mills-Higgs Theory
  5. Magnetic Ansatz
  6. Numerical Method
  7. Properties of the MAP configurations
  8. Results and Discussion
  9. The Anomalous Scaling of Pole Separation
  10. The Higgs Repulsion
  11. The Z-Boson Repulsion
  12. Conclusion

Figures (10)

  • Figure 1: Higgs modulus $|\Phi|$ comparison between (a) an SU(2) MAP and (b) a Cho-Maison MAP.
  • Figure 2: Determining the pole separation $d_z$ of an MAP solution from (a) $\Phi_1$ surface plot and (b) the cross-section $\Phi_1(x_c,0)$.
  • Figure 3: Pole separation $d_z$ vs. Higgs self-coupling $\beta$ for SU(2) MAP solutions with different $\phi$-winding number $n$.
  • Figure 4: Pole separation $d_z$ vs. Higgs self-coupling $\beta$ for Cho-Maison MAP solutions with different $\phi$-winding number $n$.
  • Figure 5: Evolution of the asymptotic repulsive interaction (large $x_c$) in $x^2\sin\theta\cdot T_{33}^{\text{Higgs}}$ with increasing Higgs self-coupling $\beta$ for both (a) an SU(2) MAP and (b) a Cho-Maison MAP. Note that their qualitative behaivors are identical.
  • ...and 5 more figures