Monopole-Antimonopole Pair With Higher Energy Branch In SU(2) x U(1) Weinberg-Salam Theory

TL;DR

This paper explores complex monopole-antimonopole solutions in the Weinberg-Salam model, revealing bifurcations and higher-energy vortex-ring configurations at specific Higgs coupling constants.

Contribution

It identifies new bifurcating monopole-antimonopole solutions with higher energy branches in the SU(2) x U(1) Weinberg-Salam theory, expanding understanding of topological configurations.

Findings

Discovery of two new bifurcating solution branches at critical Higgs coupling.

Higher energy solutions form vortex rings with finite diameter.

Behavior of solutions differs from SU(2) Yang-Mills-Higgs vortex rings.

Abstract

We investigate the monopole-antimonopole pair solution in the SU(2) x U(1) Weinberg-Salam theory with $\phi$-winding number, $n=3$ for bifurcation phenomena. The magnetic monopole merges with antimonopole to form a vortex ring with finite diameter at $n=3$. Other than the fundamental solution, two new bifurcating solution branches were found when Higgs coupling constant $\lambda$, reaches a critical value $\lambda_c$. The two new branches possess higher energies than the fundamental solutions. These bifurcating solutions behave differently from the vortex ring configuration in SU(2) Yang-Mills-Higgs theory since thery are full vortex-ring. We investigate on the total energy $E$, vortex ring diameter $d_{\rho}$, and magnetic dipole moment $\mu_m$, for $0 \leq \lambda \leq 49$.