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

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 $0 \leq \lambda \leq 49$.
Comment: 8 pages, 3 figures