Electroweak Monopole-antimonopole Pair in the Standard Model

We present the first numerical solution that corresponds to a pair of Cho-Maison monopole and antimonopole (MAP) in the SU(2)$\times$U(1) Weinberg-Salam (WS) theory. The monopoles are finitely separated, while each pole carries magnetic charge $\pm 4\pi \mathrm{/}e$. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho-Maison MAP was investigated for a range of Weinberg angle, $0.4675\le \tan {\theta }_W\le 10$, and Higgs self-coupling, $0\le \beta \le 1.7704$. Magnetic dipole moment (${\mu }_m$) and pole separation ($d_z$) of the numerical solutions are calculated and analyzed. Total energy of the system, however, is infinite due to point singularities at the locations of monopoles.