Sphaleron and Sphaleron-Antisphaleron Pair of the Weinberg-Salam Model

摘要

In this paper we present the full solutions of the Weinberg-Salam equations of motion for (1) the sphaleron and (2) the sphaleron-antisphaleron pair using numerical methods. In the SU(2) field part of the theory, the solutions obtained are (1) the one monopole-antimonopole pair and (2) the two monopole-antimonopole pairs respectively while in the U(1) field part, the solutions are (1) a one current loop and (2) two current loops respectively. In these sphaleron and sphaleron-antisphaleron pair solutions, both the sphaleron and antisphaleron are monopole-antimonopole pair (MAP) lying along the z-axis with an electromagnetic current loop circulating around it. The monopole and antimonopole in the MAP is joined by a flux string of the neutral &~0 field. In these solutions, the Weinberg angle is not arbitrary but it takes the value of θ_w = π/4. The magnetic charges of the monopole and antimonopole in each MAP is which is half the magnetic charge of a Cho-Maison monopole. Hence the MAP poles are half-monopoles. These new axially symmetric solutions possess finite energy and magnetic dipole moment and they are investigated for a range of Higgs field mass term 0≤ μ~2 ≤ 40. Their total energies are found to increase almost linearly with μ, whereas the magnetic dipole moments decrease exponentially fast with μ.