SPHALERONS AT FINITE MIXING ANGLE

The classical sphaleron is constructed for the full SU(2) X U(1) electroweak theory. Unlike the sphaleron of the SU(2) Yang-Mills-Higgs theory, it is not spherically symmetric due to the coupling to the U(I) field. It is symmetric only under rotations around the z axis and parity reflections. The mixing angle theta(W) is varied over the full range 0 less-than-or-equal-to theta(W) less-than-or-equal-to pi/2. When the mixing angle is increased the energy of the sphaleron decreases, and the energy density changes its shape from a sphere at theta(W)=0 to a very elongated spheroid at large values of the mixing angle. At the physical value of the mixing angle, however, the electroweak sphaleron differs only a little from the spherical sphaleron.