Exact computation of the small-fluctuation determinant around a sphaleron

We compute exactly, in the high-temperature limit, the determinant κ of small fluctuations around the sphaleron configuration of electroweak theory, exploiting the symmetry of the sphaleron under spatial rotations combined with isospin and custodial SU(2) transformations. For the ratio λg² of scalar four-point coupling λ to gauge coupling g² near unity, we find that κ is 0.03. For λg² large corresponding to a strongly coupled Higgs phase, or for λg² very small tending to the Coleman-Weinberg limit, we find that the determinant strongly suppresses the rate of baryon-number-changing processes.