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 λ/g2 of scalar four-point coupling λ to gauge coupling g2 near unity, we find that κ is 0.03. For λ/g2 large corresponding to a strongly coupled Higgs phase, or for λ/g2 very small tending to the Coleman-Weinberg limit, we find that the determinant strongly suppresses the rate of baryon-number-changing processes