EXACT COMPUTATION OF THE SMALL-FLUCTUATION DETERMINANT AROUND A SPHALERON

We compute exactly, in the high-temperature limit, the determinant 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 g2 of scalar four-point coupling to gauge coupling g2 near unity, we find that is 0.03. For g2 large corresponding to a strongly coupled Higgs phase, or for g2 very small tending to the Coleman-Weinberg limit, we find that the determinant strongly suppresses the rate of baryon-number-changing processes. © 1990 The American Physical Society.