We compute exactly, in the high-temperature limit, the determ~nant K 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 h / g 2 of scalar four-point coupling ?, to gauge coupling g 2 near unity, we find that K is 0.03. For h / g 2 large corresponding to a strongly coupled Higgs phase, or for h / g 2 very small tending to the Coleman-Weinberg lim…
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