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The rate per unit volume for anomalous electroweak baryon number violation athigh temperatures, in the symmetric phase, has been estimated in the literatureto be $O(\alpha_W^4 T^4)$ based on simple scaling arguments. We argue thatdamping effects in the plasma suppress the rate by an extra power of $\alpha_W$to give $O(\alpha_W^5 T^4)$. We show how to understand this effect in a varietyof ways ranging from an effective description of the long-distance modesresponsible for baryon number violation, to a microscopic picture of theshort-distance modes responsible for damping. In particular, we resolve an oldcontroversy as to whether damping effects are relevant. Finally, we argue thatsimilar damping effects should occur in numerical simulations of the rate inclassical thermal field theory on a spatial lattice, and we point out apotential problem with simulations in the literature that have not found suchan effect.Comment: 27 pages, Latex, uses revtex, epsf macro package

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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The hot baryon violation rate isO(αw5T4)