**
Do We Know the Hot Sphaleron Rate? **

First, to answer the question; we know it at leading log with accuracy, and the value at realistic coupling we probably have to around 20 or 30 percent.

Three talks so far, those of Dietrich Bodeker, Peter Arnold, and Christina Manuel have dealt with finding effective theories for the real time violation of baryon number. My talk was about applying those effective theories to get an answer.

There are 4 effective theories to consider:

0) the Minimal Standard Model

1) classical Yang-Mills theory with added hard thermal loops

2) same, cut off between gT and g^2 T so there are collisions

3) Bodeker's effective theory.

The larger the number the easier it is to treat the theory but the less intrinsic accuracy the theory can provide. Theory 0) is hopeless, and I will only address 3) and 1).

Theory 3) is UV finite and contains only one scale, the g^2T scale, which means that we can strive to get an accurate answer. Using the matching between lattice and continuum theories discussed here and the topological measurement methods for Chern-Simons numbers discussed here and here we can get an accurate answer. The calculation is presented here and gives a rate = (10.8 +- 0.7) alpha^5 T^4 (g^2T^2/m_D^2) log(1/g) plus nonlogarithmic corrections, discussed in Peter Arnold's talk.

Theory 1) is harder to deal with; it is not UV finite and including the hard thermal loops is difficult. There are two proposals, that of Hu and Muller and that of Bodeker, McLerran, Smilga also discussed by Iancu. Both have been successfully implemented; the Hu Muller work here and the other method here. The answers are in good agreement and also appear to agree with the leading log result when the subleading correction found by Arnold and Yaffe is included. Numerically, at the real value of the coupling, a baryon number excess at a temperature above the electroweak phase transition dissipates in around 10^5/T time.