Effect of CP-violation on the sphaleron rate

We calculate the effect of two CP-violating (dimension-eight) operators of the SU(2)-Higgs model on the motion along a particular path from the vacuum to the sphaleron. It turns out that CP-violation may introduce a difference between the sphaleron rate towards larger Chern-Simons number and the rate towards smaller Chern-Simons number. Such a difference induces a non-zero baryon-number without a first order phase transition.