Higgs sector CP violation at the electroweak phase transition

We consider explicit and spontaneous CP violation related to the profile of the two Higgs doublers at the MSSM electroweak phase transition. We find, in accordance with previous results, that in principle spontaneous CP violation could exist in the MSSM at finite temperatures, but when the constraints from experiment and the strength of the transition are taken into account, the relevant region of the parameter space is rather restricted. Nevertheless, we show that in this small region, perturbative estimates need not be reliable, and non-perturbatively the region might be slightly larger (or smaller). To allow for more precise perturbative studies and for a lattice study of the non-perturbative corrections, we construct an effective 3d theory for the light stops and the two Higgses in the regime of large m(Q). The 3d theory involves CP-violating parameters and allows to determine CP-odd observables. (C) 1999 Elsevier Science B.V.