Asymmetric Chern–Simons number diffusion from CP-violation Original Research Article

We study Chern–Simons number diffusion in a SU(2)-Higgs model with CP-odd dimension-eight operators. We find that the thermal average of the magnitude of the velocity of the Chern–Simons number depends on the direction of the velocity. This implies that the distribution function of the Chern–Simons number will develop an asymmetry. It is argued that this asymmetry manifests itself through a linear growth of the expectation value of the third power of the Chern–Simons number. This linear behavior of the third power of a coordinate of a periodic direction is verified by a numerical solution of a one-dimensional Langevin equation. Further, we make some general remarks on thermal averages and on the possibility of the generation of the baryon asymmetry in a non-equilibrium situation due to asymmetric diffusion of the Chern–Simons number.