Asymmetric Chern–Simons number diffusion from CP-violation

Abstract

We study Chern-Simons number diffusion in a SU(2)-Higgs model with CP-odd dimensioneight 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.

On Asymmetric Chern-Simons Number Diffusion

“…In out-of-equilibrium situation this operator can generate an effective chemical potential for baryons, and therefore it introduces a bias in the sphaleron transitions 4 . However, we found that, within the chosen approach, in thermal equilibrium the dimension-six operator does not lead to any asymmetry 5 . But we also found that CP-odd dimensioneight operators induce an asymmetry in the average velocity with which a configuration crosses the sphaleron barrier 5 .…”

“…However, we found that, within the chosen approach, in thermal equilibrium the dimension-six operator does not lead to any asymmetry 5 . But we also found that CP-odd dimensioneight operators induce an asymmetry in the average velocity with which a configuration crosses the sphaleron barrier 5 . Unfortunately, we have not succeeded to relate this asymmetry in the velocity to an asymmetry in the distribution of the Chern-Simons number after several sphaleron transitions.…”

“…The study of asymmetric Chern-Simons number diffusion is motivated by the the question how the baryon asymmetry in the universe was generated. It has been argued that asymmetric diffusion may result in a non-zero expectation value of the baryon number in a time-dependent effective potential 5 .…”

“…We start with the third power. It can be shown that in the long-time limit [N CS (t) − N CS (0)] 3 in thermal equilibrium either goes to a constant or grows linearly in time (for a one-dimensional system this was shown in 5 ).…”

Electroweak vacuum angle at finite temperature and implications for baryogenesis

“…In the Higgs phase, sphaleron diffusion is Boltzmann suppressed, γ diff ∼ T 4 e −E sph /T , and we expect that G 2 acquires a similar suppression. It is also worth noting that CP-violating effects in the sphaleron sector do not shift the equilibrium point away from n b+l = 0 [23][24][25].…”