Kinetic Equations for Baryogenesis via Sterile Neutrino Oscillation

TL;DR

This paper develops kinetic equations for sterile neutrino oscillations in the νMSM to explain baryogenesis, revealing a non-equilibrium momentum distribution that influences the generated asymmetry.

Contribution

It introduces momentum-dependent kinetic equations for sterile neutrino oscillations, providing detailed numerical analysis of the resulting non-equilibrium distributions in baryogenesis.

Findings

Momentum distribution is significantly distorted from equilibrium.

Most important mode for asymmetry is around k ≈ 2 T.

Enhanced production at low momenta, suppressed at high modes.

Abstract

We investigate baryogenesis in the $\nu$MSM (neutrino Minimal Standard Model), which is the MSM extended by three right-handed neutrinos with masses below the electroweak scale. The baryon asymmetry of the universe can be generated by the mechanism via flavor oscillation of right-handed (sterile) neutrinos which are responsible to masses of active neutrinos confirmed by various experiments. We present the kinetic equations for the matrix of densities of leptons which describe the generation of asymmetries. Especially, the momentum dependence of the matrix of densities is taken into account. By solving these equations numerically, it is found that the momentum distribution is significantly distorted from the equilibrium one, since the production for the modes with lower momenta $k \ll T$ ($T$ is the temperature of the universe) is enhanced, while suppressed for higher modes. As a result, the most important mode for the yields of sterile neutrinos as well as the baryon asymmetry is $k \simeq 2 T$, which is smaller than < k > inferred from the thermal average. The comparison with the previous works is also discussed.