# Relativistic and spectator effects in leptogenesis with heavy sterile neutrinos

## TL;DR

This paper investigates how relativistic effects and spectator fields influence leptogenesis with heavy sterile neutrinos, revealing significant impacts on asymmetry generation depending on washout strength and initial conditions.

## Contribution

It derives momentum-averaged fluid equations for leptogenesis with two sterile neutrinos, incorporating relativistic effects and spectator interactions, providing new insights into asymmetry outcomes.

## Key findings

- Relativistic corrections can flip the sign of the asymmetry.
- Spectator fields can enhance the final asymmetry by up to two orders of magnitude.
- Relativistic CP-violating sources are less suppressed than nonrelativistic approximations suggest.

## Abstract

For leptogenesis with heavy sterile neutrinos above the electroweak scale, asymmetries produced at early times (in the relativistic regime) are relevant, if they are protected from washout. This can occur for weak washout or when the asymmetry is partly protected by being transferred to spectator fields. We thus study the relevance of relativistic effects for leptogenesis in a minimal seesaw model with two sterile neutrinos in the strongly hierarchical limit. Starting from first principles, we derive a set of momentum-averaged fluid equations to calculate the final $B-L$ asymmetry as a function of the washout strength and for different initial conditions at order one accuracy. For this, we take the leading fluid approximation for the relativistic $CP$-even and odd rates. Assuming that spectator fields remain in chemical equilibrium, we find that for weak washout, relativistic corrections lead to a sign flip and an enhancement of the asymmetry for a vanishing initial abundance of sterile neutrinos. As an example for the effect of partially equilibrated spectators, we consider bottom-Yukawa and weak-sphaleron interactions in leptogenesis driven by sterile neutrinos with masses $\gtrsim 5\times10^{12}$ GeV. For a vanishing initial abundance of sterile neutrinos, this can give rise to another flip and an absolute enhancement of the final asymmetry in the strong washout regime by up to two orders of magnitude relative to the cases either without spectators or with fully equilibrated ones. These effects are less pronounced for thermal initial conditions for the sterile neutrinos. The $CP$-violating source in the relativistic regime at early times is important as it is proportional to the product of lepton-number violating and lepton-number conserving rates, and therefore less suppressed than an extrapolation of the nonrelativistic approximations may suggest.