Full Boltzmann equations for leptogenesis including scattering

TL;DR

This paper employs full classical Boltzmann equations, including quantum statistics and scattering effects, to analyze leptogenesis, revealing significant suppression of lepton asymmetry in weak wash-out regimes and minimal impact in strong wash-out regimes.

Contribution

It introduces a comprehensive Boltzmann framework for leptogenesis that accounts for scattering and quantum effects, improving accuracy over previous simplified models.

Findings

Lepton asymmetry can be suppressed by up to 1.5 times in weak wash-out regimes.

In strong wash-out regimes, full and integrated approaches yield similar results.

Quantum statistics effects tend to cancel out, reducing the net impact of scattering.

Abstract

We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukawa couplings by means of the full Boltzmann equations. We find that in our full Boltzmann treatment the final lepton asymmetry can be suppressed by as much as a factor of 1.5 in the weak wash-out regime (K<1), compared to the usual integrated approach which assumes kinetic equilibrium and neglects quantum statistics. This suppression is in contrast with the enhancement seen in some previous studies that considered only decay and inverse decay of the right-handed neutrino. However, this suppression quickly decreases as we increase K. In the strong wash-out regime (K>1), the full Boltzmann treatment and the integrated approach give nearly identical final lepton asymmetries (within 10 % of each other at K>3). Finally, we show that the opposing effects of quantum statistics on decays/inverse decays and the scattering processes tend to reduce the net importance of scattering on leptogenesis in the full treatment compared to the integrated approach.