Relativistic and spectator effects in leptogenesis with heavy sterile neutrinos

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 5 × 10 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.

Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis

“…Partially equilibrated spectator fields may lead to an effective protection of the asymmetry from washout, which is of importance in some regions of the parameter space discussed in Refs. [86,103].…”

“…Notably, the solutions to Eqs. (86) with the rates (87) for leptogenesis have relatively simple analytic approximations, and the derivation of these offers some insights into the mechanism [115].…”

“…Consequently, one can then distinguish between lepton-number conserving and lepton-number violating reactions [35,45,46,[105][106][107][108], where the latter are mediated by the Majorana mass that is small compared to the temperature. Moreover, both types of rates play a role in the source term for the asymmetry [86,127]. Within the CTP approach, accounting for helicity asymmetries can be dealt with by accounting for the axial and pseudoscalar density (in contrast to the approximations made in Section 6), as it is worked out in Refs.…”

“…For leptogenesis with heavy RHNs with masses way above the electroweak scale, these findings have important implications [86]. Provided asymmetries that are produced at early times, when the RHNs are relativistic, persist until lepton-number violating processes freeze out, tracking the helicity asymmetries within the RHNs and distinguishing lepton-number conserving from lepton-number violating rates is important for the dynamics of washout as well as for the source term.…”

Type I seesaw mechanism as the common origin of neutrino mass, baryon asymmetry, and the electroweak scale

“…[90]. In doing so, we will neglect the effect of spectator processes [91][92][93][94] and make use of the fact that, at temperatures T ∼ 10 5 GeV, all SM interactions eventually reach chemical equilibrium [95].…”