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 × 1012 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.
Highlights
Reactions occurring at early times can affect the final asymmetry even in the strong washout regime due to spectator effects.2 If the spectator interactions become faster than the Hubble rate during leptogenesis, their net effect is to enforce chemical equilibrium constraints among the abundances of the participating particles [9,10,11]
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
For the toy model we present a semianalytical approximation of the asymmetry in the weak washout regime, and in the realistic model we isolate the effects from partially equilibrated spectator fields by comparing with the results based on the assumption of fully equilibrated spectators
Summary
The expansion of the universe is captured by following the approach in [39, 43], where it was assumed that leptogenesis takes place in a spatially flat Friedman-Robertson-Walker (FRW) cosmology during the radiation dominated period In this case, one can work in a comoving Minkowski frame in which the effect of the expansion is captured by masses that grow with the scale factor. We assume that the Standard Model particles remain in kinetic equilibrium throughout leptogenesis This is a good approximation for physical temperatures well below the equilibration temperature of the electroweak gauge interactions in the Standard Model, Tphys Teq ∼ 1016 GeV. It should be straightforward to combine both, partial flavour decoherence and partial equilibration of spectator fields in one single calculation
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