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.

中文翻译：

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重无菌中微子轻生中的相对论和旁观者效应

对于具有高于电弱尺度的重无菌中微子的轻质发生，早期（在相对论体系中）产生的不对称性是相关的，如果它们被保护免于冲刷。这可能发生在弱冲刷或当不对称性通过转移到观众场而得到部分保护时。因此，我们研究了相对论效应与具有强等级限制的两个无菌中微子的最小跷跷板模型中的轻质发生的相关性。从第一性原理出发，我们推导出一组动量平均流体方程，以计算最终的 B-L 不对称性，作为冲刷强度的函数，并在不同的初始条件下以一级精度计算。为此，我们采用相对论 CP 偶率和奇率的领先流体近似。假设观众场保持化学平衡，我们发现，对于弱冲刷，相对论校正会导致符号翻转和不对称性增强，从而导致无菌中微子的初始丰度消失。作为部分平衡旁观者效应的一个例子，我们考虑了由质量 ≳ 5 × 10 12 GeV 的无菌中微子驱动的轻质形成中的底部-汤川和弱-闪锌矿相互作用。对于初始丰度消失的惰性中微子，这会引起另一次翻转，并且相对于没有旁观者或完全平衡的情况，强冲刷区的最终不对称性增加了两个数量级。对于无菌中微子的热初始条件，这些影响不太明显。