Baryon number freeze-out in the Standard Model, precisely

Abstract

Weak sphaleron transitions turn a lepton asymmetry of the Standard Model plasma in the early Universe into a baryon asymmetry, conserving baryon-minus-lepton number $B-L$ and its individual flavored charges. A baryon asymmetry can thus also arise from flavored lepton asymmetries with vanishing $B-L$. Standard equilibrium calculations in the symmetric and broken phases are performed at constant temperature and hence neglect the fact that both the Higgs expectation value and the sphaleron rate vary as functions of temperature across the electroweak crossover. We derive a Boltzmann equation for the baryon number evolution across the crossover and calculate the freeze-out abundance including higher-order corrections to both the grand canonical partition function and the perturbative Higgs expectation value. This yields two sphaleron conversion factors: $C_\text{sph} = 0.3328(5)$ for $B-L$ and $\mathcal{F}_\text{sph} = 0.0279(19)$ for the flavored charges weighted by the charged-lepton Yukawa couplings.