Abstract
Electroweak baryogenesis (EWBG) is sourced by nonstandard $CP$-violating interactions of the Higgs boson with fermions, usually taken to be the top quark, enhanced by its large Yukawa coupling. Numerous papers have studied EWBG sourced by lighter fermions, including the tau lepton and off-diagonal quark mass terms. We critically reassess the viability of EWBG in these scenarios, comparing the predictions based on the semiclassical (WKB) formalism for the source term to those from the VEV insertion approximation (VIA), using updated values for the collision terms, and clarifying discrepancies in the definition of the weak sphaleron rate. The VIA systematically predicts a baryon asymmetry that is orders of magnitude larger than the WKB formalism. We trace this to the differing shapes of the $CP$-violating source terms in the two formalisms, showing that the additional spatial derivative in the WKB source term causes large cancellations when it is integrated over the bubble wall profile. An important exception is a source term from $c$-$t$ quark mixing, where the WKB prediction also allows for a realistically large baryon asymmetry. In contrast, the analogous $b$-$s$ mixing source is found to be orders of magnitude too small.
Highlights
Electroweak baryogenesis (EWBG) has been extensively studied since its introduction [1,2,3], in part because of its highly predictive nature
The two methods are known respectively as the vacuum expectation value insertion approximation (VIA) [4,5] and the semiclassical or WKB approximation [6,7,8]. Both frameworks agree that a spatially varying CP-violating phase should be present within the bubble wall in order to generate a nonvanishing baryon asymmetry of the universe (BAU), but the WKB source term involves an additional spatial derivative relative to the VIA source, leading to significant quantitative differences in the predicted BAU
The VIA predictions of [39] become roughly consistent with this when we take into account the correction factors 1=3 × 1=2 arising from the strong and weak sphaleron rates discussed in sections II C–II D, under which the BAU scales as ηVBIA ∼ ΓWS=ΓSS
Summary
Electroweak baryogenesis (EWBG) has been extensively studied since its introduction [1,2,3], in part because of its highly predictive nature. The two methods are known respectively as the vacuum expectation value insertion approximation (VIA) [4,5] and the semiclassical or WKB approximation [6,7,8] Both frameworks agree that a spatially varying CP-violating phase should be present within the bubble wall in order to generate a nonvanishing baryon asymmetry of the universe (BAU), but the WKB source term involves an additional spatial derivative relative to the VIA source, leading to significant quantitative differences in the predicted BAU.
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