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Top transport in electroweak baryogenesis

Lars Fromme, Stephan J. Huber

TL;DR

This work addresses top-quark–driven electroweak baryogenesis in thick-wall regimes by presenting a consistent, boosted dispersion relation that reconciles Dirac-equation and Schwinger-Keldysh results, and by refining transport equations to include finite-rate $W$-scatterings and spatially dependent thermal averages. The leading CP-violating source arises from $S_\theta$ and, when combined with the improved transport treatment and a dimension-6 extension of the SM, yields a substantially larger predicted baryon asymmetry, potentially increasing $\eta_B$ by up to a factor of $~5$ in favorable regions (e.g., for certain wall thickness, transition strength, and cut-off scales). The analysis stresses the importance of the Lorentz-frame choice, the proper handling of kinetic momentum, and the sensitivity to wall velocity $v_w$ and wall profile, highlighting remaining transport-uncertainties. The results motivate applying the refined framework to other models, such as two-Higgs-doublet scenarios, to assess robustness across electroweak baryogenesis setups.

Abstract

In non-supersymmetric models of electroweak baryogenesis the top quark plays a crucial role. Its CP-violating source term can be calculated in the WKB approximation. We point out how to resolve certain discrepancies between computations starting from the Dirac equation and the Schwinger--Keldysh formalism. We also improve on the transport equations, keeping the W-scatterings at finite rate. We apply these results to a model with one Higgs doublet, augmented by dimension-6 operators, where our refinements lead to an increase in the baryon asymmetry by a factor of up to about 5.

Top transport in electroweak baryogenesis

TL;DR

This work addresses top-quark–driven electroweak baryogenesis in thick-wall regimes by presenting a consistent, boosted dispersion relation that reconciles Dirac-equation and Schwinger-Keldysh results, and by refining transport equations to include finite-rate -scatterings and spatially dependent thermal averages. The leading CP-violating source arises from and, when combined with the improved transport treatment and a dimension-6 extension of the SM, yields a substantially larger predicted baryon asymmetry, potentially increasing by up to a factor of in favorable regions (e.g., for certain wall thickness, transition strength, and cut-off scales). The analysis stresses the importance of the Lorentz-frame choice, the proper handling of kinetic momentum, and the sensitivity to wall velocity and wall profile, highlighting remaining transport-uncertainties. The results motivate applying the refined framework to other models, such as two-Higgs-doublet scenarios, to assess robustness across electroweak baryogenesis setups.

Abstract

In non-supersymmetric models of electroweak baryogenesis the top quark plays a crucial role. Its CP-violating source term can be calculated in the WKB approximation. We point out how to resolve certain discrepancies between computations starting from the Dirac equation and the Schwinger--Keldysh formalism. We also improve on the transport equations, keeping the W-scatterings at finite rate. We apply these results to a model with one Higgs doublet, augmented by dimension-6 operators, where our refinements lead to an increase in the baryon asymmetry by a factor of up to about 5.

Paper Structure

This paper contains 5 sections, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The semiclassical force
  3. Transport equations
  4. Top transport: an example
  5. Conclusions

Figures (2)

  • Figure 1: The baryon asymmetry as a function of $v_{w}$ for $\xi=1.5$, $M=6$ and $L_{\rm w}=8$. The labeling is explained in the text.
  • Figure 3: The baryon asymmetry in the SM with low cut-off for two different Higgs masses as a function of $M$ (in units of GeV) for $v_w=0.01$ (solid) and $v_w=0.3$ (dashed). The horizontal lines indicate the error band of the observed value.