Yukawa and Tri-scalar Processes in Electroweak Baryogenesis

TL;DR

This work develops a first-principles, non-equilibrium treatment of electroweak baryogenesis in the MSSM by deriving three-body source terms from decays and inverse decays induced by tri-scalar and Yukawa interactions using the Closed Time Path formalism. It shows that these ${\cal O}(α_s^0)$ contributions can dominate over traditional ${\cal O}(α_s)$ scattering terms and that the common fast-Yukawa approximation breaks down in the broken phase, requiring full numerical solutions of the transport equations. The authors quantify how finite Yukawa rates modify the baryon-to-entropy ratio $Y_B$ (typically by 20–100% depending on MSSM parameters and resonant conditions) and map the interplay between CP-violating sources, relaxation, and density transfer. They further connect these results to phenomenology, updating EDM constraints and highlighting how MSSM parameter choices impact viable regions for successful baryogenesis, with implications for collider and EDM searches in non-minimal Higgs sectors as well.

Abstract

We derive the contributions to the quantum transport equations for electroweak baryogenesis due to decays and inverse decays induced by tri-scalar and Yukawa interactions. In the Minimal Supersymmetric Standard Model (MSSM), these contributions give rise to couplings between Higgs and fermion supermultiplet densities, thereby communicating the effects of CP-violation in the Higgs sector to the baryon sector. We show that the decay and inverse decay-induced contributions that arise at zeroth order in the strong coupling, α_s, can be substantially larger than the O(α_s) terms that are generated by scattering processes and that are usually assumed to dominate. We revisit the often-used approximation of fast Yukawa-induced processes and show that for realistic parameter choices it is not justified. We solve the resulting quantum transport equations numerically with special attention on the impact of Yukawa rates and study the dependence of the baryon-to-entropy ratio Y_B on MSSM parameters.

Figures (8)

• Figure 1: Leading contributions to the self-energies $\Sigma_{B,F}$ generated by scattering from Higgs vevs.
• Figure 2: Self energies for scalar and fermion fields induced by the Yukawa and triscalar interaction lagrangians of Eqs. (\ref{['eq:lagYs']}) and (\ref{['eq:lagYf']}).
• Figure 3: Left panel: $\mathcal{I}_F/T^3$ as a function of $m_\phi/T$ for $m_1/T = 1$ and $m_2/T = 1,2,5$. Right panel: $\mathcal{I}_B/T^3$ as a function of $m_H/T$ for $A_s/T=1$, $m_L/T=1$ and $m_R/T=1,2,5$.
• Figure 4: $\Gamma_Y$ (solid red line), $\bar{\Gamma}_Y$ (dashed green line), and $\Gamma_Y^{\rm scattering}$ (dashed straight blue line) in units of GeV as a function of $\mu$ (GeV), for $T=100$ GeV and SUSY mass parameters as described in the text. In large regions of parameter space we find $\Gamma_Y^{\rm decay} > \Gamma_Y^{\rm scattering}$.
• Figure 5: We plot here the ratio $F_1/Y_B^{\rm WMAP}$ versus $\Gamma_Y$ for two values of the SUSY $\mu$ parameter: $|\mu| = 200$ GeV (solid line) and $|\mu| = 250$ GeV (dashed line), corresponding to on-resonance and off-resonance baryogenesis, respectively. All other parameters are fixed at the reference values of Table \ref{['tab:susy']}. We use the central value $Y_B^{\rm WMAP}=9.2 \times 10^{-11}$wmap.