Resonant Relaxation in Electroweak Baryogenesis

TL;DR

The paper develops a closed-time-path framework to study electroweak baryogenesis in the MSSM, deriving quantum transport equations for chiral charges and performing a systematic ε expansion to capture leading CP-violating sources and relaxation terms. It reveals resonant enhancements in both CP sources and relaxation rates when relevant superpartner masses are nearly degenerate, highlighting that enhanced relaxation can mitigate the source-driven baryon asymmetry. Through analytic diffusion solutions in a simplified wall profile, the work links microphysical transport coefficients to the resulting baryon asymmetry, and uses MSSM benchmarks to illustrate feasibility and tension with EDM and collider constraints. The approach provides a principled method to connect electroweak-scale baryogenesis with phenomenology, while outlining necessary extensions (additional transport coefficients, resummations) for a fully robust MSSM analysis.

Abstract

We compute the leading, chiral charge-changing relaxation term in the quantum transport equations that govern electroweak baryogenesis using the closed time path formulation of non-equilibrium quantum field theory. We show that the relaxation transport coefficients may be resonantly enhanced under appropriate conditions on electroweak model parameters and that such enhancements can mitigate the impact of similar enhancements in the CP-violating source terms. We also develop a power counting in the time and energy scales entering electroweak baryogenesis and include effects through second order in ratios $ε$ of the small and large scales. We illustrate the implications of the resonantly enhanced ${\cal O}(ε^2)$ terms using the Minimal Supersymmetric Standard Model, focusing on the interplay between the requirements of baryogenesis and constraints obtained from collider studies, precision electroweak data, and electric dipole moment searches.

Figures (7)

• Figure 1: Contributions to the relevant self-energies from scattering of particles from the spacetime varying Higgs vevs.
• Figure 2: Contributions to the relevant self-energies from Yukawa interactions
• Figure 3: Representative contributions to self-energies from (super)gauge interactions.
• Figure 4: Left panel: $CP$-violating Higgsino source $\hat{S}_{\widetilde{H}} = -S_{\widetilde{H}}^{CP\!\!\!\!\!\!\!\!\hbox{\normalsize$\diagup$}}/(v^2 \dot{\beta} \sin \phi_\mu)$, as a function of $|\mu|$. Right panel: relaxation rate $R_{\Gamma} = (\Gamma_h + \Gamma_{M}^{-})/(\Gamma_h + \Gamma_m)_{H.N.}$, normalized to the value used in Huet:1995sh, as a function of $|\mu|$. We have taken $M_2 = 200\text{ GeV}$, and the values of all other parameters as indicated in the text.
• Figure 5: Left panel: Higgsino contribution to $Y_B$ ( Cf Eq. (\ref{['eq:pheno1']})), normalized to the observed value. $F_{1}$ displays residual resonant behavior for $|\mu| \sim M_2$. All other input parameters are given in the text. Right panel: Stop contribution to $Y_B$ ( Cf Eq. (\ref{['eq:pheno1']})) normalized to the observed value. The upper curve is for $M_{\tilde{b}_L}=M_{\tilde{t}_L}$, while the lower one is for $M_{\tilde{b}_L} \gg M_{\tilde{t}_L}$. We have taken here $M_{\tilde{t}_R}= 100$ GeV, $| \mu | = 200$ GeV, and have allowed $M_{\tilde{t}_L}$ to reach unrealistically low values to explore the size of the squark resonance. For realistic input parameters $F_2 \ll F_1$.