Supergauge interactions and electroweak baryogenesis

TL;DR

This paper extends electroweak baryogenesis analysis in the MSSM by treating diffusion ahead of the bubble wall with explicit, separate chemical potentials for particles and their superpartners. By computing three-body, Yukawa, and supergauge interaction rates within the closed-time-path formalism, the authors quantify when superequilibrium holds and when it can break, exploring both analytic approximations and full numerical solutions. They show that Yukawa-driven equilibration generally enforces superequilibrium across much of parameter space, but heavy gauginos or bottlenecks from heavy superpartners can disrupt it, altering the predicted baryon asymmetry Y_B, with Y_B increasing or decreasing depending on tanβ and spectrum. The work thus provides a comprehensive, parameter-sensitive framework for predicting Y_B in supersymmetric EWB and highlights the importance of not assuming immediate, universal superequilibrium in beyond-the-Standard-Model scenarios.

Abstract

We present a complete treatment of the diffusion processes for supersymmetric electroweak baryogenesis that characterizes transport dynamics ahead of the phase transition bubble wall within the symmetric phase. In particular, we generalize existing approaches to distinguish between chemical potentials of particles and their superpartners. This allows us to test the assumption of superequilibrium (equal chemical potentials for particles and sparticles) that has usually been made in earlier studies. We show that in the Minimal Supersymmetric Standard Model, superequilibrium is generically maintained -- even in the absence of fast supergauge interactions -- due to the presence of Yukawa interactions. We provide both analytic arguments as well as illustrative numerical examples. We also extend the latter to regions where analytical approximations are not available since down-type Yukawa couplings or supergauge interactions only incompletely equilibrate. We further comment on cases of broken superequilibrium wherein a heavy superpartner decouples from the electroweak plasma, causing a kinematic bottleneck in the chain of equilibrating reactions. Such situations may be relevant for baryogenesis within extensions of the MSSM. We also provide a compendium of inputs required to characterize the symmetric phase transport dynamics.

Figures (9)

• Figure 1: Examples of absorption/decay (a) and scattering (b) processes which lead to superequilibrium.
• Figure 2: We plot $\Gamma_{\widetilde{V}}^{(q, \widetilde{q})}$ (gluino-only) as a function of $m_{\widetilde{q}_L}$. The solid and dotted lines denote, respectively, the particle and hole ($\times 10$) contributions to this rate. The dashed line indicates $\Gamma_{\widetilde{V}}^{(q, \widetilde{q})}$ calculated using free thermal Green's functions with a thermal mass, corresponding to the last term in Eq. (\ref{['eq:GammaVtilde']}c).
• Figure 3: Charge densities over $z$. Numerical results are represented by thick lines and analytical results by thin lines. Left panel: $q_3$ (pink, dot-dashed), $\ell_3$ (green, dotted), $n_{\rm left}$ (red, solid). Right panel: $H=H_1+H_2+\widetilde{H}$ (blue, solid), $q_1+q_2$ (orange, dot-dashed).
• Figure 4: Chemical potentials over $z$ illustrating supergauge-equilibrium. Key: $\mu_{H_1}$ (pink, dotted), $\mu_{H_2}$ (green, dashed), $\mu_{\widetilde{H}}$ (red, solid), $\mu_{q,\ell,t,b,\tau}$ (red, solid), $\mu_{\widetilde{q},\widetilde{\ell},\widetilde{t},\widetilde{b},\widetilde{\tau}}$ (pink, dotted).
• Figure 5: Chemical potentials over $z$, illustrating Yukawa-equilibrium. The key is $\mu_t-\mu_q$, $\mu_q-\mu_b$, $\mu_\ell-\mu_\tau$ (red, solid), $\mu_{H_1}$, $\mu_{H_2}$ (green, dashed).