Electroweak Baryogenesis: Concrete in a SUSY Model with a Gauge Singlet

TL;DR

Huber and Schmidt present a concrete SUSY framework with a gauge singlet that yields a strong first-order EWPT and CP-violating bubble-wall dynamics to drive electroweak baryogenesis. They combine a detailed NMSSM-like model (with μ-term and singlet interactions) with a robust finite-temperature potential, bubble-wall shape analysis, and a semi-classical WKB/diffusion formalism to compute CP-violating sources and the resulting baryon asymmetry. Their results show that, for reasonable parameter choices, both explicit CP violation (with μ ≈ M2) and transitional CP violation in the singlet sector can generate the observed BAU without conflicting EDM constraints, especially when sfermion spectra are non-degenerate. The work provides a concrete, testable mechanism linking Higgs-singlet physics, SUSY-breaking patterns, and baryogenesis, with clear dependencies on wall thickness, velocity, and the squark spectrum that could guide future collider and EDM studies. It demonstrates that the NMSSM can realize successful electroweak baryogenesis in a regime distinct from the MSSM, leveraging the singlet sector to enhance the EWPT and CP-violating transport effects.

Abstract

SUSY models with a gauge singlet easily allow for a strong first order electroweak phase transition (EWPT) if the vevs of the singlet and Higgs fields are of comparable size. We discuss the profile of the stationary expanding bubble wall and CP-violation in the effective potential, in particular transitional CP-violation inside the bubble wall during the EWPT. The dispersion relations for charginos contain CP-violating terms in the WKB approximation. These enter as source terms in the Boltzmann equations for the (particle--antiparticle) chemical potentials and fuel the creation of a baryon asymmetry through the weak sphaleron in the hot phase. This is worked out for concrete parameters.

Figures (11)

• Figure 1: Sketch of our procedure to fix the weak scale parameters using RGEs and saddle point conditions.
• Figure 2: Scan of the $M_0$-$A_0$ plane for two different sets of $(x,\tan\beta,k)$. The colored regions represent the phenomenologically viable range of the parameters before cuts from the Higgs boson search are applied. The dashed lines are curves of constant mass of the lightest CP-even Higgs boson. In the blue (green) areas, the lightest Higgs boson is predominantly a singlet (Higgs) state.
• Figure 3: Scan of the $M_0$-$A_0$ plane for the two different sets of $(x,\tan\beta,k)$ which have already been considered in fig. \ref{['f_phT0']}. In the red (yellow) areas the PT is strongly (weakly) first order, i.e. $v_c/T_c>1$ ($v_c/T_c<1$). The dotted lines are curves of constant mass of the lightest CP-even Higgs boson. In the regions below (above) the dashed lines the lightest Higgs boson is predominantly a Higgs (singlet) state.
• Figure 4: (a): Bubble wall profile at the critical temperature for the parameter set of fig. \ref{['f_phT0']}a with $M_0=300$ GeV and $A_0=0$. (b): The corresponding trajectory in the $H$-$S$ plane (solid line) and the straight connection between the symmetric and the broken minimum (dashed line). (All units in GeV.)
• Figure 5: (a): Variation of $\tan\beta$ in the bubble wall at the critical temperature for the parameter set of fig. \ref{['f_dwall']}. (b): Shape of the critical bubble for the same parameter set at $T=108.5$ GeV. (Units in GeV.)