Electroweak Phase Transition in Two Higgs Doublet Models

TL;DR

The paper assesses whether extended Higgs sectors can yield a strong first-order electroweak phase transition suitable for baryogenesis. It advances the analysis by computing a one-loop finite-temperature effective potential with ring resummation, incorporating Goldstone boson contributions consistently, and employing an accurate V_eff approximation across mass regimes while using the measured top mass. In two-Higgs-doublet models, sizable regions of parameter space yield phi_c/T_c>1, suggesting viability for electroweak baryogenesis, whereas in the MSSM the extra Higgs bosons have limited impact on the transition. The work emphasizes perturbative uncertainties, underscores the value of nonperturbative lattice cross-checks, and clarifies the conditions under which perturbation theory remains trustworthy near the transition.

Abstract

We reexamine the strength of the first order phase transition in the electroweak theory supplemented by an extra Higgs doublet. The finite-temperature effective potential, $V_{eff}$, is computed to one-loop order, including the summation of ring diagrams, to study the ratio $φ_c/T_c$ of the Higgs field VEV to the critical temperature. We make a number of improvements over previous treatments, including a consistent treatment of Goldstone bosons in $V_{eff}$, an accurate analytic approximation to $V_{eff}$ valid for any mass-to-temperature ratios, and use of the experimentally measured top quark mass. For two-Higgs doublet models, we identify a significant region of parameter space where $φ_c/T_c$ is large enough for electroweak baryogenesis, and we argue that this identification should persist even at higher orders in perturbation theory. In the case of the minimal supersymmetric standard model, our results indicate that the extra Higgs bosons have little effect on the strength of the phase transition.

Figures (5)

• Figure 1: self-energy diagram responsible for IR-divergent contribution of Goldstone bosons to the Higgs boson mass at $p^2=0$, in Landau gauge.
• Figure 2: Evolution of the effective potential with temperature, showing the pathological case of two nontrivial minima, indicative of negative squared boson masses. The parameter values are $m_{h_0}=125$ GeV, ${\mu_3^2} = (30$ GeV)$^2$ and all other Higgs boson masses 187 GeV.
• Figure 3: Contours of constant $\phi_c/T_c$ (first three columns) and the perturbative expansion parameter $\epsilon$ (defined in eq. (\ref{['epseq']})) for three values of ${\mu_3^2}$, in the plane of $m_{A^0}=m_{H^0}=m_{H^\pm}$ versus $m_{h^0}$. The first three columns use different approximations for the critical temperature or the effective potential, described in the text. Units are 100 GeV for masses, (100 GeV)$^2$ for ${\mu_3^2}$. Increasing values are represented by darker shades, with white being $<1$ and increasing in steps of $1$. The regions labeled by "m." in the last column are where the false vacuum is metastable, and those labeled "s.o." are where the phase transition is second order, as illustrated in figure 4. In neither case is there a first order transition. The values of $\epsilon$ are computed using the boson masses corresponding to the second column.
• Figure 4: Examples of the evolution of the potential with temperature which illustrate the absence of a first order phase transition. In the first one the false vacuum is metastable, and in the second the phase transition is second order. The parameter values are $m_{h^0}=60$ GeV, other masses $= 325$ GeV, ${\mu_3^2} = 0$ for the first one, and $m_{h^0}=300$ GeV, other masses $= 250$ GeV, ${\mu_3^2} = 0$ for the second.
• Figure 5: Contours of $\phi_c/T_c$ in the plane of $m_{A^0}$ versus $m_{h^0}$, using the same three respective methods as in figure 3, setting the other Higgs boson masses to their tree-level values in the minimal supersymmetric standard model. The horizontal strip at the bottom, labeled "s," shows the corresponding values in the standard model.