Two Higgs doublet dynamics at the electroweak phase transition: a non-perturbative study

TL;DR

The paper investigates electroweak baryogenesis in the MSSM by analyzing a three-dimensional effective field theory with two Higgs doublets and a light stop via non-perturbative lattice simulations. It systematically uncovers that spontaneous CP violation is not realized in MSSM-relevant parameter regions, even after finite-temperature effects are included. For a physical parameter point with m_H around 105 GeV, the electroweak phase transition is found to be stronger than both one- and two-loop perturbation theory, supporting the viability of MSSM baryogenesis near m_H ≈ 115 GeV when a light stop is present; the study also characterizes the phase boundary and related observables. The results yield quantitative benchmarks for Tc, v/T, latent heat, and surface tension, and demonstrate that the transition remains robust close to the triple point, with CP-violating effects in the wall remaining small.

Abstract

Using a three-dimensional (3d) effective field theory and non-perturbative lattice simulations, we study the MSSM electroweak phase transition with two dynamical Higgs doublets. We first carry out a general analysis of spontaneous CP violation in 3d two Higgs doublet models, finding that this part of the parameter space is well separated from that corresponding to the physical MSSM. We then choose physical parameter values with explicit CP violation and a light right-handed stop, and determine the strength of the phase transition. We find a transition somewhat stronger than in 2-loop perturbation theory, leading to the conclusion that from the point of view of the non-equilibrium constraint, MSSM electroweak baryogenesis can be allowed even for a Higgs mass mH \approx 115 GeV. We also find that small values of the mass parameter mA (\lsim 120 GeV), which would relax the experimental constraint on mH, do not weaken the transition noticeably for a light enough stop. Finally we determine the properties of the phase boundary.

Figures (16)

• Figure 1: Projections of the region of spontaneous C violation ($|\cos\phi|<1$) onto various planes. Here $M_{12}^2 = m_{12}^2(T) + (1/2)(\lambda_6 v_1^2 + \lambda_7 v_2^2)$, $M= \sqrt{2} m_U(T)/h_t$, $\cos\alpha_6 = \lambda_6 / (2\sqrt{\lambda_1\lambda_5})$, $\cos\alpha_7 = \lambda_7 / (2\sqrt{\lambda_2\lambda_5})$, cf. Eqs. (\ref{['M122']}), (\ref{['GHMdef']}), (\ref{['lam6']}), (\ref{['lam7']}). Thin contours (equally spaced, arbitrary normalization) indicate roughly the thickness of the allowed region of the parameter space in the orthogonal directions.
• Figure 2: The 1-loop phase diagram for the transition from the C violating phase to the usual broken and symmetric phases as $y$ is varied, for fixed $\lambda_5=0.001, \lambda_6 = \lambda_7 = 0$ ($\alpha_6=\alpha_7=\pi/2$), $\cos\phi=0.5$, $M/T=0.5$ ($m_U(T)/T = 0.35$), $\hat{A}_t = \hat{\mu} = 0$. The transition from the C violating phase can lead either directly to the symmetric phase ("s.") or to the usual broken phase ("b."), and it can be either of 1st or 2nd order.
• Figure 3: Top: Mean field estimates for the $y$-dependence of different expectation values, corresponding to the physical volume obtained with $\beta_w=8$, $N_1N_2N_3=20^3$. For $I$ the absolute value of the volume average is taken. Bottom: Lattice results at $\beta_w=8$. For the first two sets the transition is strongly of the first order, and a small volume has been used; in spite of this, some $y$-values allow for separate measurements in two different metastable phases. For the middle set, the transition goes on the lattice directly to the C conserving symmetric phase, rather than to the C conserving broken phase seen in the perturbative plot.
• Figure 4: The tadpole graph leading to Eq. (\ref{['f_full']}). The effective local quartic vertex shown, the second line in Eq. (\ref{['action']}) with $\gamma_i$'s from Eq. (\ref{['gpar']}), is a good approximation as long as $m_U^2 \ll m_Q^2$.
• Figure 5: The perturbative 2-loop phase diagram for $m_Q=1$ TeV. The values of $v/T$ at the transition point are also shown. Lattice results are displayed at $\tilde{m}_U = 65$ GeV (square), and at the triple point (triangle). The lattice triple point errorbars include only statistical errors (see the text), and are thus an underestimate.