Nonperturbative Analysis of the Electroweak Phase Transition in the Two Higgs Doublet Model

We perform a nonperturbative study of the electroweak phase transition (EWPT) in the two Higgs doublet model (2HDM) by deriving a dimensionally reduced high-temperature effective theory for the model, and matching to known results for the phase diagram of the effective theory. We find regions of the parameter space where the theory exhibits a first-order phase transition. In particular, our findings are consistent with previous perturbative results suggesting that the primary signature of a first-order EWPT in the 2HDM is $m_{A_0}>m_{H_0}+m_Z$.

Figure 1

Heat maps with fixed $\tan (\beta )$, showing regions of first-order EWPT ($0<x<0.11$ and $y\simeq 0$) in the alignment limit. The dotted lines correspond to $m_{A_0}=m_{H_0}$ and $m_{A_0}=m_{H_0}\pm m_Z$.

Figure 2

Slices with different values of $\mu$, $\mu =50\mathrm{GeV}$ (top) and 75 GeV (bottom), and fixed $\tan (\beta )=2.0$. The validity of DR is estimated by showing the relative effect of the neglected dimension-six operators ${\mathcal{O}}_{A,1}^{(6)}$, ${\mathcal{O}}_{A,2}^{(6)}$. The white regions are either unphysical or there is no transition. At large $m_{H_0}$ the effects of dimension-six operators render the first DR step unreliable.

Figure 3

Two-loop effective potential in the final effective theory with the dominant six-dimensional operator ${\mathcal{O}}_B^{(6)}$ of the last DR step included, evaluated at the critical temperature. At small $x$, integrating out the second doublet causes significant error, as is seen from the shift in the potential minimum.