breaking is of order $v^2/\tilde{m}^2$ in the present model, while the one in Ref. [@Hall:2013eko] requires an extra factor of order $\tilde{m}^2/\Lambda^2$ to keep $\mu^2$ and $\mu B$ to be of order $\tilde{m}^2$. While none of the above issues excludes the model in Ref. [@Hall:2013eko], their absence adds an aesthetic appeal to the model discussed here.

The electroweak symmetry is broken by the VEV of the light SM Higgs doublet $h$, whose mass-squared parameter (and thus VEV) is fine-tuned to be of order the weak scale due to environmental selection. Specifically, the mass-squared matrix for the two Higgs doublets at the scale $\tilde{m}$ is given by $${\cal M}_{\rm H}^2 = \begin{pmatrix}
    |\mu|^2 + m_{H_u}^2 & \mu B \\
    \mu B & |\mu|^2 + m_{H_d}^2
 \end{pmatrix},
\label{eq:MH2}$$ where $|\mu|^2$, $|\mu B|$, $|m_{H_u}^2|$, $|m_{H_d}^2|$ are of order $\tilde{m}^2$. These parameters are chosen such that one Higgs doublet remain below $\tilde{m}$, i.e. the determinant of the matrix ${\cal M}_{\rm H}^2$ to be extremely small compared with its natural size $\sim \tilde{m}^4$. The resulting SM Higgs doublet is given by the combination $h \approx \sin\beta\, h_u + \cos\beta\, h_d^\dagger$ with $$\tan^2\!\beta = \frac{|\mu|^2 + m_{H_d}^2}{|\mu|^2 + m_{H_u}^2}.
\label{eq:tan-beta}$$ Since the quartic coupling for the 