In Standard Model, are both the Higgs doublet and its complex conjugate present in the universe, or not the complex conjugate one?

Question

In Standard Model, the Higgs doublet is \begin{equation} \Phi=\left(\begin{array}{c}\phi^+\\ \phi^0\end{array}\right) =\frac{1}{\sqrt{2}}\left(\begin{array}{c} \phi_1+i\phi_2\\ \phi_3+i\phi_4 \end{array}\right) \end{equation}

The complex conjugate of Higgs double is

\begin{equation} \Phi^*=\left(\begin{array}{c}\phi^-\\ \phi^{0*}\end{array}\right) =\frac{1}{\sqrt{2}}\left(\begin{array}{c} \phi_1-i\phi_2\\ \phi_3-i\phi_4 \end{array}\right) \end{equation}

Question : restricting to the topic of Higgs physics, what is present in the universe :

1. The Higgs doublet only ?
2. The complex conjugate of the Higgs doublet ?
3. Both the Higgs doublet and its complex conjugate ?

The picture in wikipedia there : https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#/media/File:Standard_Model_Of_Particle_Physics--Most_Complete_Diagram.png

would make believe that only the Higgs doublet is present in the universe. But is it true ?

Answer 1

The two field doublets you are writing down involve the same four $\phi_i$s, and they constitute different arrangements of them, so they make no difference in the amplitudes involved and their physics implications. (The physical Higgs particle is linked to $\phi_3-v$.)

They are all "present" in our universe, as would any other rewriting of them, such as $\tilde \Phi$, etc... As long as the interactions and couplings of each are specified clearly, and each is fit into the SM we know, there should be no issue. Recall both $\Phi$ and $\Phi^*$ are present in the real covariant kinetic term in the SM Lagrangian written in the practical notation.