So, I am giving the following interaction term in a real-complex scalar Yukawa theory, $$\mathcal{L}_{int} = -g\phi^\dagger\phi\chi^2$$ with $\chi$ the real scalar and $\phi$ the complex scalar. I have seen everywhere the usual interaction term for the real scalar part on the interaction term is not squared, so if I am computing the interaction, $\phi\chi\rightarrow\phi\chi$ how does it change and what new does the potential in this form give? $\textbf{Or where should I start in finding the proper vertex interaction for this potential?}$
The name of the theory (as I have read online) is called "Scalar Yukawa Theory" with the following Lagrangian, \begin{equation} \mathcal{L} = \partial_\nu\phi^\dagger\partial^\nu\phi - m^2\phi^\dagger\phi + \frac{1}{2}(\partial_\nu\chi\partial^\nu\chi - \mu^2\chi) - \lambda\phi^\dagger\phi\chi^2. \end{equation}
We (the class I am in) has not even been told what does this theory describe and why modify the potential is such a way.
Any hints are helpful, thanks.