I am considering a theory with two fields, say $\phi$ and $\psi$. The Lagrangian contains quadratic terms, i.e., propagators for both fields and a quartic interaction term for one of the fields. However, I have also the terms $\psi^*\phi + \phi^*\psi$. I have never encountered such terms before and I don't really know how to handle them in perturbation theory. If you would perform perturbation theory in these terms, I guess up to second order they are just corrections to the propagators for both fields, is that right?
I was wondering if somebody knows a reference in which such a theory is treated.