I want to understand drawing Feynman Diagrams better, therefore I wanted to draw some for the Lagrangian with a Yukawa interaction term: $$L = \bar{\psi}(i \partial\!\!\!/ - m)\psi - g \bar{\psi}\phi \psi + \frac{1}{2}(\partial^\mu \phi) \partial_\mu \phi) - \frac{M^2}{2}\phi^2 - \frac{\lambda}{4} \phi^4. \tag{1}$$ where $\phi$ is a scalar field and $\psi$ is a Dirac field.
For order $g^3 \lambda$, in my intuition, this would yield diagrams like:
As the $\phi^4$ contribution leis in the scalar photon for scalar QED. This confuses me a bit, however, as I thought there was no photon-photon vertex, the only vertex, that could be is between two fermions and a photon.
This question was resolved by the fact that it is indeed not scalar QED. I am not sure how I drew to the conclusion that this is a scalar fermion vertex; it just isn't. The last question, however, remains.
I know that the Dirac Propagators only go between $\bar{\psi}$ and $\psi$ what I do with the phi field. Like when I have: $$\bar{\psi}(x) \ \phi(x) \ \psi(x) \ \bar{\psi}/y) \ \phi(y) \ \psi(y)$$ I can make the propagator $D(x-x)$ between the $\bar{\psi}(x)$ and $\psi(x)$, which would give me a fermion line in the Feynman diagram, but when I now to the propagator from $\phi(x)$ to $\phi(y)$ for example, where does it start and end? Is it then just a disconnected diagram? Or how do I distinguish the propagator between $\bar{\psi}$ and $\psi$ or $\psi$ and $\phi$?
Apart from that I am also confused when I try to make the propagators from the time ordered product with Wicks theorem, when I have the propagator between a $\bar{\psi}(x) \phi(y)$ is this a fermion or photon propagator, thus would this be a straight line or a curly one in the manner of the diagram? This part is not quite relevant anymore since it is not a photon field here.
