# Scalar QED, are there any scalar-fermion vertices in this theory?

Consider QED with an additional charged (complex) scalar field, $\phi$:$$\require{cancel} \mathcal{L} = -{1\over4} F^{\mu\nu} F_{\mu\nu} + (D^\mu \phi)^*(D_\mu \phi) - \mu^2 \phi^* \phi - \overline{\psi}(i\cancel{D} - m) \psi.$$I know what the Feynman rules are for this theory and can derive them. My question is, though, are there any scalar-fermion vertices in this theory?

• In your Lagrangian there is no term that couples $\psi$ and $\phi$ directly, so no, there are no scalar-fermion vertex in the Feynman rule. You can effectively generate coupling between $\psi$ and $\phi$ by an intermediate photon, but that is not a fundamental Feynman rule, and the coupling is different from something like $\bar{\psi}\psi\phi$. – Meng Cheng Dec 1 '15 at 3:10