# What is the leading order Feynman diagram for nucleon-anti-nucleon annihilation into two mesons ($\psi^{\dagger} \psi \to \phi\phi$)?

I am working with a standard basic scalar Yukawa theory. I.e. the only interaction term is $-g\psi^\dagger\psi\phi$, where the $\phi$ field quanta are the mesons, the $\psi$ field quanta are the nucleons and the $\psi^\dagger$ field quanta are the anti-nucleons.

I have tried fiddling around with various combinations and have looked at some relevant papers, but I have not found a solution which does not invoke other interaction terms. Is this process possible?

• Do you know what's the tree level diagram for $e^+ e^- \rightarrow \gamma \gamma$ (electron-positron to two photons in standard QED)? – fqq May 30 '14 at 12:07

It is basically the image below, replacing $e^-, e^+$ with $\psi, \psi^\dagger$ and $\gamma$ with $\phi$. At each vertex, this just picks up a factor of $g$ instead of the $-ie \gamma^\mu$ that you have in QED.