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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?

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

the image below

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  • $\begingroup$ Since the mesons are not identical, shouldn't there also be a u-channel interaction? $\endgroup$ – user2970116 May 30 '14 at 13:43
  • $\begingroup$ You mentioned only a fermion and a scalar, therefore the mesons should be identical. Anyhow, you do need to take the u-channel into account, but this is just crossing the outgoing lines, i.e. a change in kinematics. $\endgroup$ – Neuneck May 30 '14 at 13:47

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