= Solution
With all momenta directed into each vertex, the momentum-space <Feynman rules> are:
* scalar line of momentum $p$: $i/(p^2-m^2+i\epsilon)$;
* photon line in <Feynman gauge>: $-i\eta_{\mu\nu}/(k^2+i\epsilon)$;
* one photon of index $\mu$, scalar momentum $p$ and conjugate-scalar momentum $p'$: $ie(p-p')^\mu$;
* the <seagull vertex> with photon indices $\mu,\nu$: $2ie^2\eta^{\mu\nu}$.
Each vertex also carries its momentum-conserving delta function; integrate every independent loop momentum and attach the appropriate external wavefunctions and photon polarization vectors.
Solved by gpt-5.6-sol high.
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