# Feynman Diagram setup for 4-fermion interaction loop

 P: 328 I'm not sure if I understood your question correctly. However, the Fermi Lagrangian just tells you that, at low energy, the coupling between two fermionic currents is $G_F/\sqrt{2}$; that's what should appear at every four-fermion vertex. The presence of the Dirac algebra, i.e. of spinors, just tells you that you have to use spinors for the external legs of you diagrams and fermionic propagators for the internal ones. In your case you need to choose a direction for the loop momenta and then write down the integral correctly (don't forget the additional - sign for every fermionic loop). If, for example, $p$ is the momentum of the incoming/outgoing fermion, you can choose the upper internal line to go from left to right with a momentum $q$, the middle internal line to go from left to right with momentum $p-q+k$ and the lower one to go from right to left with momentum $k$. In this case I would say that you diagram is given by: $$\left(\frac{G_F}{\sqrt{2}}\right)^2\bar u_L(p)\int \frac{d^4q}{(2\pi)^4}\frac{d^4k}{(2\pi)^4}\frac{1}{q^\mu\gamma_\mu-m}\frac{1}{(p-q+k)_\mu \gamma^\mu-m}\frac{1}{k_\mu \gamma^\mu-m} u_L(p),$$ where by $u_L(p)$ I mean the left-handed spinor.