How to deduce the Feynman rules?

[Mr rabbit]

1. The declaration of the problem, all variables and data given / known

Calculate the decay amplitude of $\pi ^ 0$ in an electron-positron pair $\pi^0 \rightarrow e^+ e^-$, assuming that the interaction is of the form

$\mathcal {L}_{int} = g \: \partial_{\mu} \phi \: \overline{\psi} \: \gamma ^ {\mu} \: \gamma^5 \: \psi$

where g is a coupling constant, $\phi$ is the scalar field corresponding to $\pi^0$ and $\psi$ is the electron field.

Homework Equations

3. The attempt of a solution

I don't know how to deduce in general the Feynman rules for a given Lagrangian. We made some examples with some theories ($\phi^4$, scalar Yukawa, QED scalar, QED) but for example the term $\partial_{\mu} \phi$ confuses me

 

[vanhees71]

How does the interaction term look in energy-momentum space, i.e., for fields $\propto \exp(-\mathrm{i} x \cdot p)$?

 

[MathematicalPhysicist]

I think this appears in Drell and Bjorken the Fields textbook.