Mr rabbit
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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.
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
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 solutionI 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