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If I have a scalar field $\alpha$ and a Dirac particle $\beta$ and its anti particle $\overline{\beta}$, such that the three couple to give a vertex factor of $-ik$ when evaluating the Feynman diagram (where $k$ is a dimensionless coupling constant), how do I evaluate the first order diagram of $\alpha \longrightarrow \beta + \overline{\beta}$?

JamalS
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cplusplusguru
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1 Answers1

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Basically this is a tree-level diagram of an $\alpha$ particle decaying into a pair of $\beta \overline{\beta}$ pair.

You need to draw the Feynman diagram. And now, single "internal" lines are propagators, and external lines are currents.

But you need to direct the external lines so as to have a current.

enter image description here

For reference look at this diagram, you need to direct the muon lines like in the picture.

And then you need to construct the current. Every current is bit different depending on the pertinent Lagrangian. for instance the electron current in QED is given by: $$ J =\overline{u}(p')\gamma^{\mu}u(p) $$ Where $\overline{u}$ is the outgoing "particle", the non overlined $u$ is the ingoing current and there's a $\gamma$ matrix in the middle...

You can look up some basic Feynman rules online to help you.

BeastRaban
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