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I am looking at the decays of Heavy sterile neutrinos in the their mass states to Z bosons.

Using the feynman rules, how would I go about calculating the decay amplitude. I have only ever seen cases where the Z boson is a propagator. Would my expression look something like this:

[itex]

M = \kappa\frac{g}{2\cos\theta_{W}}\overline{\nu_{1}}(2)\gamma^{\mu}P_{L}N_{m}(1)\epsilon_{\mu}^{*}(3)

[/itex]

where [itex]\kappa[/itex] is some constant. Essentially the Feynman diagram looks like a standard weak vertex between two neutrinos. The only difference is that one of them is Heavy (GeV-TeV) scale. However my question really is about whether I just take the standard vertex and include the [itex]\epsilon^{*\mu}[/itex] vector for the outgoing Z-boson.

The standard vertex factor reads

[itex]

-i\frac{g}{2\cos\theta_{W}}\kappa\gamma^{\mu}P_{L}

[/itex]

Is it enough for me to just add [itex]\epsilon^{\mu *}[/itex] for the outgoing Z boson?

Thank you to anyone who can help.

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# Heavy sterile neutrino decay into Z bosons. (Feynman Diagram)

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