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The decoupling theorem of Appelquist-Carazzone says that if you want to decouple a particle, the low energy resulting theory need to be renormalizable. You can't do that for the top, because you break $SU(2)$ gauge symmetry, in fact, top is the bottom's partner in the doublet.

So when I use decoupling theory for $W$ and $Z$. Does the top remain in my theory, or I can substitute it with point-like vertex? If not, how do I handle a particle heavier than gauge boson $W$, in my effective theory?

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  • $\begingroup$ bit puzzled with this formulation "resulting theory need to be renormalizable" ... Is not the decoupled W, Z theory simply Fermi theory? $\endgroup$
    – arivero
    Sep 16, 2015 at 14:18
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    $\begingroup$ You need to take into account the QCD and QED interactions in your point-like theory, you can see Buras for that. But yes the simplest decoupled theory is the Fermi theory. For the phrase "resulting theory need to be renormalizable" you can see Iain Stewart and his lessons on EFT. Anyway this is an old question, now I know much more about EFT. $\endgroup$
    – Karozo
    Sep 16, 2015 at 22:55

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