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I am bit confused with a statement I read. It talks about $H\to 4\ell$ decay width (higgs to 4 lepton). Now, higgs can decay through different modes. But, as far as I know it doesn't decay directly to 4 leptons (atleast not at leading order).But anyways, it can also decay (generally) to Z Z* which then decay to 4 leptons. So, my question is what does h->4l decay width means? I should add the decay width of the intermediate decay process of Z to dileptons to the decay width to Higgs to Z Z boson to get h->4l decay width?

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    $\begingroup$ Please see that answer of mine: physics.stackexchange.com/a/338251/154997 $\endgroup$ – user154997 Jun 12 '17 at 17:21
  • $\begingroup$ Yes, but is doesn't answer my question. My question is that should I add the decay width of higgs to z boson and that of z boson to dileptons to get decay width of higgs to 4 leptons? $\endgroup$ – kbg Jun 12 '17 at 17:25
  • $\begingroup$ ah, yes, sorry, I forgot how much I had written!!! $\endgroup$ – user154997 Jun 12 '17 at 17:28
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I general, one needs to compute the matrix elements of the whole diagram: the first one I have drawn in that answer to another question, then sum it with the matrix element for the second one, and any other relevant ones. Indeed $Z$ bosons are typically off-shell when the invariant mass of the final state is above twice the mass of $Z$. So, no, you can't just add decay widths.

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  • $\begingroup$ In the diagram you have drawn, in NLO, if I consider that mass of top quark as infinite, then can I consider the diagram thus having effective coupling as a leading order diagram? Also, what constraints do we actually put when I make a loop coupling effective? $\endgroup$ – kbg Jun 12 '17 at 17:43
  • $\begingroup$ What do you mean by constraints? I actually don't know how good an approximation it would be to treat the top triangle as an effective vertex. I am not an active particle physicists anymore but I can browse the literature. Give it a couple of days though! $\endgroup$ – user154997 Jun 12 '17 at 17:56

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