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Why should a graviton (if it exists) decay into 2 Z bosons?

My understanding is that the graviton is supposed to be a massless spin-2 boson and that it is the conservation laws for energy and spin and the rest of quantum numbers that allow a decay.

Now I see that the above prediction makes sense, since the z boson is spin-1 and it is its own antiparticle, thus, all of its flavour quantum numbers and charges are zero. But what I find a bit more problematic or involved is that the Z boson is massive (almost 80 times as massive as the proton). For example in the case of the observation of ttH production, they say that the Higgs can not decay into top quarks because they're too heavy... Can someone shed some light here?

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    $\begingroup$ Since gravitons (if they exist) would be the gravitational equivalent of photons , they should come with any energy. Such energetic ones would only exist near black holes. $\endgroup$ – Lewis Miller Jun 30 '18 at 17:20
  • $\begingroup$ @LewisMiller Kaluza–Klein black holes! Right, thanks. $\endgroup$ – user1892538 Jun 30 '18 at 17:59
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    $\begingroup$ A massless graviton isn't expected to decay, because normally massless particles aren't expected to decay. A particle's half-life is normally its half-life in its rest frame, but a massless particle doesn't have a rest frame. If a massless particle does decay, special relativity predicts that it has to have a lifetime (in any frame) that is proportional to its energy, and it has to decay into massless particles. The symmetrymagazine article is misleading, because it's apparently talking about hypothetical massive gravitons, but it doesn't say so. More info: arxiv.org/abs/hep-th/9508018 $\endgroup$ – Ben Crowell Jul 19 '18 at 12:40
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This article explains the Kaluza Klein gravitational model, where there are both zero mass and massive gravitons.

For a theory of everything which would follow on the lines of the current standard model of particle physics adding gravitation ,the graviton will be the gauge boson of the gravitational interactions and will be of zero mass. On these lines the gravitational waves observed by LIGO will be emergent from a superposition of a zillion zero mass gravitons.

The graviton discussed in the link you give is one of the $n>0$ modes of the Kaluza Klein gravitons. In page 11 of above link,

From the equation of motion we can say that only the zero modes $(n=0)$ will be massless and observable at our present energy and all the excited states, called as Kaluza-Klein states,will have masses .

KK theory has only one extra dimension. If the future theory of everything is a string theory, there are even more extra dimensions , and the KK massive excitations are expected to be there and detectable given a lot of energy. The KK graviton for decaying to these particles should have at least the mass of the particles it decays into, and a lot more, in order to be able to "bind temporarily" heavy mesons like Z, and to be detectable in the LHC experiments.

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The question's link to a Fermilab research suggests to look for more detailed articles from the CMS Collaboration.

Specifically the results here are relevant of a search for a KK graviton decaying into ZZ.

But what I find a bit more problematic or involved is that the Z boson is massive

Indeed they refer to the existence of Kaluza–Klein (KK) excitations of a spin-2 boson, the graviton, and their search covers a graviton mass range between 400 and 1200 GeV (consider that KK gravitons with masses in the range 0.5-3 TeV are compatible with current collider constraints).

Update

Given the currently observed deviation from the SM, what would be exciting to see is if the spin correlation of top quarks can be attributed to some extradimensions of Kaluza Klein gravitons (as part of Randall-Sundrum model, etc...).

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