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Cernette: a bound state of two \(Z'\)-bosons?

TV: John Oliver gave a totally sensible 20-minute tirade explaining why "scientific study says" stories in the media are mostly bullšit.
I am giving a popular talk on LIGO in 90 minutes and Tristan du Pree has offered me a distraction via Twitter. How do you get distracted if you think about LIGO too much? Yes, by hearing about the LHC:
Did you find already a good model for a possible \(375/750/1500\) tower of \(Z\gamma/\gamma \gamma\)?
Well, I didn't, I wrote him: it seemed increasingly clear to me that the invariant masses in the \(Z\gamma\) and \(\gamma\gamma\) decays should better be the same. So the numerological explanation of the coincidence doesn't work.

But then I decided that I haven't carefully enough investigated a loophole that could explain why the \(\gamma\gamma\) signal isn't observed near \(375\GeV\): the Landau-Yang theorem. A massive spin-one boson cannot decay to two identical massless spin-one bosons – or, if you wish, a \(Z\)-boson or \(Z'\)-boson cannot decay to two photons.

The reason for or the proof of the theorem? Well, there's no trilinear function of the three polarization vectors \(\vec \epsilon_{1,2,3}\) that may also depend on the massless particle's momentum \(\vec k\) but that is also symmetric under the exchange of the two final photons.

That seems to be the only possible explanation of the absence of the \(\gamma\gamma\) signal at \(375\GeV\) given the assumption that the excesses of \(Z\gamma\) at \(375\GeV\) are real new physics. So if that's the case, there has to be a new \(Z'\)-boson at \(375\GeV\). Or maybe even a composite particle, such as a toponium, could be OK?

And if the coincidence \(750/2=375\) is more than just a coincidence, then the \(750\GeV\) cernette should better be a bound state of the two \(375\GeV\) \(Z'\)-bosons. Probably a tightly bound state, indeed, but the large width observed especially by ATLAS could potentially be explained by this composite character of the object.

I realize that the interactions felt by the new \(Z'\)-boson would have to be immensely strong and it probably doesn't work but I am running out of time so I expect some commenters to tell me whether it could work.

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