## Monday, May 09, 2016 ... //

### 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.