A suitable shortcut is offered by blogs. Your best bet is Resonaances, who continues to post on the matter and does a spectacular job in general. Here, instead, I have not posted anything on the matter for a while, and somebody suggested that I should. So heck, I will do my homework today. Let's start from the paper on top of the pile, which is brand new and is signed by a very respectable theorist, Steven Giddings, along with his colleague Hao Zhang at Santa Barbara.
The paper, titled "Kaluza-Klein graviton phenomenology for warped compactifications, and the 750 GeV diphoton excess", is reasonably readable -it means I found it not totally over my head. So I can report on it here. I find it useful as the idea that the 750 GeV diphoton bump is due to a graviton is one of the most credible in the large pool of hypotheses.
The idea of the underlying theory is that large extra dimensions exist, and that the gravity can propagate there. A signature of such a scenario would be the existence of so-called "Kaluza-Klein" excitations of the mediator of gravitational interactions, the graviton. The extra dimensions of space-time need to be "warped" if this model can be given enough freedom to explain some new physics signatures without being ruled out by existing observations. (For instance, in the absence of warping rather than a single resonance one would expect to see a continuum of such resonant states).
The phenomena that this new physics model gives rise to, at low energy (where "low" is in relation to the larger energy scales of the theory), can be rather simple, and be described by the presence of a resonance state - a graviton, if you will - and a characteristic parameter Λ dictating the coupling of the graviton to standard model particles.
If we take 750 GeV as the mass of the lightest excitation, the only other parameter is lambda. One can then try to fit the observed data to the model, to extract the resulting lambda. The relation between the rate of graviton signal and the parameter is a simple one: Giddings and Zhang find
σ (pp → G) = 7.74+1.43−1.10 pb × (10TeV / Λ)^2 .
Their fit of the ATLAS Run 2 data yields a nice interpretation of the observed diphoton mass spectrum, as shown below, and a value of lambda in the ballpark of 60 TeV can be extracted by a combined fit to both ATLAS and CMS results.
The article then considers what constraints are posed to the above scenario by other data produced by ATLAS and CMS. The graviton of course does not decay only to photon pairs: quite on the contrary, its most frequent decays are to jet pairs. However, the most stringent bounds come from the analysis of dilepton final states. There, the absence of a signal at 750 GeV brings in some tension to the above mentioned fit, but it does not rule it out. Giddings and Zhang explain that if the signal is real, the 2016 data should soon put in evidence a dilepton signal at the same mass.
So here you are - a testable prediction and a possible exciting scenario for 2016, when not only gravitational waves are discovered (by LIGO and VIRGO - as will be announced tomorrow), but where the LHC discovers the particle itself, and then proceeds to investigate a wide new world, full of new particles and of large extra dimensions! There is enough to stay wide awake, if you are a believer....
As for me, I remain a sceptic. By looking at the graph above I cannot help observing that all those 27 points have uncertainty bars passing through the fit. But the fit is supposed to pass only through 68% of them, on average... What I am trying to say is that we are overfitting our data. Our desire to "fully understand" our histograms is the main driver of false claims. But I do not wish to convince you, dear reader: dreaming is a beautiful occupation, and I detest playing the part of the alarm clock.