While it is undeniable at this point that the new "instant literature" topic is quite likely to be a passing fashion, as the 2016 data is due soon and it will probably put a full stop to the speculations of new physics around the 750 GeV bump, one can also entertain the alternate hypothesis and decide which, among the 200 or so new physics models (ok, many of the papers discuss basically the same scenarios, but still), is the one worth putting one's money on. If you are such a betting person, I would ask you to consider the paper recently published on the arxiv, "The NMSSM Lives - With the 750 GeV Diphoton Excess", by F. Domingo, S. Heinemeyer, J.S. Kim, and K. Rolbiecki.
The NMSSM is a variant among many of the "minimal supersymmetric extension of the Standard Model", MSSM. The MSSM is a very useful benchmark as it enshrines all the basic properties of Supersymmetric theories in a "minimal" way that William of Ockham would have approved (if forced to accept Supersymmetry as a possibility). The NMSSM variant is "next-to-minimal" in the sense that it adds a few bits to the MSSM by trying to address the so-called "μ problem" of that theory. It is a variant on which many phenomenologists have turned their attention in the last few years, and it appears to be not entirely disfavoured by LHC searches.
Within the elasticity of the NMSSM, one can try to accommodate the diphoton bump by assuming that it is due to the decay of not one, but two new particles, call them Σ. These Σ particles would be very light (I mean *very*) and this would make it "normal" for them to preferentially decay to pairs of photons, much like the neutral pion does. If you produce one such particle and impart it with a large momentum, the two produced photons it decays into cannot be distinguished experimentally, and one observes a single photon-like deposit in the calorimeter. So the two photons observed by ATLAS and CMS might be actually four photons, two on each side travelling very close together. In this case you can imagine that a particle H of mass in the 750 GeV ballpark decayed into these two very light bosons, and each produced two collinear photons.
The idea appears weird at first sight, and yet the authors bring us along through a set of calculations aimed at showing that the phenomenology of the hypothesized new objects is not excluded by current measurements. In particular, I found fascinating the study of the neutral pion characteristics, for instance, with which the new sigma boson supposedly mixes. Also interesting is the study constraining the lifetime of the sigma particles such that they would decay within the detectors, preserving the observed features of the diphoton signal.
I think that summarizing further the ideas in the paper for the sake of distributing the information to laypersons is not a very meaningful occupation given the quite specialistic nature of the topic; and neither is it for physicists who can read the paper by themselves - so I will just advise the latter to have a look. As for the former, well - let me summarize as well as I can what the prediction is.
The authors suppose that there are heavy, neutral Higgs boson states at 750 GeV. They mainly decay to two neutral particles of 135 MeV mass - the mass of the neutral pion. This enables the mixing of neutral pion and the new state, in a way that does not violate the constraints posed by present knowledge of pizero phenomenology. Nor is the map of decays of the Higgs boson at 125 GeV modified in a way that contrasts with the present knowledge of its phenomenology.
The scenario "lives" in the NMSSM and specifically for some preferred values of the main parameters controlling the phenomenology. The authors consider several benchmark points of the allowed parameter space which can give rise to the mentioned phenomenology, and also discuss how they can be studied in the upcoming Run 2 of the LHC.
I do not know about you, but I find this quite cool, and while I remain sceptical about these new physics models -mainly because I believe the 750 GeV bumps are a fluctuation- I do hope that some of these 200 new models ends up being proven true! We are in a very nice situation then, as we are going to test these models quite soon. Already showing that in 10 inverse femtobarns of collisions there is no bump in diphotons at 750 GeV would be enough to wipe 200 papers off the table! So let us sit and wait - I doubt there is anything more meaningful to do if you don't have your hands on LHC data!