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All ideas discussed above appeared in recent articles by various authors addressing the 750 GeV excess. If I were to include all references the post would be just one giant hyperlink, so you need to browse the literature yourself to find the original references.

A new paper last week straightens out the story of the diphoton background in ATLAS. Some confusion was created because theorists misinterpreted the procedures described in the ATLAS conference note , which could lead to a different estimate of the significance of the 750 GeV excess. However, once the correct phenomenological and statistical approach is adopted, the significance quoted by ATLAS can be reproduced, up to small differences due to incomplete information available in public documents. Anyway, now that this is all behind, we can safely continue being excited at least until summer. Today I want to discuss different interpretations of the diphoton bump observed by ATLAS. I will take a purely phenomenological point of view, leaving for the next time the question of a bigger picture that the resonance may fit into. Phenomenologically, the most straightforward interpretation is the so-called: a 750 GeV singlet scalar particle produced in gluon fusion and decaying to photons via loops of new vector-like quarks. This simple construction perfectly explains all publicly available data, and can be easily embedded in more sophisticated models. Nevertheless, many more possibilities were pointed out in the 750 papers so far, and here I review a few that I find most interesting.For a particle decaying to two photons, there is not that many possibilities: the resonance has to be a boson and, according to young Landau's theorem, it cannot have spin 1. This leaves at the table spin 0, 2, or higher. Spin-2 is an interesting hypothesis, as this kind of excitations is predicted in popular models like the Randall-Sundrum one. Higher-than-two spins are disfavored theoretically. When more data is collected, the spin of the 750 GeV resonance can be tested by looking at the angular distribution of the photons. The rumor is that the data so far somewhat favor spin-2 over spin-0, although the statistics is certainly insufficient for any serious conclusions. Concerning the parity, it is practically impossible to determine it by studying the diphoton final state, and both the scalar and the pseudoscalar option are equally viable at present. Discrimination may be possible in the future, but only if multi-body decay modes of the resonance are discovered. If the true final state is more complicated than two photons (see below), then the 750 GeV resonance may have any spin, including spin-1 and spin-1/2.The total width is an inverse of particle's lifetime (in our funny units). From the experimental point of view, the width larger than detector's energy resolution will show up as a smearing of the resonance due to the uncertainty principle. Currently, the ATLAS run-2 data prefer the width 10 times larger than the experimental resolution (which is about 5 GeV in this energy ballpark), although the preference is not very strong in the statistical sense. On the other hand, from the theoretical point of view, it is much easier to construct models where the 750 GeV resonance is a narrow particle. Therefore, confirmation of the large width would have profound consequences, as it would significantly narrow down the scope of viable models. The most exciting interpretation would then be that the resonance is a portal to a dark sector containing new light particles very weakly coupled to ordinary matter.One resonance is enough, but a family of resonances tightly packed around 750 GeV may also explain the data. As a bonus, this could explain the seemingly large width without opening new dangerous decay channels. It is quite natural for particles to come in multiplets with similar masses: our pion is an example where the small mass splitting π± and π0 arises due to electromagnetic quantum corrections. For Higgs-like multiplets the small splitting may naturally arise after electroweak symmetry breaking, and the familiar 2-Higgs doublet model offers a simple realization. If the mass splitting of the multiplet is larger than the experimental resolution, this possibility can tested by precisely measuring the profile of the resonance and searching for a departure from the Breit-Wigner shape. On the other side of the spectrum is the idea is that there is no resonance at all at 750 GeV, but rather at another mass, and the bump at 750 GeV appears due to some kinematical accidents. The most plausible production process is definitely the gluon-gluon fusion. Production in collisions of light quark and antiquarks is also theoretically sound, however it leads to a more acute tension between run-2 and run-1 data. Indeed, even for the gluon fusion, the production cross section of a 750 GeV resonance in 13 TeV proton collisions is only 5 times larger than at 8 TeV. Given the larger amount of data collected in run-1, we would expect a similar excess there, contrary to observations. For a resonance produced from u-ubar or d-dbar the analogous ratio is only 2.5 (see the table), leading to much more tension. The ratio climbs back to 5 if the initial state contains the heavier quarks: strange, charm, or bottom (which can also be found sometimes inside a proton), however I haven't seen yet a neat model that makes use of that. Another possibility is to produce the resonance via photon-photon collisions. This way one could cook up a truly minimal and very predictive model where the resonance couples only to photons of all the Standard Model particles. However, in this case, the ratio between 13 and 8 TeV cross section is very unfavorable, merely a factor of 2, and the run-1 vs run-2 tension comes back with more force. More options open up when associated production (e.g. with t-tbar, or in vector boson fusion) is considered. The problem with these ideas is that, according to what was revealed during the talk last December, there isn't any additional energetic particles in the diphoton events. Similar problems are facing models where the 750 GeV resonance appears as a decay product of a heavier resonance, although in this case some clever engineering or fine-tuning may help to hide the additional particles from experimentalist's eyes. While a simple two-body decay of the resonance into two photons is a perfectly plausible explanation of all existing data, a number of interesting alternatives have been suggested. For example, the decay could be 3-body, with another soft visible or invisible particle accompanying two photons. If the masses of all particles involved are chosen appropriately, the invariant mass spectrum of the diphoton remains sharply peaked. At the same time, a broadening of the diphoton energy due to the 3-body kinematics may explain why the resonance appears wide in ATLAS. Another possibility is a cascade decay into 4 photons. If the intermediate particles are very light, then the pairs of photons from their decay are very collimated and may look like a single photon in the detector.and the possibilities are endless. The situation is completely different than during the process of discovering the Higgs boson, where one strongly favored hypothesis was tested against more exotic ideas. Of course, the first and foremost question is whether the excess is really new physics, or just a nasty statistical fluctuation. But if that is confirmed, the next crucial task for experimentalists will be to establish the nature of the resonance and get model builders on the right track.