Anyway, in this post I will brush off the doubt and discuss what sort of dark matter models could explain the monochromatic gamma-ray line in the current Fermi data. One definitely needs something non-trivial. Dark matter cannot carry an electric charge, therefore, in a generic model, annihilation into photons is mediated by a loop diagram, leading to the cross section naively suppressed by 3-4 orders of magnitude compared to other annihilation channels. This would be problematic for two reasons. Firstly, given the strength of the Fermi line, that total annihilation cross section would by far exceed the thermal cross section 3*10^-26 cm^3/sec, so one would have to invoke some non-thermal mechanism of populating dark matter in the universe. Secondly, Fermi observations of the continuum gamma-ray flux from Milky Way satellite galaxies constrain the allowed annihilation cross sections to about 10^-25 cm^3/sec for a 130 GeV dark matter particle. the precise value depending on the annihilation channel.
For this reason, models fitting the Fermi line have to somehow shut off the tree-level annihilation channels and make the annihilation into photons dominant or nearly dominant. This is tricky and typically requires introducing a turtle standing on an elephant standing upon a giant turtle, as you can see on arXiv every day. Here I pick 3 models on the market that involve imo the smallest number of elephants.
- Chern-Simon portal.In this model the mediator between the dark and visible matter is a Z' vector boson, who is coupled in a funny way to the Standard Model via the Chern-Simons term Z' Z γ (one can consider it an effective coupling after some exotic chiral fermions charged both under the Standard Model and Z' have been integrated out). One assumes dark matter is charged under Z' thus it can annihilate into a pair of Z' as well as (via the Chern-Simons coupling) into Zγ. Since these two processes depend on two independent adjustable parameters, it is no surprise one can fit both the line (via annihilation into Zγ) and the thermal cross section (via annihilation into Z'Z').
- Higgs is space! Here Z' is also the mediator, however this time on the visible side it couples to the top quark (this can even be motivated in some composite Higgs or Randall-Sundrum constructions). This means dark matter annihilates dominantly into a pair of top quarks, and one can choose the couplings of Z' such that the cross section is the thermal one. But if the dark matter mass is lighter that the top mass the annihilation rate can be suppressed by phase space. On the other hand, the subleading annihilation channels into Zγ or Hγ proceeding via a loop of the top quark do not suffer from that phase space suppression, therefore their rate can be relatively large, so as to explain the strength of the Fermi line.
- Box-shaped line. It is hard to annihilate dark matter into photons, but it is much easier to annihilate it into another exotic particle X who, at least part of the time, decays into photons. Of course, this in general does not produce a line, but rather a box-shaped photon spectrum, as the observed photon energy gets smeared by the motion of the X particle. However, as the mass of X approaches that of dark matter (so that dark matter annihilates into X at rest) the box gets narrower and at some point becomes a line for all practical purpose. So the Fermi line could be explained e.g by a 265 GeV dark matter particle annihilating with the thermal cross section into a 260 GeV particle X, who in turn decays about 10% of the times into a pair of photons.
Which means: hurry up with your gamma-ray line paper, before it's gone ;-)