Jester notes significant restrictions on dark photon parameter space from a variety of recent experiments.
[T]he mixing angle in the minimal model has to be less than 0.001 as long as the dark photon is lighter than 10 GeV. This is by itself not very revealing, because there is no theoretically preferred value of ε or mA'. However, one interesting consequence the . . . result is that it closes the window where the minimal model can explain the 3σ excess in the muon anomalous magnetic moment.I would agree with Jester that there is no theoretically preferred value for ε, which is the parameter determining the extent to which dark photons and ordinary photons mix.
But, I would disagree with him that there is no theoretically preferred value for mA' which is the mass of the dark photon (hypothesized as a boson that carries a force by which dark matter interacts with other dark matter). Most studies I have seen have favored a dark photon mass in the MeV range and certainly a mass of less than 10 GeV.
The constraint on mixing between dark photons and ordinary photons is significantly tighter for dark photon masses of under 10 MeV, which is the preferred mass range for dark photons.
The mass of a dark photon impacts the effective range of the force it carries. A dark photon with a mass of 80 Gev-90 GeV would have a range similar to that of the weak force bosons, i.e. on the order of the size of an atomic nucleus. An MeV range dark photon, in contrast, would have a long enough range to produce meaningful interactions of dark matter particles that are near each other sufficiently to tweak the dark matter halo shape in galaxies and galactic clusters.
Thus, this data, collectively, and together with other data attempting to detect dark matter directly, further buttresses the idea that if dark matter exists, that it has almost no interactions with ordinary matter except via gravity.
Interactions between ordinary photons and dark photons aren't important to the overall character of self-interacting dark matter models, but these studies do strictly narrow the classes of self-interacting dark matter models that can be consistent with empirical evidence.
UPDATE: A new study reanalyzes the estimates of the strength of dark matter self-interactions based upon the observations of a galaxy falling into a galactic cluster. The value reached is similar to, but a bit higher than, that estimated from the Bullet Cluster.