This post will mention my very own crackpot idea!
Right now we have some blog coverage (Reference Frame, Resonaances) of a paper claiming a signal of dark matter annihilation in the galactic center, producing gamma rays of about 130 GeV.
Now, a few years back there was a claim of "lepton jets" that might be produced by "three new states with energies 15 GeV, 7.3 GeV, and 3.6 GeV. The heavier states cascade decay to the lighter ones while the lightest one decays into a tau pair after 20 ps or so: so the 15 GeV particle should decay to 8 tau's! To say that the masses of some dark sector states should be fine-tuned to be 2m_tau, 4m_tau, and 8m_tau surely looks bizarre." (Quote from Lubos Motl.)
Now I notice that this new claim of 130 GeV, plus or minus a few GeV [*], is around 64m_tau. It's producing photons, not muons, but that just means there's a different decay channel available for this mass, right?
A more urgent theoretical question is whether we suppose that there is a sequence of states with mass 2x, 4x, 8x, 16x, 32x, 64x... m_tau, or whether we just jump straight from 2, 4, 8 to 64. Interestingly, the latter four numbers have a status as "Hermite constants" related to hyperspatial packing densities. Those are the Hermite constants for 3, 4, 5 and 7 dimensions. Hyperspace theorists, this is your chance!
[*] quite a few