[mattheww]

As you can imagine, the long-lived particles can have "any" lifetime. Since the lifetime is unknown, it makes sense to probe many lifetimes. The experiment being suggested by Lubatti and his collaborators probes lifetimes on the order of 10^5 - 10^7 m. There aren't strong constraints on this range, which can appear as missing energy in CMS or ATLAS (or not). CMS, ATLAS, and LHCb are giving constraints at 10^-6 to 10^2 m. Interestingly, the different experiments are probing mostly different ranges.

To correct something in the grandparent (?) post, the LHC experiments do not know the incoming energy. Even though the beam energy is 6.5 TeV on 6.5 TeV, the collisions are only a fraction of that. We only know that the energy has to balance in the perpendicular direction. However, if a collision produces two invisible particles that balance each other, it would appear that there is no missing energy. In many of models, pair production of new particles is preferred, so if the particles are long-lived, they can be hard to find.