Are there extra dimensions? If so are they large? Flat? Small? Warped? This positronium decay to nothing experiment can help answer these questions. The basic idea was suggested by S.N. Gninenko, N.V. Krasnikov, and A. Rubbia, "Extra dimensions and the invisible decay of orthopositronium," Phys. Rev. D 67, 075012 (2003). If there are extra dimensions in which ordinary interactions do not propagate but in which gravity does, then energy in the normal, familiar dimensions can vanish by coupling to gravitons in these other dimensions. That's a not-technically correct simple explanation.
To detect such effects, one needs a relatively long-lived system which wouldn't violate too many other conserved quantities by vanishing. It should also contain as much energy as possible, as the probability for such processes is (loosely speaking) proportional to the energy divided by the "mass scale" of extra dimension physics to some large power. Ortho-Ps is practically nothing to begin with, has a decent energy content (1 MeV), and lives a relatively long time (~ 150 ns). Possibly the best one could do would be to use a proton-antiproton bound state to look for inivisible decays, but the lifetime stinks, and it would be a hard experiment. Invisible decays of Ps may be a system in which the experiment is possible.
Ortho-Ps can also decay to 3-gammas. The upper bound for the Ps
-> nothing process is set by the Z -> nothing process, lower
bound is from the hypothesis that extra dimensions would fix gauge
hierarchy. The branching ratio is the probability that the o-Ps would
"vanish" into extra dimensions divided by its usual decay rate to three