In fact, the huge size of the extra dimensions (compared to the Planck length) is not stable under quantum corrections, which tend to shrink it down until $M_s \sim R_c^{-1} \sim M_P \sim
10^{19}$ GeV, at which stage the original hierarchy problem is reinstated. Nevertheless, there are several variants of the ADD model which address this problem in various ways, and some of these ideas may not be far from the truth. From a phenomenological point of view, it is, therefore, reasonable to postpone addressing the stability issue, and proceed to study the minimal ADD model and its consequences for experiment.

The experimental consequences of ADD gravity have been mainly studied in the context of of ($a$) real graviton emission and ($b$) virtual graviton exchange. In the former case the final state gravitons in the ADD model are ‘invisible’, escaping the detector because of their feeble individual interactions ($\sim M_P^{-1}$) with matter. The final state, involving missing energy due to gravitons, will be built up by making an incoherent sum over the tower of graviton modes. In the case of virtual gravitons, the final state is built up by making a coherent sum. In either case, it may be shown[@GRW; 