"Soft" Hadronic Cross Sections Challenge Hidden Dimensions

High energy measurements of the inelastic proton-proton cross sections, at the LHC at $\sqrt s$=7 TeV and by Auger at 57 TeV, have validated previous evidence from data collected over a wide range of energies that the total and inelastic cross sections for $pp$ and $\bar pp$ interactions saturate the Froissart bound of $\ln^2 s$. Although the data themselves did not cover truly asymptotic energies, our recent analysis of these data obtained the asymptotic ratio $\sigin/\sigtot=0.509\pm 0.021$, consistent with the value of 1/2 required for scattering by a black disk; further, the forward scattering amplitude became purely imaginary for $s\rightarrow \infty$, confirming the black disk interpretation. In addition, the limiting black disk behavior has been independently confirmed by an analysis of Schegelsky and Ryskin including LHC data on the shrinkage of the slope of the forward elastic scattering cross section. Unless one considers these results, emerging from an analytic amplitude analysis of data over an energy range of $6\le \sqrt s\le 57000$ GeV, a complete numerical accident, we rule out any new physics thresholds that contribute higher powers of $\ln s$ or, worse, powers of $s$ to the energy dependence of cross sections {\it at any energy}. This includes theories with additional dimensions of space-time, whose existence is challenged.