Eikonal regime of gravity-induced scattering at higher energy proton colliders

We compute transplanckian parton scattering in flat extra-dimensional theories at the LHC and at the recently discussed high-energy upgrade (HE LHC). We report new leading-order calculations of the QCD background. We apply appropriate cuts to satisfy the necessary conditions for the eikonal approximation to be valid while at the same time maximising the signal to background ratio at LHC energies. We study the computability of the eikonal signal and consider the effect of a possible 33 TeV high-energy upgrade to the LHC, which serves to extend the calculable region and to enhance the signal to background ratio.