Remarks on the high-energy behaviour of cross-sections in weak-scale string theories

We consider the high-energy behaviour of processes involving Kaluza-Klein (KK) gravitons of weak-scale string theories. We discuss how form-factors derived within string theory modify the couplings of KK gravitons and thereby lead to an exponential fall-off of cross sections in the high-energy limit. Further, we point out that the assumption of Regge behaviour for a scattering amplitude in the high energy limit, $T\propto s^{\alpha(t)}$, combined with a linear growth of the total cross-section, $\sigma_{tot}(s)\propto s$, violates elastic unitarity. Regge behaviour leads to a stringent bound on the growth of the total cross-section, $\stot (s) \leq 32\pi \alpha' \ln(s/s_0)$