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

Abstract

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, $\text{stot}(s)\le 32\pi {\alpha }^{\prime }\ln (s/s_0)$.

Comments: 5 pages, no figures