The universal $\ln^{2}s$ increase in total cross sections

Abstract

While it has long been known that many models of high energy scattering give cross sections which rise as $\ln^{2}s$, the determination of the coefficient of this term is rarely given. We show that in gaussian and exponential eikonal models an exact expression for the cross section can be obtained, which demonstrates the $\ln^{2}s$ asyptoptic behaviour and determines its coefficient. The coefficient is universal, as found empirically, and the value of the constant obtained from the gaussian model is in good agreement with the empirical value.