Are constant asymptotic total cross sections ruled out by high-energy measurements?

Abstract

It is a common belief that the conventional contributions of the Pomeron pole and the two-Pomeron cut in the Gribov Reggeon calculus cannot give enough rise of the $pp$ total cross section at CERN ISR energies. However, we find from a detailed analysis of $\frac{d\ensuremath{\sigma}}{dt}$ at small $t$ that one can, in fact, get a reasonable rise of the $pp$ total cross section at CERN ISR energies. The ${K}^{+}p$ total cross sections are also fitted; however, their consistency with $\frac{d\ensuremath{\sigma}}{dt}$ has to be checked out when the data are available.