Soft gluon radiation and energy dependence of total hadronic cross sections

Abstract

An impact parameter representation for soft gluon radiation is applied to obtain both the initial decrease of the total cross section (${\ensuremath{\sigma}}_{\mathrm{tot}}$) for proton-proton collisions as well as the later rise of ${\ensuremath{\sigma}}_{\mathrm{tot}}$ with energy for both $pp$ and $p\overline{p}$. The nonperturbative soft part of the eikonal includes only limited low energy gluon emission and leads to the initial decrease in the proton-proton cross section. On the other hand, the rapid rise in the hard, perturbative jet part of the eikonal is tamed into the experimentally observed mild increase by soft gluon radiation whose maximum energy rises slowly with energy.