Rising total cross sections and amplitudes at large impact parameter froms- andt-channel unitarity

Abstract

Production processes which involve pion exchange at large impact parameter cause a rise in ${\sigma }_T$, an increased slope of $\frac{d\sigma }{\mathrm{dt}}$ near $t=0\mathrm{}$, and shrinkage of the forward slope with energy. The remarkably high energy-scale for the rise in ${\sigma }_T$, $s_0\simeq \frac{m^2{m}^{\prime 2}}{{m_{\pi }}^2}$, follows from the kinematical opening of phase space near the pion pole. The magnitude is determined by known coupling constants. The effects are due to two-pion-exchange cut terms in the imaginary part of the elastic amplitude, and therefore involve both $s$- and $t$-channel unitarity.