The real part of Kp forward scattering with rising total cross sections

Abstract

Forward dispersion relations have been applied to Kp elastic scattering with the assumption that the total cross sections continue to rise with primary energy ω like log ω and log 2 ω respectively. The results depend on the way of approach with ω of the two total cross sections. In this connection, we further discuss the consequences of a generalized version of the Pomeranchuk theorem when total cross sections are rising like log β ω. The ratio α + of real and imaginary parts of the forward elastic scattering amplitude for K + p is seen to change sign, and becomes positive at some high energy (e.g. at about 400 GeV in the log 2 case). If the total cross section difference behaves like 1/ ω b , then α_ will remain positive at all (high) energies. However, if the cross sections approach each other as slowly as allowed by the generalized Pomeranchuk theorem, then also α_ will change sign at some very high energy.