Non-Regge and hyper-Regge effects in pion-nucleon charge exchange scattering at high energies

The experimental data on the charge exchange differential cross-section and on the difference of the π+p and π-p total cross-sections in the range psub(L)=5GeV/c to 200 GeV/c are shown to be incompatible with conventional Regge asymptotic behaviour. It is shown that an additional term is required which grows in importance with energy. The precise form of the new term cannot be ascertained, but it is shown that it corresponds to a singularity at J=1 in the complex-angular-momentum plane. Amongst the possible types of additional term there are two which are aesthetically favoured and which have been closely analysed. These correspond to (i) a non-Regge behaviour associated with the maximal growth permitted in axiomatic field theory; (ii) a ''hyper-Regge'' term, i.e. an odd-signatured Regge pole, the analogue of the pomeron pole, with intercept α=1 at t=0. Very striking predictions, in particular for the charge exchange polarization, follow as a consequence of the non-Regge or hyper-Regge asymptotic behaviour of the crosssing-odd amplitude