Backward scattering of pions by nucleons

Backward elastic scattering of pions by nucleons is an elementary form of excitation with baryon exchange. The backward scattering cross section is very small and decreases rapidly with increasing energy. The cross section becomes maximal when the scattering angle approaches 180$^\circ$, i.e., a peak is observed in the backward scattering. In contrast to forward scattering, in backward scattering the processes in which positive and negative pions participate are not similar. This is confirmed by the exchange character of the backward scattering. In the energy interval up to 5 GeV, backward scattering has an extremely pronounced resonant character, due to the influence of the $s$-channel baryon resonances. Experimental data on backward scattering in the intermediate energy region (up to 20 GeV) are satisfactorily described by the Regge theory of complex angular momenta. The energy dependence of the cross section agrees with the model with linear baryon trajectories. In the Serpukhov-accelerator energy range (20–40 GeV), however, a weakening of the energy dependence is observed in the backward $\pi^-n$ scattering. It is difficult to reconcile this behavior within the framework of the Regge phenomenology, with the linear form of the nucleon trajectory. A phenomenon that has a bearing on the observed behavior of the backward scattering at high energies was unexpectedly observed in an entirely different region. A phase-shift analysis of $\pi N$ scattering at low energies (to 1 GeV) has shown that one of the partial waves (corresponding to the quantum numbers of the nucleon) experiences an appreciable rise when the energy approaches zero. It turns out that this singularity can be connected with the asymptotic behavior of the backward scattering. The two phenomena–the behavior of the backward scattering at high energies and the singularity of the partial wave near zero–indicate in a consistent manner that the effective spin of the nucleon reggeon greatly exceeds the value that follows from the linearity of the nucleon trajectory. In contrast to backward $\pi^-n$ scattering, the behavior of backward $\pi^-p$ scattering (pure $\Delta$ exchange) reveals no singularities whatever in the Serpukhov-accelerator energy interval and continues to have the same energy dependence as observed at lower energies. As to the angular distributions, a very narrow backward peak is observed in the $\pi^-p$ scattering, and has a slope comparable with the peak of the $\pi^-n(\pi^+p)$ scattering. The closeness of the $\pi^\pm n$ angular distributions, which has been observed for the first time at high energies (25–40 GeV), suggests the possibility of a geometrical interpretation–scattering by an extended object. The analogy between backward scattering of pions by nucleons and glory–an optical effect observed when light is backscattered from a raindrop–is discussed. In conclusion, radiative corrections to backward scattering are considered.