K-meson-nucleon scattering and relativistic dispersion relations

Abstract

Relativistic K-meson-nucleon dispersion relations are subjected to the type of analysis which leads one to expect a resonance in the pion-nucleon system. The P-wave equations for scalar mesons show no indication of any resonance. But the S-wave equations strongly suggest a resonant K +−p scattering and a repulsive K - nucleon potential, both in contradiction with experiment. However, for pseudo-scalar K-particles, analogous to the pion, the P-wave equations are consistent with a resonance in the I = 1, j = 3 2 and one of the I = 0 states. This conclusion is not borne out by the present experimental findings and calls for detailed information about the angular distributions and the high energy behaviour of the scattering cross-section to decide the issue. For the K particles no such resonance states are found. For the pseudoscalar K particles it is concluded, in the absence of the “accidental cancellation” which characterizes the pion case, that the I = 1 phase-shift at threshold should be given correctly by the “Born” term corresponding to a repulsive interaction, in agreement with experiment. No definitive conclusion about the S-wave behaviour of the K particles can really be drawn for reasons mentioned below. The main conclusion of the present work is thus that the dispersion theoretic analysis of non-forward scattering is capabee of discriminating between a scalar and pseudoscalar K-meson on qualitative grounds alone; it strongly indicates that these mesons are pseudoscalar.