The puzzle of the near-saturation of isospin bounds in πN→πN, KN→KN and πN→KΣ

A detailed analysis of the phenomenon of near-saturation of isospin bounds is performed using available experimental information on πN→πN, KN→KN and πN→KΣ. The puzzle, previously observed mainly in low energy πN→πN at 1800, is found to exist also elsewhere, in particular in KN→KN at 1800 and at intermediate angles in terms of the O3 invariant bound of Doncel, Michel and Minnaert. The widespread occurrence of the phenomenon makes one suggest the hypothesis that it is a general approximate property of nondiffractive scattering. The significance of the effect is studied with a statistical model and the extent to which well known phenomenology can explain it is discussed, but it is concluded that the effect is more general than can be expected from simple arguments. (Auth.)