Some consequences of the vanishing of the triple-pomeronchukon-vertex

Starting with the assumption that the triple-pomeronchukon-vertex vanishes when all three pomeronchukons have zero mass, we show that in the absence of pionization, total cross sections would fall at least logarithmically with energy, while the mean multiplicity would approach a constant. Several reasons are presented to suggest that some pionization must occur and that, otherwise, limiting fragmentation itself would vanish. A secondary result, that the P-P-P′ coupling will also vanish in certain regions, is also proved.