Model-independent bound on the triple-Pomeron pole coupling

We derive an upper bound on the triple-Pomeron coupling $g_{P}^{}{}_{}{}^{2}(0)$ assuming the actual Pomeron is a pole below one. Our result corresponds to an estimate of $g_{P}^{}{}_{}{}^{2}(0)$ obtained by Abarbanel, Chew, Goldberger, and Saunders on the basis of a multiperipheral model. We show that if indeed the bound is an estimate of $g_{P}^{}{}_{}{}^{2}(0)$, Pomeron exchange in multiparticle production should constitute a significant fraction of the total cross section. We indicate how this can be true even in the limit of vanishing Pomeron couplings. It is also shown how our calculation can be applied to obtain a bound on the "bare" triple-Pomeron coupling.