Two-Pomeranchukon Cuts and Vanishing of the Triple-Pomeranchukon Coupling

Abstract

It is shown that the Gribov-Migdal lower bound on the magnitude of the two-Pomeranchukon cut is not valid unless both the triple-Pomeranchukon coupling $g_{\mathrm{PPP}}(t, {q_1}^2, {q_2}^2)$ and its derivative $\frac{dg(t, q^2, q^2)}{d{q}^2}$ vanish when $t={q_1}^2={q_2}^2=0\mathrm{}$. A numerical estimate of the cut is given. We give the connection between the behavior of $g_{\mathrm{PPP}}$ and the validity of the Bronzan and Jones unitarity condition on the discontinuity of the cut at $t=0\mathrm{}$.