Arguments Supporting a Positive Two-Pomeranchukon Discontinuity

Abarbanel's derivation of the 2-Pomeranchukon discontinuity is examined at $t=0\mathrm{}$, where the physics is especially transparent. By slightly altering the significance of Abarbanel's decomposition of the total cross section, arguments are given to support the crucial and controversial assumption that his "single-fireball" vertices do not contain the 2-Pomeranchukon branch point. It is shown further how Abarbanel's discontinuity formula gives a semiquantitative realization of the Finkelstein-Kajantie requirement of small Pomeranchukon couplings if ${\alpha }_P\mathrm{}\left(0\right)\mathrm{}$ is close to unity. This demonstration, which shows that the triple-Pomeranchukon coupling ${g_P}^2$ is proportional to $1-{\alpha }_P\mathrm{}\left(0\right)\mathrm{}$, depends critically on the positive sign of the Abarbanel discontinuity.