Comment on Positive Regge-Cut Discontinuities

Abstract

Abarbanel has recently derived a formula for the discontinuity across the branch point using direct-channel unitarity. His derivation assumes that a two-Reggeon irreducible kernel does not contain $J$-plane singularities in the vicinity of the branch point. We investigate this assumption for the two-Pomeranchon cut using an extension of the multi-Regge arguments of Finkelstein and Kajantie. We verify the assumption for ${\ensuremath{\alpha}}_{P}(0)=1$, but the result is inconclusive otherwise.