Absorption Picture as a Consequence of Multi-Regge Iteration of Low-Energy Peripheral Resonances
Phys. Rev. D 6, 3241 – Published 1 December, 1972
DOI: https://doi.org/10.1103/PhysRevD.6.3241
Abstract
Using the empirical fact that the dominant low-energy resonances are peripheral (i.e., they satisfy the relation ), the imaginary part, , of the low-energy amplitude is written in the factorized form . The resonance contribution to near the resonance position is , which is ; and thus the well-known value for the vector-tensor trajectory intercept of follows simply from peripherality. From finite-energy sum rules the residue of the trajectory is . The quantity , which in the channel corresponds to a fixed pole at , through the multi-Regge iteration gives rise to a moving pole; and the imaginary part of the total amplitude with satisfies the dual absorption result, . A crude estimate gives and . Thus, for non-diffractive processes, the multi-Regge (or multiperipheral) model is consistent with the absorption picture and as a consequence an approximate bootstrap solution is obtained. The physical interpretation in terms of -plane cuts is discussed.