Absorption Picture as a Consequence of MultiRegge Iteration of LowEnergy Peripheral Resonances
Abstract
Using the empirical fact that the dominant lowenergy resonances are peripheral (i.e., they satisfy the relation j_{s}+12=kR~12Rs), the imaginary part, A_{0}(s,t), of the lowenergy amplitude is written in the factorized form F(s)J_{0}(Rt). The resonance contribution to F(s) near the resonance position is ~(2j_{s}+1), which is ~s^{12} and thus the wellknown value for the vectortensor trajectory intercept of ~12 follows simply from peripherality. From finiteenergy sum rules the residue of the trajectory is ~J_{0}(Rt). The quantity A_{0}(s,t), which in the t channel corresponds to a fixed pole at j_{t}=12, through the multiRegge iteration gives rise to a moving pole; and the imaginary part of the total ππ amplitude A(s,t) with I_{t}=1 satisfies the dual absorption result, s^{α}J_{0}(Rt). A crude estimate gives α(0)~12+(Γ_{ρ}m_{ρ}) (=0.6) and α'(0)~14(Γ_{ρ}m_{ρ})R^{2}(=1.0 BeV^{2} for R=1F). Thus, for nondiffractive processes, the multiRegge (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 jplane cuts is discussed.
 Publication:

Physical Review D
 Pub Date:
 December 1972
 DOI:
 10.1103/PhysRevD.6.3241
 Bibcode:
 1972PhRvD...6.3241D