Absorption Picture as a Consequence of Multi-Regge Iteration of Low-Energy Peripheral Resonances

Using the empirical fact that the dominant low-energy resonances are peripheral (i.e., they satisfy the relation j_s+12=kR~12Rs), the imaginary part, A₀(s,t), of the low-energy amplitude is written in the factorized form F(s)J₀(R-t). The resonance contribution to F(s) near the resonance position is ~(2j_s+1), which is ~s¹² and thus the well-known value for the vector-tensor trajectory intercept of ~12 follows simply from peripherality. From finite-energy sum rules the residue of the trajectory is ~J₀(R-t). The quantity A₀(s,t), which in the t channel corresponds to a fixed pole at j_t=12, through the multi-Regge 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^αJ₀(R-t). A crude estimate gives α(0)~12+(Γ_ρm_ρ) (=0.6) and α'(0)~14(Γ_ρm_ρ)R²(=1.0 BeV^-2 for R=1F). 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 j-plane cuts is discussed.