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 js+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 ~(2js+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 jt=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 It=1 satisfies the dual absorption result, sαJ0(R-t). A crude estimate gives α(0)~12+(Γρmρ) (=0.6) and α'(0)~14(Γρmρ)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.
Physical Review D
- Pub Date:
- December 1972