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 $j_s+\frac{1}{2}=kR\approx \frac{1}{2}R\sqrt{s}$), the imaginary part, A₀(s,t), of the low-energy amplitude is written in the factorized form $F\left(s\right)J_0\left(R\sqrt{-t}\right)$. The resonance contribution to F(s) near the resonance position is ≈(2j_s+1), which is $\approx s^{\frac{1}{2}}$; and thus the well-known value for the vector-tensor trajectory intercept of ≈1/2 follows simply from peripherality. From finite-energy sum rules the residue of the trajectory is $\approx J_0\left(R\sqrt{-t}\right)$. The quantity A₀(s,t), which in the t channel corresponds to a fixed pole at $j_t=\frac{1}{2}$, 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, $s^{\alpha }{J}_0\left(R\sqrt{-t}\right)$. A crude estimate gives $\alpha \left(0\right)\approx \frac{1}{2}+\left(\frac{{\Gamma }_{\rho }}{m_{\rho }}\right)(=0.6)$ and ${\alpha }^{{}^{\prime }}\left(0\right)\approx \frac{1}{4}\left(\frac{{\Gamma }_{\rho }}{m_{\rho }}\right)R^2(=1.0{BeV}^{-2}forR=1F)$. 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.