Pomeranchuk Trajectory and Its Relation to Low-Energy Scattering Amplitudes

Abstract

While "ordinary" Regge trajectories can be bootstrapped using the resonance approximation to finite-energy sum rules, we suggest that the Pomeranchuk trajectory is mostly built from the nonresonating background at low energies. This hypothesis (a) explains the constancy of $\mathrm{KN}$ and $\mathrm{NN}$ total cross-sections (in contrast to $\overline{K}N$ and $\overline{N}N$ over a wide energy range; (b) predicts many other interesting relations which are experimentally satisfied; and (c) leads to no obvious inconsistencies.