Some bootstrap calculations with rising trajectories

Abstract

We study the dynamical properties of rising Regge trajectories. In this dynamics crossing symmetry is an essential dynamical ingredient and unitarity is used only in some approximate form. The crossing is used through the finite energy sum rules. We first work in the narrow resonance approximation (when unitarity is not used) and consider the questions of scalar meson bootstrap and the bootstrap of p in π-π scattering. Next we consider the question of p bootstrap by using unitarized Regge parameters through the solution of Cheng-Sharp equations. Two approximate forms of unitarity are considered - one corresponding to a single Regge pole term representation of the amplitude and the other corresponding to Khuri representation. In either case unitarity seems to make only a small difference to the results of narrow resonance approximation. We find that the values x = 1 GeV(^-2) and p = 140 MeV for the slope and width of the p are self-consistent when the cut-off parameter is chosen somewhere between the p and the fo the degenerate p-fo trajectory.