Phase Contours and Bootstraps. II

Abstract

The phase-contour method is applied to reactions of the types $\mathrm{PP}\ensuremath{\rightarrow}\mathrm{PP}$, $\mathrm{PP}\ensuremath{\rightarrow}\mathrm{PV}$, and $\mathrm{PP}\ensuremath{\rightarrow}\mathrm{PT}$, where $P$, $V$, and $T$ denote, respectively, the pseudoscalar mesons $\ensuremath{\pi}$, $\ensuremath{\eta}$, $K$; the vector mesons $\ensuremath{\rho}$, $\ensuremath{\omega}$, ${K}^{*}$; and the tensor mesons ${A}_{2}$, ${f}^{0}$, ${K}^{**}$. Relations are obtained between zeros of the collision amplitudes and the resonance poles associated with the appropriate Regge trajectories. In a narrow-resonance approximation, and with a unitarity hypothesis that relates certain residue zeros and symmetry zeros of a collision amplitude, bootstrap constraints, which are generalizations of the Veneziano constraint, are obtained on the trajectory functions. A number of other ways of deriving these constraints are discussed. These constraints are then studied for all allowed meson reactions of the types noted above, and are compared with data on the Regge parameters that have been obtained from experiment.