Regge-Pole Content of Chiral and Gauge Field Theories

Abstract

The high-energy limits of the 4-pion and 6-pion tree-approximation amplitudes in the nonlinear chiral-invariant Lagrangian and of the $\rho -\rho$ scattering amplitude in massive Yang-Mills theory are investigated in order to see whether Reggeization of elementary particles occurs. We find that the 4- and 6-pion amplitudes are dominated asymptotically by exchange of Regge poles with quantum numbers of the $\rho$ and $A_1$ mesons, respectively. These trajectories are regarded as "ancestors," because $\rho$ and $A_1$ particles are not present in the initial Lagrangian. The $\rho -\rho$ scattering amplitude is dominated by the exchange of quantum numbers of the $\rho$ meson, but there are two trajectories present, so that Reggeization does not occur. Nevertheless, in all amplitudes computed there is a striking regularity in the dominance of high-energy limits by the exchange of quantum numbers of the $\rho$ and $A_1$ mesons.