Spin and Parity Analysis in the Double-Regge Model

The formalism is given for a partial-wave analysis of a low-mass two-body subsystem produced via a double-Regge amplitude at small momentum transfer. This method is applied to the Reggeized Deck amplitude for the reaction $\pi N\to \rho \pi N$ in the $\rho -\pi$ mass region of the $A$ enhancement. At lower mass values the results are less sensitive to the exact form of the pion Regge trajectory, and about 75-80% of the cross section in the $A_1$ region is given by a $1^{+}$ $S$- wave $\rho -\pi$ state. This amplitude is largely real and the Argand diagrams for the partial waves do not show resonant structure. However, phenomenologically it is difficult to distinguish between the Berger amplitude and an $A_1$-resonance production amplitude. The spin-parity decomposition in the $A_2$ mass region is also discussed.