Ghost-Eliminating Modifications in Multipion Amplitudes: Factorization on Leading Trajectories

Abstract

The modification of ${B}_{n}$ to eliminate the ghost at ${\ensuremath{\alpha}}_{\ensuremath{\rho}}=0$ is investigated. The ${J}_{1}{J}_{2}{J}_{3}$ leading three-particle vertex in ${B}_{n}$ is calculated. Using this form, it is shown that $\mathrm{no}$ finite number of term modification of ${B}_{n}$ without trajectory depression satisfies consistent factorization in all multipion amplitudes. Allowing trajectory depression, although daughter levels still presumably do not factorize, a solution is found in which (a) all leading trajectories factorize, (b) are nondegenerate, and (c) the $\ensuremath{\rho}\ensuremath{\rho}\ensuremath{\rho}$ vertex need not be zero. We believe this to be the suitable generalization of the Lovelace $4\ensuremath{-}\ensuremath{\pi}$ amplitude.