First and Second Factorization in a Dual Multiparticle Theory with Nonlinear Trajectories

The $N$-point tree graphs of a dual-resonance theory with nonlinear trajectories are factorized. The factorization procedure applies equally well with the external lines on or off the mass shell. The particle spectrum of the theory is found to have a degeneracy of approximately $6^l$ for the lth level. Since the trajectory is logarithmic, the asymptotic density of levels grows only as some power of the mass. The techniques used in first factorization are applied to second factorization to arrive at an amplitude for processes involving two external particles with nonzero spins. Two sets of linear-dependence relations among the amplitudes obtained by factorization are proven.