Lorentz Poles in Equal-Mass Scattering from Analyticity and Factorization

It is shown, by means of factorization, that the daughter Regge trajectories implied by analyticity in unequal-mass scattering amplitudes constitute a single Lorentz pole when they couple to an equal-mass channel. At zero energy the equal-mass elastic amplitude has the form $\mathrm{const}\times D_{-\alpha \mathrm{}\left(0\right)-2\mathrm{}}^{}{}_{}{}^1\mathrm{}(-z)\mathrm{}$.