The regge formalism for relativistic particles with spin

Abstract

The scattering amplitude for particles of spin σ₁ and σ₂ is examined in the angular-momentum plane, and the perturbation terms are found to have poles at the positive integers below σ₁+σ₂ or at the corresponding half-integers if σ₁+σ₂ is half-integral. In the complete amplitude, the poles begin to move away from these values as the coupling is turned on. However, the amplitude in the j-plane, obtained by analytically continuing the amplitude from values ofj greater than σ₁ + σ₂- 1, will not be equal to the physical partial-wave amplitudes at the points in question. In the presence of a third double-spectral function, the states of the wrong signature will have essential singularities of the Gribov-Pomeranchuk type at these points. Our results are also valid in processes which can have an intermediate state with particles of spin σ₁ and σ₂. If the spinning particles are themselves Regge particles, all these statements may require modification.