Spin Dependence of High-Energy Scattering Amplitudes. I

A formalism, useful for discussing spin dependence of scattering amplitudes in terms of complex angular momentum, is given. The question of the spin dependence of elastic scattering amplitudes, its relationship to coupling to Regge poles, fixed poles in the angular-momentum plane, and superconvergence relations are discussed. It is concluded that general principles permit the coupling at a vertex of a Regge pole of integer spin $J_0$ and two particles whose spin projection is greater than $J_0$, provided the Regge pole has the wrong signature to be a particle of spin $J_0$. In particular, the Pomeranchuk trajectory at $t=0\mathrm{}$ ($J_0=1\mathrm{}$) can flip helicities by two or more units and hence yield spin-dependent cross sections. Several models which support this conclusion are given. The possibility that a particular Regge pole's coupling does vanish is not ruled out, however.