Restrictions Imposed by the Optical Theorem on Exchanged Quantum Numbers

Abstract

Crossing relations for particles of arbitrary spin are used to express the amplitudes for $A+B\to A+B$ in terms of amplitudes for the crossed reaction $A+\overline{A}\to B+\overline{B}$. Using the optical theorem, it is demonstrated that crossed amplitudes with positive parity, positive $G$ parity, and positive signature cannot be negligible for forward scattering. Implications of this result for the spin dependences of high-energy scattering amplitudes are discussed.