Positivity properties of absorptive elastic and inelastic differential cross sections

Abstract

We consider the scattering processes a+b→a'+b', with a, b, a', b' specifying the particles involved as well as their helicities, and n, n' denoting the momentum directions of a, a' respectively. We show that in the c.m. system, k²_a(dσ^A/dΩ)_n'a'b';nab=Σ^∞_l=0(2l+1)P_l(n·n')(σ_l(s))_a'b';ab where dσ/dΩ^A is the contribution of the absorbed part to differential cross section, k^a is the magnitude of the momentum of a, √s the total energy, and σ_l(s) is a matrix with non-negative eigenvalues.