Angular Dependence of Scattering at High Energies

Experimental evidence indicates that for nonforward (and nonbackward) scattering angles θ, differential scattering cross sections fall off exponentially with increasing barycentric energy s; namely, dσdΩ~_s→∞e^-φ(s,cosθ), where φ(s, cosθ) is a positive quantity increasing as some power of s. From assumptions of boundedness and analyticity in cosθ, we obtain certain constraints on the cosθ dependence of the exponent function φ(s, cosθ).