Theorem on the Shrinking of Diffraction Peaks

Abstract

It is shown that the width of a diffraction peak divided by $\frac{1}{2}\sigma (s, t=0)$ cannot decrease faster at high energies than a constant times ${\left(\ln s\right)}^{-6\mathrm{}}$. This follows from unitarity and analyticity in the largest Lehmann ellipse consistent with perturbation theory.