Lower Bounds on the Shrinking of Diffraction Peaks

Lower bounds on the width of a diffraction peak are found using unitarity and analyticity in $cos\theta$ in Lehmann-type ellipses. When the forward elastic-scattering amplitude is predominantly imaginary, the lower bound obtained is proportional to ${\left(\ln s\right)}^{-2\mathrm{}}$. In deriving this result no restrictions, except those imposed by unitarity and analyticity, were made concerning the asymptotic behavior of the total cross section.