Unitarity Upper Bound on the Absorptive Parts of Elastic-Scattering Amplitudes

Abstract

We derive a unitarity upper bound on the absorptive part $A(s, t)$ of the elastic-scattering amplitude in the physical region. In the diffraction peak region the bound on $\frac{A(s, t)}{A(s, 0)}$ is a function only of the parameter $\frac{{{\sigma }_{\mathrm{tot}}}^2\mathrm{}(-t)\mathrm{}}{4\pi {\sigma }_{\mathrm{el}}}$. Assuming the diffraction scattering to be purely absorptive and spin independent we find the $\mathrm{pp}$, $\overline{p}p$, and ${\pi }^{\pm }p$ data to lie a little below the theoretical upper bound. Further the experimental curve of $\frac{X\left(t\right)\mathrm{}}{X\left(0\right)\mathrm{}}$ vs $-\frac{4tX\left(0\right)\mathrm{}}{{\sigma }_{\mathrm{el}}}$, where $X\left(t\right)\mathrm{}\equiv \frac{d\sigma }{\mathrm{dt}}$, seems "universal."