Improved Upper Bound on the Imaginary Part of Elastic Scattering Amplitudes

Abstract

The method of Singh and Roy, which obtains a bound on the imaginary part of the elastic scattering amplitude, given ${\ensuremath{\sigma}}_{\mathrm{tot}}$ and ${\ensuremath{\sigma}}_{\mathrm{el}}$, is generalized to allow inclusion of other given data such as $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ at fixed points. A calculation is described in which one additional experimental point is given. The upper bound is compared with the experimental data for ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$, ${K}^{\ifmmode\pm\else\textpm\fi{}}p$, $\mathrm{pp}$, and $p\overline{p}$ elastic scattering at various energies in the nearforward direction. It is found that this single extra piece of given data extends by a factor of about 3 the range for which the original bound remained close to the data and at the largest $t$ value considered ($t\ensuremath{\approx}\ensuremath{-}0.5$ Be${\mathrm{V}}^{2}$) improves this bound by a factor of about 4.