Improved upper bound on the imaginary part of elastic scattering amplitudes

The method of Singh and Roy, which obtains a bound on the imaginary part of the elastic scattering amplitude, given σtot and σel, is generalized to allow inclusion of other given data such as dσdt 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 π±p, K±p, pp, and pp̄ 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-0.5 BeV2) improves this bound by a factor of about 4.