Strip Approximation and the Shape of the Diffraction Peak

Abstract

It is pointed out that the sharpness of the diffraction peak is incompatible with the usual justification of the strip approximation to the Mandelstam representation. Discrepancies between the Regge residue functions needed to fit experiment and those obtained from dynamical calculations using the new form of the strip approximation are discussed. It is shown that if the correct shape of the diffraction peak is to be reproduced there are special requirements as to the form of the force—that it oscillate in sign within the strip—which are not satisfied by the Born approximation to that force. We indicate how the correct expression for the force may rectify this, and try to discover what difference having the right sort of residues would make in the slope of the trajectories in $\pi -\pi$ scattering, by imposing the experimental shape on the residues artificially. The trajectory slopes are found to be improved, but the drastic nature of the change produced by imposing the experimental form on the output residues makes a bootstrap impossible if only the Born approximation to the force is used.