Regge-Pole Model forppandp¯pElastic Scattering at High Energies

High-energy data for $\mathrm{pp}$ and $\overline{p}p$ elastic scattering are confronted with the simple Regge-pole model in an attempt to discover which features of these data, if any, are beyond the power of this model. The simplest representation, with only three poles ($P$, $P^{\prime }$, and $\omega$), gives a reasonable fit to all the data except the "dip" structure in the $\overline{p}p$ differential cross sections (DCS). Several types of parametrizations were tested, including various ghost-eliminating mechanisms, and all produced comparable fits. To account for the $\overline{p}p$ DCS structure, and simultaneously circumvent the factorization difficulties caused by the universal zero in the $\omega$ amplitude, a fourth pole (the ${\omega }^{\prime }$) was introduced. The four-pole parametrizations (several were tested) provide adequate fits to all the data, including the $\overline{p}p$ DCS structure, and in addition come much closer to satisfying the sum-rule constraints imposed, through factorization, by the $\pi N$ and $\mathrm{KN}$ analyses. For completeness, another vacuum-type pole (the $P^{\prime \prime }$) is introduced and five-pole fits parametrized as in cut models are compared with pure pole models. The results are somewhat ambiguous, showing that the high-energy differential and total cross sections, polarization, ratio of real to imaginary part, and Serpukhov slope data all together are still not sufficient for determining the differences between many possible parametrizations.