Self-Consistent Multiple-Quark-Scattering Analysis of Consistency Relations amongpp,pp¯,πp, andππCross Sections

Abstract

The self-consistent multiple-quark-scattering (SCMQS) picture that was previously used to analyze and account for the details of the $\mathrm{pp}$ differential cross section at high energy is here extended to a comprehensive analysis of high-energy hadron scattering according to a set of consistency relations among $\mathrm{pp}$, $p\overline{p}$, $\ensuremath{\pi}p$, and $\ensuremath{\pi}\ensuremath{\pi}$ scattering cross sections and the form factors of $p$ and $\ensuremath{\pi}$. The consistency relations are a consequence of the SCMQS picture and the composite $S{U}_{3}$-quark model which has been suggested on non-group-theoretical grounds by the results of the SCMQS analysis of $\mathrm{pp}$ scattering, which also indicate very small pointlike quarks. The essence of the consistency relations is illustrated with the first-order single-quark-scattering analysis, and then they are analyzed according to the generalized higher-order SCMQS treatment. Results of the higher-order SCMQS analysis of $\ensuremath{\pi}p$ scattering indicate that the pion radius and the inverse diffraction width for $\ensuremath{\pi}\ensuremath{\pi}$ diffraction are significantly smaller than indicated by the previously reported results of the single-scattering treatment. We obtain here ${{r}_{\ensuremath{\pi}}}^{E}\ensuremath{\cong}0.36\ifmmode\pm\else\textpm\fi{}0.12$ F and ${\ensuremath{\xi}}_{\ensuremath{\pi}\ensuremath{\pi}}\ensuremath{\cong}4.8$ ${(\mathrm{B}\mathrm{e}\mathrm{V}/\mathit{c})}^{\ensuremath{-}2}$, respectively, for the pion charge radius and the inverse diffraction width for $\ensuremath{\pi}\ensuremath{\pi}$ scattering. Our results also indicate that the pion form factor falls off rapidly at high momentum transfer. Multiple-scattering effects and the interferences among them are seen to be very important characteristics of high-energy hadron-scattering phenomena.