Self-Consistent Multiple-Quark-Scattering Analysis of Consistency Relations among $\mathrm{pp}$, $p\overline{p}$, $\pi p$, and $\pi \pi$ Cross Sections

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 $\mathrm{pp}$, $p\overline{p}$, $\pi p$, and $\pi \pi$ scattering cross sections and the form factors of $p$ and $\pi$. 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 $\pi p$ scattering indicate that the pion radius and the inverse diffraction width for $\pi \pi$ diffraction are significantly smaller than indicated by the previously reported results of the single-scattering treatment. We obtain here ${r_{\pi }}^E\cong 0.36\pm 0.12$ F and ${\xi }_{\pi \pi }\cong 4.8$ ${(\mathrm{B}\mathrm{e}\mathrm{V}/\mathit{c})}^{-2\mathrm{}}$, respectively, for the pion charge radius and the inverse diffraction width for $\pi \pi$ 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.