Systematic study of ${\pi }^{\pm }p$, $K^{\pm }p$, $\mathrm{pp}$, and $\overline{p}p$ forward elastic scattering from $3 \mathrm{to} 6 \frac{\mathrm{GeV}}{c}$

Measurements of ${\pi }^{\pm }p$, $K^{\pm }p$, $\mathrm{pp}$, and $\overline{p}p$ elastic scattering are presented for incident momenta of 3, 3.65, 5, and $6 \frac{\mathrm{GeV}}{c}$ and momentum transfers typically $0.03 \mathrm{to} 1.8 \mathrm{Ge}{\mathrm{V}}^2$. The angle and momentum of the scattered particle were measured with the Argonne Effective Mass Spectrometer for 300 000 events, yielding 930 cross-section values with an uncertainty in absolute normalization of ±4%. Only the $K^{+}$ and proton data show any significant change in slope of the forward diffraction peak with incident momentum. The particle-antiparticle crossover positions are consistent with no energy dependence, average values being 0.14 ± 0.03, 0.190 ± 0.006, and 0.162 ± 0.004 Ge${\mathrm{V}}^2$ for $\pi$' s, $K$' s, and protons, respectively; these errors reflect both statistics and the ±1.5% uncertainty in particle-antiparticle relative normalization. Differences between particle and antiparticle cross sections isolate interference terms between amplitudes of opposite $C$ parity in the $t$ channel; these differences indicate that the imaginary part of the odd-$C$ nonflip-helicity amplitude has a $J_0\left(r{\mathrm{}(-t)\mathrm{}}^{\frac{1}{2}}\right)$ structure for $-t<\mathrm{}0.8\mathrm{}$ Ge${\mathrm{V}}^2$, as predicted by strong absorption models. The cross-section differences for $K^{\pm }$ and proton-antiproton are in qualitative agreement with the predictions of $\omega$ universality, the agreement improving with increasing energy. The corresponding quark-model predictions relating the ${\pi }^{\pm }$ and $K^{\pm }$ differences failed by more than a factor of 2. We have combined our ${\pi }^{\pm }$ cross sections with other data to better determine the $\pi N$ amplitudes in a model-independent way; results of this analysis are presented.