Study of the Two-Charged-Particle Final States of 3.9-GeVcπ±pInteractions Including a Longitudinal-Momentum Analysis of the One-Pion-Production Channels

We have analyzed the two-prong final states in ${\pi }^{+}p$ interactions at 3.9 $\frac{\mathrm{GeV}}{c}$. Our result for elastic scattering is $\sigma$ (elastic) = 6.50±0.1 mb (statistical error only). We find the elastic slope to be 6.61±0.14 ${\left(\frac{\mathrm{GeV}}{c}\right)}^{-2\mathrm{}}$. We find the elastic forward cross section to be 40.0±1.4 $\frac{\mathrm{mb}}{{\left(\frac{\mathrm{GeV}}{c}\right)}^2}$. We have applied a longitudinal-momentum analysis to the one-pion-production channel. We find the cross section for the reaction ${\pi }^{+}+p\to {\pi }^{+}+{\pi }^0+p$ to be 2.30±0.06 mb and that for ${\pi }^{+}+p\to {\pi }^{+}+{\pi }^{+}+n$ to be 1.45±0.05 mb. For resonance-production cross sections in these channels we find $\Delta \mathrm{}\left(1236\right)=0.60\mathrm{}\pm 0.07$ mb, $\rho \mathrm{}\left(760\right)=0.86\mathrm{}\pm 0.06$ mb, and diffraction dissociation = 1.69±0.11 mb. We find that we can satisfactorily fit all distributions in the one-pion-production channel without assuming any phase-space production. In the missing-mass channel we observe dominant ${\Delta }^{++}\mathrm{}\left(1236\right)\mathrm{}$ production plus evidence for ${A_2}^{+}$ production.