Unified theory ofNN→πd,πd→πd, andNN→NNreactions

Abstract

Using a set of equations that couple the $N-N$ to the $\pi -d$ channel and satisfy two- and three-body unitarity, we have studied in detail the reaction $\mathrm{pp}\to {\pi }^{+}d$, and $\pi d\to \pi d$ and $\mathrm{NN}\to \mathrm{NN}$ scattering. We find that the equations give a very good description of the differential cross sections and some of the polarization data for both $\overrightarrow{p}p\to {\pi }^{+}d$ and $\pi d\to \pi \overrightarrow{d}$ over the energy region $47<\mathrm{}{T}_{\pi }<256\mathrm{}$ MeV. We observe that for $\mathrm{pp}\to {\pi }^{+}d$, higher partial waves ($l_{\pi d}>2\mathrm{}$) contribute significantly to both the differential cross section and analyzing power. Including the $P_{11}\pi -N$ interaction and thus true absorption in $\pi -d$ elastic scattering, we find a cancellation between the pole and nonpole parts of the $P_{11}$ amplitude. A major part of the effect of true absorption is in $J^{\pi }=0^{+}$, which contributes little to the absorption cross section. The sensitivity of the results to the $D$ state of the deuteron and the choice of the $\pi \mathrm{NN}$ form factor is investigated. For $N-N$ scattering the agreement with the experimental phase shifts is better in the singlet than triplet channels. This is due to the absence of vector meson exchange in the calculation. The ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ phase shift exhibits resonance behavior in the absence of a pole in the amplitude.