Single- and Double-Pion Production by One-Pion Exchange and a Comparison with Experimental Data between 1.6 and20 GeVc

Abstract

A detailed comparison has been made between predictions of elementary one-pion exchange (OPE) and existing experimental data. The Benecke-D\"urr (BD) parametrization was used to describe the vertex functions. The BD parametrization has one free parameter $R$ for each vertex. The momentum transfer ($t$) distributions as measured between 1.6 and $10 \frac{\mathrm{GeV}}{c}$ for the reactions $\overline{p}p\ensuremath{\rightarrow}{\overline{\ensuremath{\Delta}}}^{\ensuremath{-}\ensuremath{-}}{\ensuremath{\Delta}}^{++}[\ensuremath{\Delta}\ensuremath{\equiv}\ensuremath{\Delta}(1236)]$, $\mathrm{pp}\ensuremath{\rightarrow}{\ensuremath{\Delta}}^{++}n$, ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\Delta}}^{++}{\ensuremath{\rho}}^{0}$, and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}n{\ensuremath{\rho}}^{0}$ were used to fit the parameters ${R}_{\ensuremath{\Delta}N\ensuremath{\pi}}$, ${R}_{\mathrm{NN}\ensuremath{\pi}}$, and ${R}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}$ which describe the $\mathrm{NN}\ensuremath{\pi}$, $\ensuremath{\Delta}N\ensuremath{\pi}$, and $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$ vertices. With the three-parameter fit an excellent description of the data is achieved for $|t|<1$ Ge${\mathrm{V}}^{2}$ at all energies, a result which independently of any model demonstrates that the energy dependence of these reactions is that of elementary OPE. From the $R$ parameters, values for various pionic rms radii were deduced: $〈{{{r}_{\mathrm{NN}\ensuremath{\pi}}}^{2}〉}^{\frac{1}{2}}=1.06\ifmmode\pm\else\textpm\fi{}0.04$ F, $〈{{{r}_{\ensuremath{\Delta}N\ensuremath{\pi}}}^{2}〉}^{\frac{1}{2}}=0.86\ifmmode\pm\else\textpm\fi{}0.02$ F, and $〈{{{r}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}}^{2}〉}^{\frac{1}{2}}=0.65\ifmmode\pm\else\textpm\fi{}0.05$ F. The $\mathrm{NN}\ensuremath{\pi}$ and $\ensuremath{\Delta}N\ensuremath{\pi}$ values agree with results from $\ensuremath{\pi}N$ and $\mathrm{ep}$ scattering. As a further consistency check, the BD parametrization was used to describe the ($\frac{3}{2},\frac{3}{2}$) pion nucleon phase shift ${\ensuremath{\delta}}_{33}$ in the neighborhood of the $\ensuremath{\Delta}$. A good fit to the ${\ensuremath{\delta}}_{33}$ data is found. The value of ${R}_{\ensuremath{\Delta}N\ensuremath{\pi}}$ agrees within 20% with that from the fit to the $t$ distributions. The OPE predictions were calculated for the reactions ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{-}}$ in absolute magnitude and compared with available experimental results on effective-mass and momentum-transfer distributions at beam momenta between 2.1 and $20 \frac{\mathrm{GeV}}{c}$. In general, the shape of the distributions is quite well reproduced. Bumps which are present in the $p2\ensuremath{\pi}$ mass distributions, and which may be taken as evidence for the production of nucleon isobars, can be understood as reflections of the OPE process. The OPE contributions are substantial at all energies; they amount to \ensuremath{\sim}40% near threshold and increase to \ensuremath{\sim}90% at $20 \frac{\mathrm{GeV}}{c}$, in contrast to the naive expectation that at higher energies the exchange of particles with higher spin will dominate.