Forward Peak Structure in Quasi-Two-Body Reactions and Long-Range Pion Exchange

Abstract

We find that a coherent-droplet model with long-range pion exchange successfully fits the forward peak structure of the differential cross sections for ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\Delta}}^{++}$, ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{f}^{0}{\ensuremath{\Delta}}^{++}$, ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}n$, ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}p$, $\mathrm{pp}\ensuremath{\rightarrow}n{\ensuremath{\Delta}}^{++}$, ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{*0}(890)n$, and ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{*\ensuremath{-}}(890)p$. For $\ensuremath{-}{t}^{\ensuremath{'}}l0.02$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, the measured differential cross sections exhibit anomalous behaviors: spikes and dips and no structure. The different behaviors are explained mainly by the kinematic structure of pion-pole residues. In some of the reactions, the known magnitude of the pion-pole residue leads us to expect structures near ${t}^{\ensuremath{'}}=0$ which require data with higher statistical precision for confirmation. In ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{f}^{0}{\ensuremath{\Delta}}^{++}$ at 8 GeV/c, our model can explain the absence of an anomaly near ${t}^{\ensuremath{'}}=0$ in terms of the large distance from the physical region to the pion pole. However, this distance decreases with increasing energy, and our model predicts structure near ${t}^{\ensuremath{'}}=0$ in ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{f}^{0}{\ensuremath{\Delta}}^{++}$ at 16 GeV/c.