Pion Photoproduction,NNScattering, and Photoproduction Sum Rules

Abstract

The differential cross sections for pion photoproduction have been examined along with those for $\mathrm{pn}\ensuremath{\rightarrow}\mathrm{np}$ and $p\overline{p}\ensuremath{\rightarrow}n\overline{n}$ scattering. It is found that an $M=1$ pion parity-doublet fit is consistent with both sets of data if a full dynamical zero in the $N\overline{N}\ensuremath{\pi}$ vertex function is hypothesized. If a square-root-type dynamical zero is postulated, some problems with consistency between fits arise. In the former case, the zero is at ${t}_{0}\ensuremath{\approx}\ensuremath{-}0.05$ Ge${\mathrm{V}}^{2}$. In both fits the $M=0\ensuremath{\rho}$, ${A}_{2}$, and $B$ trajectories are introduced. The possibility of an $M=1$ parity-doublet-type conspiracy for the $B$ trajectory has also been investigated qualitatively. This assignment is suggested by a $B$-trajectory photoproduction finite-energy sum rule and by consistency requirements between phenomenological fits and the Bietti-Roy-Chu pion-photoproduction sum rule which predicts ${t}_{0}\ensuremath{\approx}\ensuremath{-}0.03$ Ge${\mathrm{V}}^{2}$. Additional experimental tests for an $M=1B$ trajectory are proposed.