Pion Photoproduction,NNScattering, and Photoproduction Sum Rules

Abstract

The differential cross sections for pion photoproduction have been examined along with those for $\mathrm{pn}\to \mathrm{np}$ and $p\overline{p}\to n\overline{n}$ scattering. It is found that an $M=1\mathrm{}$ pion parity-doublet fit is consistent with both sets of data if a full dynamical zero in the $N\overline{N}\pi$ 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 $t_0\approx -0.05\mathrm{}$ Ge${\mathrm{V}}^2$. In both fits the $M=0\mathrm{}\rho$, $A_2$, and $B$ trajectories are introduced. The possibility of an $M=1\mathrm{}$ 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 $t_0\approx -0.03\mathrm{}$ Ge${\mathrm{V}}^2$. Additional experimental tests for an $M=1\mathrm{}B$ trajectory are proposed.