Single-Pion Photoproduction in a Model of Higher Baryon Couplings

Abstract

Pion photoproduction off nucleons via $s$-channel resonances up to a total c.m. energy of \ensuremath{\sim} 2 GeV, and also the electromagnetic decay widths of such resonances, are investigated in a recently proposed unified model of $\overline{B}{B}_{L}P$ and $\overline{B}{B}_{L}V$ couplings. In this phenomenological model, which uses the quark language only formally, the couplings $\overline{B}{B}_{L}P$ of baryon resonance (${B}_{L}$) with pseudoscalar ($P$) mesons in broken SU(6) \ifmmode\times\else\texttimes\fi{} O(3) are extended to incorporate electromagnetic interactions through symmetry for $\overline{B}{B}_{L}V$ couplings, together with the principle of vector-meson dominance. These supermultiplet ${L}^{P}\ensuremath{\rightarrow}{0}^{+}$ transitions are characterized by an empirical but relativistically invariant multiplying form factor, for which two different forms are considered. The calculated electromagnetic decay widths for the baryon resonances ${Y}^{*}(1520)$ and $\ensuremath{\Delta}(1238)$ are in extremely good agreement with experiment. For the other resonances no direct experimental data are available, and comparison has been made with other contemporary analyses. The results for the reactions $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p$, $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}n$, and $\ensuremath{\gamma}n\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}p$ are also presented with reference to the following types of data: (i) total cross sections, (ii) the angular distribution of the differential cross sections, (iii) the energy dependence of the cross sections at fixed angles (especially $\ensuremath{\theta}=0$, $\ensuremath{\pi}$), and (iv) recoilproton polarization. The agreement with the experimental data in all these respects is extremely good, thus suggesting that the direct $s$ channel makes a large and dominant contribution to the amplitude in the intermediate-energy region. The only discrepancy lies in the forward direction for charge-exchange processes, where the $t$-channel pion pole is known to be important, yet a partial simulation of duality seems to be indicated by our results. Also, the qualitative features of pionic photoproduction are reasonably well reproduced by our model. The Moorhouse selection rule for spin quartet states and a charge selection rule proposed recently by Copley et al. are satisfied in the limit of ${m}_{\ensuremath{\rho}}={m}_{\ensuremath{\omega}}$ in our model. The most prominent resonances turn out to be ${P}_{11}$, ${P}_{33}$, ${D}_{13}$, ${F}_{15}$, and ${F}_{37}$.