s-Channel Dominance and Charge Ratios in High-Energy Pion Photoproduction

It is shown that an explicit quark model, or duality diagrams, imply certain charge ratios of the squares of the imaginary parts of the amplitudes for $\gamma N\to {\pi }^{\pm }N$ and $\gamma N\to {\pi }^{\pm }\Delta$, which are observed to hold in experiments on the high-energy cross sections $\frac{d\sigma }{\mathrm{dt}}$ for $-0.2\mathrm{}\ge t\ge -0.8\mathrm{}$ Ge${\mathrm{V}}^2$. A fixed-$t$ dispersion-relation calculation, using knowledge of the low-energy photoproduction amplitudes, suggests that this may be due to cancellation of the contribution of the low- and medium-energy $s$- and $u$-channel resonances to the real parts of the amplitudes, so that the $s$ channel dominates the dispersion integral, and the quark-model relations also apply to the real parts of the amplitudes. In the extreme forward direction [${\mathrm{}(-t)\mathrm{}}^{\frac{1}{2}}\lesssim 0.2$] the fixed-$t$ dispersion relations indicate that the $\gamma N\to {\pi }^{\pm }N$ amplitudes are predominantly real and dominated by the contributions to the dispersion relations of the Born approximation and other very-low-energy resonances. Some possible implications for purely hadronic reactions are discussed.