Low-$t$ Theorems for Charged-Pion Photoproduction

Low-$t$ theorems for charged-pion photoproduction are proven on the basis of gauge-invariance restrictions. They can be simply formulated by means of the minimal gauge-invariant extension of pion exchange (MPE). It is shown that whereas MPE leads in $\gamma N\to {\pi }^{\pm }N$ only to weak restrictions for $\frac{d\sigma }{\mathrm{dt}}$ near the forward direction ($\mathrm{}\left|t\right|\mathrm{}\lesssim {\mu }^2$), it does actually account for all the structure observed in $\gamma p\to {\pi }^{-}{\Delta }^{++}$ in this $t$ domain. Results for these reactions as well as the other charge modes of $\gamma N\to {\pi }^{\pm }\Delta$ are discussed and compared with experiment.