We investigate the pion photoproduction off the nucleon in the $\Delta$ region in the framework of an effective chiral Lagrangian including pions, nucleon, and $\Delta \mathrm{}\left(1232\right).$ We work to third order in a small scale expansion with both $m_{\pi }$ and $M_{\Delta }-M_N$ treated as light scales. We note that in the $\Delta$ region, straightforward power counting breaks down as the amplitude becomes very large. To deal with this problem, we suggest that the appropriate way to compare the theoretical calculations with experimental data is via weighted integrals of the amplitudes through the $\Delta$ region.

• Received 29 January 1999

DOI:https://doi.org/10.1103/PhysRevC.60.064619