Low-Energy Theorem for Pion Photoproduction from the Hypothesis of Partially Conserved Axial-Vector Current

By using gauge invariance and the hypothesis of partially conserved axial-vector current, the pion-photoproduction amplitude at threshold is calculated to all orders in strong interactions neglecting terms of order ${\left(\frac{m_{\pi }}{M_N}\right)}^2$ but including terms of order $\frac{m_{\pi }}{M_N}$. The calculated cross section is consistent with experimental results for charged-pion photoproduction near threshold.