Neutral pion photoproduction on the nucleon near threshold

Neutral pion photoproduction on the nucleon near threshold is investigated using a dynamical model. Analytic properties of the final-state interaction amplitude in the energy region near π⁺n production threshold are examined in detail. It is shown that the commonly used procedure, based on an analytical continuation of the K matrix to the unphysical region, is not compatible to an approach incorporating full off-energy-shell dynamics. Our calculation indicates that the final-state interaction amplitude derived from a dynamical model could involve large cancellation between the different pion photoproduction mechanisms. This leads to the surprising result that the final-state interaction effect due to the intermediate π⁰p state can be as important as that due to the π⁺n intermediate state. At threshold, we obtain E₀₊=-1.92 x 10^-3/m_π+. This number is close to the measured value of  E₀₊=-1.5 x 10^-3/m_π+. No violation of the low-energy theorem is required to obtain good agreement between the calculated total cross sections and experimental data from threshold to about 400-MeV incident photon energy.