The Threshold Pion-Photoproduction of Nucleons In The Chiral Quark Model

In this paper, we show that the low energy theorem (LET) of the threshold pion-photoproduction can be fully recovered in the quark model. An essential result of this investigation is that the quark-pion operators are obtained from the effective chiral Lagrangian, and the low energy theorem does not require the constraints on the internal structures of the nucleon. The pseudoscalar quark-pion coupling generates an additional term at order $\mu=m_{\pi}/M$ only in the isospin amplitude $A^{(-)}$. The role of the transitions between the nucleon and the resonance $P_{33}(1232)$ and P-wave baryons are also discussed, we find that the leading contributions to the isospin amplitudes at $O(\mu^2)$ are from the transition between the P-wave baryons and the nucleon and the charge radius of the nucleon. The leading contribution from the P-wave baryons only affects the neutral pion production, and improve the agreement with data significantly. The transition between the resonance $P_{33}(1232)$ and the nucleon only gives an order $\mu^3$ corrections to $A^{(-)}$.