Threshold pion photoproduction of nucleons in the chiral quark model

Abstract

In this paper, we show that the low energy theorem (LET) of 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 constraints on the internal structures of the nucleon. Changing from pseudovector to pseudoscalar quark-pion couplings generates an additional term at order μ=${\mathit{m}}_{\mathrm{\pi }}$/M only in the isospin amplitude ${\mathit{A}}^{\left(\mathrm{-}\right)}$. The role of the transitions between the nucleon and the resonance ${\mathit{P}}_{33}$(1232) or P-wave baryons is also discussed; we find that the leading contributions to the isospin amplitudes at O(${\mathrm{\mu }}^2$) are from the transition between the P-wave baryons and the nucleon, and from the charge radius of the nucleon. The leading contribution from the P-wave baryons only affects neutral pion production, and improves the agreement with data significantly. The transition between the resonance ${\mathit{P}}_{33}$(1232) and the nucleon only gives an order ${\mathrm{\mu }}^3$ correction to ${\mathit{A}}^{\left(\mathrm{-}\right)}$.