Pion photoproduction in the skyrme model and low-energy theorems

Abstract

Threshold pion photoproduction has been calculated for the nucleon, within the framework of the Skyrme model. The calculation involves two different types of coupling between the pion and the nucleon, either as a small amplitude fluctuation or as a chiral perturbation about the nucleon soliton solution. It is shown that a correct determination of the axial coupling constant in the chiral limit is a compulsory prerequisite in order to reproduce the leading term of the charged production (Kroll-Ruderman theorem). Both methods fail to predict the higher order terms of low-energy theorems, which are of particular importance for the neutral pion production. This shortcoming is not due to the adiabatic treatment of the rotation matrices, but is a consequence of the approximations for the pion-nucleon coupling mechanism and of the neglect of the Dirac sea in the theory.