The anomaly lagrangian for the photoproduction of mesons on nucleons in the Skyrme model

Abstract

We construct the anomaly lagrangian involving baryons, mesons and photons in the Skyrme model. The simplest process described by this lagrangian is neutral pion photoproduction on nucleons. The value of the electric dipole amplitude E 0+ is calculated and compared with the experimental data. At the pion production threshold, we obtain E 0 + (anomaly)=2.99×10 −3 fm=2.12× 10 −3/ m π + . This value together with the low energy theorem prediction E 0 + (LET)=−2.4×10 −3/ m π + gives E 0 + =−0.28×10 −3/ m π + , which is in good agreement with the measured value of E 0 + =(−0.5±0.3)×10 −3/ m π + . This may reconcile the long-standing difference between the theoretical prediction and the experimental data.