Low Energy Limit of Photopion-Production Amplitudes in Chiral Dynamics
Masataka Hosoda, Kazuhiko Ozaki · Progress of Theoretical Physics · 1969
In order to understand more deeply the dynamical basis of current algebra, we reexamine the low energy limit of the amplitudes for photopion-production by expanding the nonlinear phenomenological Lagrangian in powers of coupling constant and by calculating all graphs which have a topological structure of trees. In addition to Adler's consistency conditions, the low energy theorem of the amplitudes are obtained for S-, P- and D-wave productions of the final pion. The differential cross sections at threshold are also enumerated for γp →π+n, γn →π-p, γp →π0p and γn →π0n. These are compared with the experimental data.