Soft-Photon Analysis of Pion-Proton Bremsstrahlung and the Magnetic Moment of DELTA(1232)

We have rigorously derived a special two-energy -two-angle amplitude for the pi^ +/- pgamma process near the Delta(1232) resonance. In order to take into account bremsstrahlung emission from an internal Delta line with both charge and the anomalous magnetic moment lambda(lambda_ Delta for the Delta^ {++} and lambda_ Delta^' for the Delta^0), we have applied a radiation decomposition identity to modify Low's standard prescription for constructing a soft-photon amplitude. We have also used the special two-energy-two-angle amplitude to calculate all pi^+/- pgamma cross sections which can be compared with the experimental data. Treading lambda as a free parameter in these calculations, the magnetic moments of the Delta, mu_ Delta for the Delta^ {++} and mu_Delta ^' for the Delta ^0, have been extracted from the UCLA data and the SIN data. The average value of mu _Delta determined from the experimental data is 4.35 e/(2m_{p}) (m_{p} is the proton mass), which is in good agreement with the value 4.25 e/(2m_{p}) predicted by a modified SU(6) model. The average value of mu_Delta^' determined from the experimental data is 0.5 e/(2m _{p}), which is in accord with the value predicted by the SU(6) model. Finally, we show that the overall agreement between theory and experiment is excellent if the special two-energy-two-angle amplitude is used in the calculation with the extracted mu_Delta (or mu _Delta^') as an input.