Pion-proton bremsstrahlung calculation and the "experimental" magnetic moment of Delta ++(1232).

Abstract

A bremsstrahlung amplitude in the special two-energy-two-angle (TETAS) approximation, which is relativistic, gauge invariant, and consistent with the soft-photon theorem, is derived for the pion-proton bremsstrahlung ({pi}{sup +}{ital p}{gamma}) process near the {Delta}{sup ++}(1232) resonance. In order to take into account bremsstrahlung emission from an internal {Delta}{sup ++} line with both charge and the anomalous magnetic moment {lambda}{sub {Delta}}, we have applied a radiation decomposition identity to modify Low's standard prescription for constructing a soft-photon amplitude. This modified procedure is very general; it can be used to derive the TETAS amplitude for any bremsstrahlung process with resonance. The derived TETAS amplitude is applied to calculate all {pi}{sup +}{ital p}{gamma} cross sections which can be compared with the experimental data. Treating {lambda}{sub {Delta}} as a free parameter in these calculations, we extract the experimental'' magnetic moment of the {Delta}{sup ++}, {mu}{sub {Delta}}, from recent data. The extracted values of {mu}{sub {Delta}} are (3.7--4.2){ital e}/(2{ital m}{sub {ital p}}) from the University of California, Los Angeles data and (4.6--4.9){ital e}/(2{ital m}{sub {ital p}}) from the Paul Scherrer Institute data. Here, {ital m}{sub {ital p}} is the proton mass.