Wide-Angle Pair Production and Quantum Electrodynamics at Small Distances

Abstract

Wide-angle photoproduction of high-energy electron-positron pairs in hydrogen is proposed and analyzed as a test of quantum electrodynamics at distances ≲${10}^{-13\mathrm{}}$ cm. The effect of proton structure can be removed in terms of the two form factors measured in the elastic electron-proton scattering process. Cross sections are presented for two classes of pair production experiments: (1) those detecting one of the final particles, and (2) coincidence experiments. In addition to kinematic, anomalous moment, and nucleon form-factor corrections to the Bethe-Heitler formula, dynamical corrections to the proton current and radiative corrections are calculated. The final theoretical formula is believed to be accurate to 2%. A simple cutoff model suggests that a 5% accuracy in an experiment of type (1) tests the electron propagator at distances ∼0.7×${10}^{-13\mathrm{}}$ cm, while a 10% accuracy in a coincidence arrangement of type (2) probes the electron propagator at ∼0.3×${10}^{-13\mathrm{}}$ cm.