Asymmetricμ-Pair Photoproduction and Quantum Electrodynamics at Small Distances

Abstract

A sensitive test of the theory of quantum electrodynamics as applied to muons is analyzed in this paper. The test consists of photoproducing $\mu$-pairs in hydrogen such that the negative muon is produced at small angles with respect to the incident photon and with nearly all of the available energy. The positive muon and the recoil proton are not detected. The cross section is calculated from the Bethe-Heitler amplitude treating proton recoil exactly. The effect of proton structure is analyzed in terms of the two form factors measured by elastic electron-proton scattering. These form factors are approximated by a power series in the invariant squared four-momentum $q^2$ transferred to the nucleus. Radiative corrections appropriate for the experimental resolution are calculated and are shown to reduce the Bethe-Heitler cross section by about 5 percent. The cross section for muon pairs from the decay of known heavy vector resonances is found to be negligible. The flux of negative muons from the decay of a photoproduced ${\pi }^{-}$ is calculated and is shown to be a limiting factor in choosing the energy resolution of an experiment.