Abstract
We calculate the leading-order QED radiative corrections to the process $e^- p\rightarrow e^- p l^- l^+ $ in the soft-photon approximation, in two different energy regimes which are of relevance to extract nucleon structure information. In the low-energy region, this process is studied to better constrain the hadronic corrections to precision muonic Hydrogen spectroscopy. In the high-energy region, the beam-spin asymmetry for double virtual Compton scattering allows to directly access the Generalized Parton Distributions. We find that the soft-photon radiative corrections have a large impact on the cross sections and are therefore of paramount importance to extract the nucleon structure information from this process. For the forward-backward asymmetry the radiative corrections are found to affect the asymmetry only around or below the 1\% level, whereas the beam-spin asymmetry is not affected at all in the soft-photon approximation, which makes them gold-plated observables to extract nucleon structure information in both the low- and high-energy regimes.
Highlights
Double-virtual Compton scattering on a proton, the process γÃp → γÃp with initial and final virtual photons, is a prime process to study and test models describing the electromagnetic structure of the nucleon beyond the information contained in the elastic form factors.At low energies, it allows us to extract nucleon structure constants, which enter the expansion of the nucleon Compton amplitude
We study the effect of these corrections in the soft-photon approximation on the cross section and on the forward-backward asymmetry AFB, as well as on the beam-spin asymmetry A⊙
The process contains two distinct contributions: first, the spacelike and timelike Bethe-Heitler processes which only depend on the nucleon elastic form factors and second the double-virtual Compton scattering process
Summary
Double-virtual Compton scattering (dVCS) on a proton, the process γÃp → γÃp with initial and final virtual photons (γÃ), is a prime process to study and test models describing the electromagnetic structure of the nucleon beyond the information contained in the elastic form factors. A further extension of either the DVCS or TCS process in the high-energy near-forward region has been proposed through the e−p → e−pl−lþ reaction (with l− either an e− or μ−), which accesses the double deeply virtual Compton scattering (DDVCS) process with incoming spacelike photons and outgoing timelike photons. In the high-energy regime, we use the QCD factorization theorem to express the dVCS amplitude in terms of GPDs. In Sec. IV, we calculate the virtual radiative corrections in the soft-photon approximation from the three gauge invariant types of contributions.
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