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Incoherent deeply virtual Compton scattering off $^4$He

Very recently, for the first time, the two channels of nuclear deeply virtual Compton scattering (DVCS), the coherent and incoherent ones, have been separated by the CLAS collaboration at JLab, using a $^4$He target. The incoherent channel, which can provide a tomographic view of the bound proton and shed light on its elusive parton structure, is thoroughly analyzed here in Impulse Approximation (IA). A convolution formula for the cross sections in terms of those for the bound proton is derived. Novel scattering amplitudes for a bound moving nucleon have been obtained and used. A state-of-the-art nuclear spectral function, based on the AV18 potential, exact in the two-body part, with the recoiling system in its ground state, and modelled in the remaining contribution, with the recoiling system in an excited state, has been used. Different parametrizations of the generalized parton distributions of the struck proton have been tested. A good overall agreement with the data for the beam spin asymmetry (BSA) is obtained. It is found that the predicted conventional nuclear effects are relevant in DVCS and in the competing Bethe-Heitler mechanism, but they cancel each other to a large extent in their ratio, to which the measured asymmetry is proportional. Besides, the calculated ratio of the BSA of the bound proton to that of the free one does not describe that estimated by the experimental collaboration. This points to possible interesting effects beyond the IA analysis presented here. It is therefore clearly demonstrated that the comparison of the results of a conventional realistic approach, as the one presented here, with future precise data, has the potential to expose quark and gluon effects in nuclei. Interesting perspectives for the next measurements at high luminosity facilities, such as JLab at 12 GeV and the future EIC, are addressed.