Diffractive deeply virtual Compton scattering (DiDVCS) is the process $gamma^*(- Q^2) + N rightarrow rho^0 + gamma^* (Q^2)+ N$, where N is a nucleon or light nucleus, in the kinematical regime of large rapidity gap between the $rho^0$ and the final photon-nucleus system, and in the generalized Bjorken regime where both photon virtualities $Q^2$ and $ Q^2$ are large. We show that this process has the unique virtue of combining the large diffractive cross sections at high energy with the tomographic ability of deeply virtual Compton scattering to scrutinize the quark and gluon content of nucleons and light nuclei. Its study at an electron-ion collider would enlighten the internal structure of hadrons.
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