Projective Imaging of High-Energy Nuclei via Coherent Exclusive Vector Meson Production in Electron-Nucleus Collisions

One of the major goals of modern nuclear experiments is to study the distributions of gluons inside nuclei at high energy. A key measurement is the coherent exclusive vector meson (VM) production in diffractive electron-nucleus collisions, where the gluon spatial distribution inside the nucleus can be obtained through a Fourier transform of the squared nuclear momentum transfer ($|t|$) distribution. This research aims to overcome the two main obstacles of the $|t|$ measurement: limited precision in measuring $|t|$ arising from the momentum resolution of the outgoing electron and the overwhelming incoherent background. We demonstrate that by measuring the projected $|t|$ distribution along the direction perpendicular to the electron scattering plane, the effect of the outgoing electron's momentum resolution can be effectively mitigated, and the diffractive pattern is largely restored. Furthermore, we propose to measure the angular distribution of the VM's decay daughters to statistically remove the incoherent background.