Probing the Small-x Gluon Tomography in Correlated Hard Diffractive Dijet Production in Deep Inelastic Scattering

We investigate the close connection between the quantum phase space Wigner distribution of small-x gluons and the color dipole scattering amplitude, and we propose studying it experimentally in the hard diffractive dijet production at the planned electron-ion collider. The angular correlation between the nucleon recoiled momentum and the dijet transverse momentum probes the nontrivial correlation in the phase space Wigner distribution. This experimental study not only provides us with three-dimensional tomographic pictures of gluons inside high energy protons-it gives a unique and interesting signal for the small-x dynamics with QCD evolution effects.