We generalize the Bartels-Ermolaev-Ryskin approach for the g1 structure function at small-x [1,2] to determine the small-x asymptotic behavior of the orbital angular momentum distributions in QCD. We present an exact analytical solution of the evolution equation in the double logarithmic approximation and discuss its implications for the proton spin problem.

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.

We present a full evaluation of the deeply virtual Compton scattering cross section in the dipole framework in the small-x region. The result features the cosφ and cos2φ azimuthal angular correlations, which have been missing in previous studies based on the dipole model. In particular, the cos2φ term is generated by the elliptic gluon Wigner distribution of which the measurement at the planned electron-ion collider provides important information about the gluon tomography at small x. We also show the consistency with the standard collinear factorization approach based on the quark and gluon generalized parton distributions.

We compute the transverse single spin asymmetry in light hadron production p↑p→hX and p↑A→hX including the gluon saturation effect in the unpolarized nucleon/nucleus. In the forward (large-xF) region, the dominant contribution comes from the so-called derivative term associated with the soft gluonic pole. This leads to the cancellation of nuclear effects in AN which can be tested at the RHIC. We also show that the soft fermionic pole disappears in the saturation environment.

We investigate the contributions from the so-called elliptic gluon Wigner distributions to the rapidity and azimuthal correlations of particles produced in high energy pp and pA collisions by applying the double parton scattering mechanism. We compute the ‘elliptic flow’ parameter v2 as a function of the transverse momentum and rapidity, and find qualitative agreement with experimental observations. This shall encourage further developments with more rigorous studies of the elliptic gluon distributions and their applications in hard scattering processes in pp and pA collisions.

We introduce the semiclassical Wehrl entropy for the nucleon as a measure of complexity of the multiparton configuration in phase space. This gives a new perspective on the nucleon tomography. We evaluate the entropy in the small-x region and compare with the quantum von Neumann entropy. We also argue that the growth of entropy at small x is eventually slowed down due to the Pomeron loop effect.

We investigate the effect of soft gluon radiations on the azimuthal angle correlation between the total and relative momenta of two jets in inclusive and exclusive dijet processes. We show that the final state effect induces a sizable cos(2ϕ) anisotropy due to gluon emissions near the jet cones. The phenomenological consequences of this observation are discussed for various collider experiments, including diffractive processes in ultraperipheral pA and AA collisions, inclusive and diffractive dijet production at the EIC, and inclusive dijet in pp and AA collisions at the LHC.

We compute the twist-three fragmentation contribution to the transverse single spin asymmetry (SSA) in light hadron production p↑p→hX and p↑A→hX including the gluon saturation effect in the unpolarized nucleon/nucleus. Together with the results in our previous paper, this completes the full evaluation of the SSA in this process in the "hybrid" formalism. We argue that the dependence of SSAs on the atomic mass number in the forward region can elucidate the relative importance of the soft gluon pole contribution from the twist-three quark-gluon-quark correlation in the polarized nucleon and the twist-three fragmentation contribution from the final state hadron.

We show that the diffractive forward production of two quarkonia, especially the χcJ and ηc states, in proton-proton or proton-ion collisions can access the Weizsäcker-Williams gluon Wigner distribution of the proton. We use the hybrid factorization approach where the collinear, double gluon PDF is applied for one of the protons and the kT-dependent (Wigner or GTMD) distribution for the other. The production of quarkonia is treated in the NRQCD framework. A particularly concise formula is obtained for double χJ=1 production.

Diffractive dijet production at the electron-ion collider (EIC) has been proposed to study the gluon Wigner distribution at small-x. We investigate the soft gluon radiation associated with the final state jets and an all order resummation formula is derived. We show that the soft gluon resummation plays an important role to describe E791 data on π-induced diffractive dijet production at Fermilab. Predictions for the EIC are presented, and we emphasize that the soft gluon resummation is an important aspect to explore the nucleon/nucleus tomography through these processes.