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In recent years, the theoretical foundations of small-x physics have made significant advances in two frontiers: higher-order (NLO) corrections and power-suppressed (sub-eikonal) corrections. Among the former are the NLO calculations of the linear (BFKL) and nonlinear (BK-JIMWLK) evolution equations, as well as cross sections for various processes. Among the latter are corrections to the whole framework of high-energy QCD, including new contributions from quarks and spin asymmetries. One common element to both of these frontiers is the appearance of collinear logarithms beyond the leading-order framework. The proper treatment of these logarithms is a major challenge in obtaining physical cross sections at NLO, and they lead to a new double-logarithmic resummation parameter which governs spin at small x. In this paper, I will focus on the role of these collinear logarithms in both frontiers of small-x physics, as well as give a brief sample of other recent advances in its theoretical foundations. The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.

Ultracentral collisions of heavy nuclei, in which the impact parameter is nearly zero, are especially sensitive to the details of the initial state model and the microscopic mechanism for collective flow. In a hydrodynamic “flow” picture, the final state momentum correlations are a direct response to the fluctuating initial geometry, although models of the initial geometry differ widely. Alternatively, dynamical mechanisms based in the color glass condensate (CGC) formalism can naturally lead to many-body correlations with very different systematics. Here we present a calculation of event-by-event elliptic flow in both the hydrodynamic and CGC paradigms and show that they can be qualitatively distinguished in ultracentral collisions of deformed nuclei. Specifically, the multiplicity dependence in such collisions is qualitatively opposite, with the CGC correlations increasing with multiplicity while the hydrodynamic correlations decrease. The consistency of the latter with experimental data on UU collisions appears to rule out a CGC-mediated explanation. We find that these qualitative features also persist in small deformed systems and can therefore be a valuable test of the microscopic physics in that regime. The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.

We determine the small-x asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large Nc. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small x. We then construct and solve novel small-x large-Nc evolution equations for the operator related to the dipole gluon helicity TMD. Our main result is the small-x asymptotics for the quark helicity distribution