Towards Precision Gluon Densities at Small $x$: From Resummation to Collider Observables

Abstract: Accurate gluon densities at small $x$ are essential for reducing theoretical uncertainties in collider predictions, yet remain one of the least constrained ingredients in global analyses. We report recent advances in the resummation of small-$x$ logarithms in the gluon sector, focusing on collinear distributions and their interplay with transverse-momentum-dependent formulations. Particular attention is paid to the impact of gluon-proton spin correlations and to the emergence of unintegrated gluon densities derived from resummed dynamics. These developments aim to fill the current precision gap in the small-$x$ region and enable robust applications to LHC and future-collider observables.