Power Counting the Small-$x$ Observables

We emphasize the importance of applying power counting to the small-$x$ observables, which introduces novel soft contributions usually missing and allows for a unified treatment of the Balitsky-Kovchegov (BK) evolution and various Sudakov logarithms. We use $pA \to h(p_{h\perp})X$ at forward rapidity to highlight how the power counting yields a partonic cross section with collinear and soft sectors. We show how the kinematic constraints can be obtained in the soft sector without violating the power counting. We further show how one can resum the threshold Sudakov logarithms systematically to all orders in a re-factorized framework with additional collinear-soft contributions. Direct applications to other small-$x$ processes involving heavy particles, jet (sub-)observables and EIC physics are straightforward.