Power Counting the Small-$x$ Observables

TL;DR

This paper develops a power counting framework for small-$x$ observables, unifying BK evolution and Sudakov logarithms, enabling systematic resummation and application to various high-energy processes.

Contribution

It introduces a novel power counting approach that captures soft contributions and unifies different resummation techniques in small-$x$ physics.

Findings

Power counting yields a unified treatment of BK evolution and Sudakov logs.

Kinematic constraints can be incorporated without breaking power counting.

Systematic resummation of threshold Sudakov logs is achieved in a re-factorized framework.

Abstract

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.