Helicity Evolution at Small-x

TL;DR

This paper develops small-x helicity evolution equations that incorporate saturation effects, enabling the calculation of polarized parton distributions and structure functions with resummed logarithmic contributions.

Contribution

It introduces a new operator-based formalism for small-x helicity evolution equations that include saturation effects and are valid in large-Nc limits, extending previous approaches.

Findings

Derived evolution equations for helicity TMDs and PDFs

Equations include saturation effects and resummation of logarithms

Map onto known ladder limit equations in specific approximations

Abstract

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin.