QCD expectations for the spin structure function $g_1$ in the low $x$ region

TL;DR

This paper analyzes the low-$x$ behavior of the spin structure function $g_1$ using a formalism that includes unintegrated parton distributions, LO evolution, and double $ln^2(1/x)$ resummation, relevant for polarized HERA experiments.

Contribution

It introduces a formalism combining LO Altarelli-Parisi evolution with double $ln^2(1/x)$ resummation to study $g_1$ at low $x$, highlighting the roles of ladder and non-ladder diagrams.

Findings

Non-singlet $g_1$ dominated by ladder diagrams at low $x$.

Non-ladder bremsstrahlung terms are significant for the singlet $g_1$.

Predictions for polarized gluon distribution $ riangle G(x,Q^2)$ at low $x$.

Abstract

The structure function $g_1(x,Q^2)$ is analysed within the formalism based on unintegrated spin dependent parton distributions incorporating the LO Altarelli-Parisi evolution and the double $ln^2(1/x)$ resummation at low $x$. We quantitatively examine possible role of the latter for the small $x$ behaviour of the structure functions $g_1$ of the nucleon within the region which may be relevant for the possible polarized HERA measurements. We show that while the non-singlet structure function is dominated at low $x$ by ladder diagrams the contribution of the non-ladder bremsstrahlung terms is important for the singlet structure function. Predictions for the polarized gluon distribution $\Delta G(x,Q^2)$ at low $x$ are also given.