Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution

TL;DR

This paper analyzes low-$x$ polarized DIS and SIDIS data using advanced small-$x$ helicity evolution equations, improving predictions for future EIC measurements and insights into proton spin contributions.

Contribution

It introduces a refined small-$x$ helicity evolution framework with realistic large-$N_c$ & $N_f$ limits, incorporating running coupling and SIDIS data for polarized parton distributions.

Findings

Anti-correlation between gluon and quark helicity PDFs.

Current data insufficient to fully constrain initial conditions.

Future EIC data will enable more precise predictions.

Abstract

We analyze the world polarized deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data at low values of $x < 0.1$, using small-$x$ evolution equations for the flavor singlet and nonsinglet helicity parton distribution functions (hPDFs). The hPDFs for quarks, antiquarks, and gluons are extracted and evolved to lower values of $x$ to make predictions for the future Electron-Ion Collider (EIC). We improve on our earlier work by employing the more realistic large-$N_c\, \& N_f$ limit of the revised small-$x$ helicity evolution, and incorporating running coupling corrections along with SIDIS data into the fit. We find an anti-correlation between the signs of the gluon and $C$-even quark hPDFs as well as the $g_1$ structure function. While the existing low-$x$ polarized DIS and SIDIS data are insufficient to constrain the initial conditions for the polarized dipole amplitudes in the helicity evolution equations, future EIC data will allow more precise predictions for hPDFs and the $g_1$ structure function for $x$ values beyond those probed at the EIC. Using the obtained hPDFs, we discuss the contributions to the proton spin from quark and gluon spins at small $x$.