Twist-2 Heavy Flavor Contributions to the Structure Function $g_2(x,Q^2)$

TL;DR

This work computes the twist-2 heavy-flavor contributions to the polarized structure function $g_2(x,Q^2)$ using a covariant parton model, demonstrating that these contributions satisfy the Wandzura–Wilczek relation with those of $g_1(x,Q^2)$ to all orders in $\alpha_s$. At leading order, the heavy-flavor piece of $g_1$ arises from gluon-initiated processes via a convolution with the polarized gluon density, while the corresponding $g_2$ piece is constrained by WW. A generating-functional formalism is developed to connect $g_1$ and $g_2$ and to project twist-2 terms by the $k^2\to 0$ limit. Numerical results indicate heavy-flavor effects of up to 5–10% in certain regions, emphasizing the need to include charm and bottom contributions in precision analyses of polarized DIS and in determinations of $\Lambda_{\rm QCD}$ and polarized PDFs.

Abstract

The twist--2 heavy flavor contributions to the polarized structure function $g_2(x,Q^2)$ are calculated. We show that this part of $g_2(x,Q^2)$ is related to the heavy flavor contribution to $g_1(x,Q^2)$ by the Wandzura--Wilczek relation to all orders in the strong coupling constant. Numerical results are presented.