Nonsinglet Contributions to the Structure Function g1 at Small-x

TL;DR

This work analyzes the nonsinglet polarized structure function $g_1$ in the small-$x$ (Regge) regime using the double-logarithmic approximation of perturbative QCD. It shows that terms of the form $(\alpha_s \ln^2(1/x))^k$, absent in GLAP evolution, drive a stronger small-$x$ rise, and that non-ladder bremsstrahlung graphs further enhance this growth for polarized scattering. By formulating and solving an infrared evolution equation for the nonsinglet sector (including $i\pi$ contributions) via Mellin techniques, the authors identify the leading small-$x behavior with a rightmost branch point $\omega^{(-)}$, yielding a sizeable enhancement over GLAP and even larger relative to unpolarized expectations. The results imply potentially large deviations from standard extrapolations in the HERA kinematic range and establish a framework for the yet-unresolved singlet sector, where gluon-quark mixing will further shape the small-$x$ spin structure.

Abstract

Nonsinglet contributions to the $g_1(x,Q^2)$ structure function are calculated in the double-logarithmic approximation of perturbative QCD in the region $x \ll 1$. Double logarithmic contributions of the type $(α_s \ln ^2 (1/x))^k$ which are not included in the GLAP evolution equations are shown to give a stronger rise at small-x than the extrapolation of the GLAP expressions. Further enhancement in the small-x region is due to non-ladder Feynman graphs which in the DLA of the unpolarized structure functions do not contribute. Compared to the conventional GLAP method (where neither the whole kinematical region which gives the double logs nor the non-ladder graphs are taken into account) our results lead to a growth at small-x which, for HERA parameters, can be larger by up to factor of 10 or more.