Spin structure function g_1 at small x and arbitrary $Q^2: Total resummaion of leading logarithms vs Standard Approach

TL;DR

This paper compares the standard DGLAP-based approach with a resummation method for the spin structure function g_1 at small x, showing that the latter naturally accounts for small-x behavior without singular fits and challenges the physical reality of certain power corrections.

Contribution

It introduces a resummation approach for g_1 at small x and arbitrary Q^2, demonstrating its advantages over the standard DGLAP-based approach and clarifying the origin of certain phenomenological fits.

Findings

Resummation of logarithms of x provides a natural description of g_1 at small x.

Singular initial parton densities are artifacts of extrapolating DGLAP into small x.

Power Q^2-corrections may not be physical but due to extrapolation artifacts.

Abstract

The Standard Approach (SA) for description of the structure function g_1 combines the DGLAP evolution equations and Standard Fits for the initial parton densities. The DGLAP equations describe the region of large Q^2 and large x, so there are not theoretical grounds to exploit them at small x. In practice, extrapolation of DGLAP into the region of large Q^2 and small x is done with complementing DGLAP with special, singular (~x^{-a}) phenomenological fits for the initial parton densities. The factors x^{-a} are wrongly believed to be of the non-perturbative origin. Actually, they mimic the resummation of logs of x and should be expelled from the fits when the resummation is accounted for. Contrary to SA, the resummaton of logarithms of x is a straightforward and natural way to describe g_1 in the small-x region. This approach can be used at both large and small Q^2 where DGLAP cannot be used by definition. Confronting this approach and SA demonstrates that the singular initial parton densities and the power Q^2-corrections (or at least a sizable part of them) are rather not real physical phenomena but the artefacts caused by extrapolating DGLAP into the small-x region.