Description of the spin structure function g_1 at arbitrary $x$ and arbitrary Q^2

TL;DR

This paper derives explicit expressions for the spin structure function g_1 valid across all x and Q^2, combining DGLAP evolution with resummation of leading logarithms and a shift for small Q^2, avoiding singular initial density factors.

Contribution

It introduces a unified approach for g_1 at arbitrary x and Q^2 by integrating DGLAP with leading logarithm resummation and a Q^2 shift, eliminating the need for singular initial densities.

Findings

Derived explicit expressions for g_1 at arbitrary x and Q^2.

Unified description covering small and large Q^2 regions.

Expressions do not require singular initial parton density factors.

Abstract

The explicit expressions describing the structure function g_1 at arbitrary x and Q^2 are obtained. In the first place, they combine the well-known DGLAP expressions for g_1 with the total resummation of leading logarithms of x, which makes possible to cover the kinematic region of arbitrary x and large Q^2. In order to cover the small-Q^2 region the shift Q^2 -> Q^2 + mu^2 in the large-Q^2 expressions for g_1 is suggested and values of mu are estimated. The expressions obtained do not require singular factors x^{-a} in the fits for initial parton densities.