Structure Function F_1 singlet in Double-Logarithmic Approximation
Abstract
We calculate the perturbative component of the DIS structure function F_1 singlet in the Double-Logarithmic Approximation (DLA) and account at the same time for the running QCD coupling effects. By constructing and solving evolution equations accounting for the both x- and Q^2- evolutions, we obtain the explicit expression for F_1 and, applying the saddle-point method, calculate its small-x asymptotics which proves to be of the Regge form with the intercept = 1.066. Its large value compensates for the lack of the factor 1/x in the DLA contributions. Such fast growth at small x proves that the DLA expressions are quite important for description of all QCD processes involving the vacuum (Pomeron) exchanges. We also obtain that the small-x asymptotics of F_1 depend on a single variable Q^2/x^2 and show that the small-x asymptotics reliably represent F_1 at x = 10^{-6} or less.
Cite
@article{arxiv.1706.08371,
title = {Structure Function F_1 singlet in Double-Logarithmic Approximation},
author = {B. I. Ermolaev and S. I. Troyan},
journal= {arXiv preprint arXiv:1706.08371},
year = {2018}
}
Comments
11 pages, 3 figures Relations between F_1 and F_2 are discussed in more detail. Comment on singular inputs added