# Structure Function F_1 singlet in Double-Logarithmic Approximation

## TL;DR

This paper derives the small-x asymptotics of the DIS structure function F_1 singlet in the Double-Logarithmic Approximation, revealing a Regge form with a high intercept, emphasizing the importance of DLA in QCD processes.

## Contribution

It provides an explicit expression for F_1 in DLA including running coupling effects and demonstrates its Regge-like small-x behavior with a specific intercept.

## Key findings

- F_1 exhibits Regge form with intercept 1.066 at small x.
- Small-x asymptotics depend on Q^2/x^2.
- DLA expressions are significant for QCD processes involving vacuum exchanges.

## 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.