Unpolarized DIS structure functions in Double-Logarithmic Approximation

TL;DR

This paper analyzes the small-x behavior of unpolarized deep inelastic scattering structure functions F_1 and F_2 using double-logarithmic approximation, revealing a new Pomeron and distinct Q^2-dependence compared to other approaches.

Contribution

The paper provides explicit expressions for F_2 in DLA, confirms a new Pomeron controlling F_1's asymptotics, and predicts a universal Q^2 dependence differing from DGLAP and BFKL methods.

Findings

F_1's small-x asymptotics are governed by a new Pomeron unrelated to BFKL.

F_2 exhibits growth at small x due to a small positive intercept.

Derived relations between logarithms of F_1 and F_2 can be tested with experimental data.

Abstract

We present description of the DIS structure functions F_1 and F_2 at small $x$ obtained in double-logarithmic approximation (DLA). First we clarify our previous results on F_1 and then obtain explicit expressions for F_2. Our calculations confirm our previous result that the small-$x$ asymptotics of F_1 is controlled by a new Pomeron that has nothing to do with the BFKL Pomeron, though their intercepts are pretty close. The latter means that studying the small-x dependence of the unpolarized DIS cannot ascertain which of those Pomerons is actually involved. However, we predict a quite different and universal Q^2-dependence of F_1,F_2 in DLA compared to the approaches involving the both DGLAP and BFKL. On that basis, we construct simple relations between logarithms of F_1, F_2, which can be verified with analysis of experimental data. In contrast to F_1, the intercept controlling the small-x asymptotics of F_2 is very small but positive, which ensures growth of F_2 at small x.