Unpolarized and spin-dependent DIS structure functions in Double-Logarithmic Approximation

TL;DR

This paper calculates the perturbative components of unpolarized and spin-dependent DIS structure functions in Double-Logarithmic Approximation, revealing differences due to non-ladder graphs and deriving their small-x asymptotics with implications for Pomeron contributions.

Contribution

It introduces a detailed calculation of F_1 and g_1 structure functions in DLA, highlighting the impact of non-ladder graphs and deriving their Regge asymptotics with different intercepts.

Findings

F_1 has an intercept greater than unity, indicating a new Pomeron contribution.

Small-x asymptotics of F_1 and g_1 are of Regge type with different intercepts.

Inappropriate use of asymptotics outside their validity region can mislead phenomenological models.

Abstract

We demonstrate how to calculate perturbative components of the structure functions F_1 (for unpolarized DIS) and g_1 (spin-dependent DIS) in Double-Logarithmic Approximation, studying separately the cases of fixed and running QCD coupling. We show that as long as only ladder graphs are accounted for (throughout the talk we use the Feynman gauge for virtual gluons) there is no difference at all between F_1 and g_1. However, accounting for contributions of non-ladder graphs brings an essential difference between them. Applying the Saddle-Point method to the obtained expressions for F_1 and g_1 allows us to arrive at their small-x asymptotics. The both asymptotics are of the Regge kind but with different intercepts. The intercept of F_1 proved to be greater than unity, so it is a new contribution to Pomeron. Finally, we discuss the applicability region of the Regge asymptotics and demonstrate that inappropriate replacement of F_1 and g_1 by their asymptotics outside the applicability region can lead to introducing phenomenological Pomerons for both unploarized and spin-dependent processes.