Power Corrections and Renormalons in Deep Inelastic Structure Functions

TL;DR

This work shows that non-singlet deep inelastic scattering coefficient functions receive only two infrared renormalon–driven power corrections, scaling as $1/Q^2$ and $1/Q^4$, with calculable Bjorken-$x$ dependence. Using the dispersive BPY framework, the authors relate these corrections to two log-moments $A'_2$ and $A'_4$ of a low-scale effective coupling, deriving explicit coefficient functions $C_2(x)$ and $C_4(x)$ for $F_2$, $F_1$, $F_3$, and $g_1$ along with their Mellin moments. They provide numerical illustrations and argue that these two parameters could be fitted to data to model dominant higher-twist effects, offering a practical tool for incorporating power corrections into DIS analyses. The results highlight a potentially universal, infrared-finite interpretation of the dominant power corrections and outline avenues for extending the approach to higher orders and other processes.

Abstract

We study the power corrections (infrared renormalon contributions) to the coefficient functions for non-singlet deep inelastic structure functions due to gluon vacuum polarization insertions in one-loop graphs. Remarkably, for all the structure functions $F_1$, $F_2$, $F_3$ and $g_1$, there are only two such contributions, corresponding to $1/Q^2$ and $1/Q^4$ power corrections. We compute their dependence on Bjorken $x$. The results could be used to model the dominant higher-twist contributions.

Figures (2)

• Figure 1: Coefficients of $1/Q^2$ contributions to $F_2$ (solid), and to $F_1$ and $F_3$ (dashed).
• Figure 2: Coefficients of $1/Q^4$ contributions to $F_2$ (solid), $F_1$ (dashed) and $F_3$ (dot-dashed).