Renormalon Variety in Deep Inelastic Scattering

TL;DR

This paper analyzes infrared power corrections in non-singlet deep inelastic scattering using renormalon methods and contrasts them with the operator product expansion (OPE). It shows that multiple infrared parameters (e.g., $\lambda$, $m$, $\epsilon$, $\Lambda_{QCD}$) can drive $1/Q^2$ corrections, and that the predicted $x$-dependence is highly sensitive to the chosen infrared prescription and the argument of the running coupling. In particular, renormalon analyses with a gluon mass $\lambda$ reproduce dispersive results for $F_L$, while a Landau-pole ( $\Lambda_{QCD}$) approach can yield two arbitrary scales due to collinear divergences, especially for $F_2$, signaling infrared instability. The quark-mass treatment further reveals both kinematic Nachtmann-like contributions and genuine IR-sensitive pieces, with differing operator anomalous dimensions implying that power corrections are not infrared-safe and require independent higher-twist structure functions. Overall, the work highlights the contextual dependence and limitations of renormalon-based power corrections in DIS and clarifies when OPE and renormalon methods align or diverge.

Abstract

We discuss the renormalon-based approach to power corrections in non-singlet deep inelastic scattering structure functions and compare it with the general operator product expansion. The renormalon technique and its variations relate the power corrections directly to infrared-sensitive parameters such as the position of the Landau pole Λ_{QCD} or the infinitesimal gluon mass λ. In terms of the standard OPE these techniques unify evaluations of the coefficient functions and of matrix elements. We argue that in case of deep inelastic scattering there is a proliferation of competeing infrared sensitive parameters. In particular we consider the gluon and quark masses, virtuality of quarks and Λ_{QCD} as possible infrared cut offs and compare the emerging results. In the standard renormalon technique where Λ_{QCD} is the infrared parameter, the argument of the running coupling is crucial to obtain the correct x dependance of the structure functions. Finally we discuss the limitations of the use of the renormalon based methods for determining of the x dependance of the power corrections.