Renormalon Variety in Deep Inelastic Scattering

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.