Infrared finite coupling in Sudakov resummation: the precise set-up

Abstract

I show that Sudakov resummation takes a transparent form if one deals with the second logarithmic derivative of the short distance coefficient functions for deep inelastic scattering and the Drell-Yan process. A uniquely defined Sudakov exponent emerges, and the constant terms not included in the exponent are conjectured to be given by the second logarithmic derivative of the massless quark form factor. The precise framework for the implementation of the dispersive approach to power corrections is set-up, yielding results in agreement with infrared renormalon expectations, but which are not tied to the single (dressed) gluon exchange approximation. Indications for a Banks-Zaks type of perturbative fixed point in the Sudakov effective coupling at low N_f are pointed out. Existence of a fixed point in the Sudakov coupling is argued to imply its universality.