Evidence for infrared finite coupling in Sudakov resummation: a revised view-point

Abstract

I show that Sudakov resummation takes a particularly 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 I conjecture that the leftover constant terms not included in the exponent are given by the second logarithmic derivative of the massless quark form factor. The meaning of a previously obtained large $N_f$ evidence for an infrared finite perturbative Sudakov coupling is reconsidered. This coupling is reinterpreted as a Minkowskian coupling, making the introduction of a low-energy non-perturbative modification of the corresponding Euclidean coupling a priori necessary. Some hints for a Banks-Zaks type of fixed point in the Euclidean coupling at finite $N_f$ are nevertheless pointed out, and strong evidence is provided in favor of its universality. A criterion to select in a unique way the proper Euclidean Sudakov coupling relevant to the issue of power corrections is suggested.