Infrared finite coupling in Sudakov resummation

TL;DR

This work argues for an infrared finite coupling framework to parametrize power corrections within Sudakov resummation, highlighting how specific combinations of Sudakov anomalous dimensions can acquire regular IR behavior at large Nf. It analyzes the tension with IR renormalons, proposing a resolution through the freedom to redefine exponentiated constant terms, and develops a large-Nf, SDG-based formalism to obtain IR-finite perturbative Sudakov couplings. A key result is the emergence of an IR finite coupling in the Drell-Yan process under natural exponentiation schemes, while DIS can exhibit controlled, limited power corrections depending on the constant-term input. The author then proposes a universal, non-perturbative large-Nf ansatz for the Sudakov effective coupling and outlines a phenomenology strategy at finite Nf that integrates left-over constants and potential NP corrections, offering an alternative to the shape function approach and suggesting directions for experimental tests.

Abstract

New arguments are presented to emphasize the interest of the infrared finite coupling approach to power corrections in the context of Sudakov resummation. The more regular infrared behavior of some peculiar combinations of Sudakov anomalous dimensions, free of Landau singularities at large Nf, is pointed out. A general conflict between the infrared finite coupling and infrared renormalon approaches to power corrections is explained, and a possible resolution is proposed, which makes use of the arbitrariness of the choice of exponentiated constant terms. A simple ansatz for a 'universal' non-perturbative Sudakov effective coupling at large Nf follows naturally from these considerations. In this last version, a new result is presented: the striking emergence of an infrared finite perturbative effective coupling in the Drell-Yan process at large Nf (at odds with the infrared renormalon argument) within the framework of Sudakov resummation for eikonal cross sections of Laenen, Sterman and Vogelsang. Some suggestions for phenomenology at finite Nf, alternative to the shape function approach, are given.