The Quark Form Factor at Higher Orders
S. Moch, J. A. M. Vermaseren, A. Vogt
TL;DR
This work advances the understanding of infrared structure in massless QCD by deriving the complete pole terms of the quark form factor at three loops and extending the resummation of Sudakov logarithms to NNl accuracy. By exploiting high-order DIS structure-function results and the evolution equations for the form factor, the authors obtain explicit epsilon-expanded expressions for the form factor and its associated G- and A-series, fixing the leading poles to all orders. They also analyze the time-like vs space-like ratio, provide a fourth-order prediction for the Drell-Yan relevant quantity, and discuss universality with QED and MSYM through highest-transcendentality. Together, these results sharpen the understanding of infrared factorization in QCD amplitudes and offer precise inputs for cross-sections and for exploring non-QCD gauge theories.
Abstract
We study the electromagnetic on-shell form factor of quarks in massless perturbative QCD. We derive the complete pole part in dimensional regularization at three loops, and extend the resummation of the form factor to the next-to-next-to-leading contributions. These results are employed to evaluate the infrared finite absolute ratio of the time-like and space-like form factors up to the fourth order in the strong coupling constant. Besides for the pole structure of higher-loop QCD amplitudes, our new contributions to the form factor are also relevant for the high-energy limit of massive gauge theories like QED. The highest-transcendentality component of our results confirms a result recently obtained in N=4 Super-Yang-Mills theory.