Summing up Subleading Sudakov Logarithms

TL;DR

This work develops a region-based, dimensional-regularization framework to sum Sudakov logarithms for the Abelian form factor and four-fermion amplitudes in SU(N), deriving evolution equations and computing next-to-leading logarithmic contributions from one-loop inputs. It then solves these equations to resum leading and subleading logs, and applies the formalism to electroweak corrections in high-energy e+e− annihilation, extracting one- and two-loop LL and NL corrections and providing numerical estimates at TeV scales. The analysis clarifies the roles of hard, collinear, soft, and ultrasoft regions, and separates QED from weak effects to deliver practical predictions for future colliders. The methodology is extendable to higher logarithmic accuracy (NNLL) through higher-loop expansions and master integral analyses, offering a path toward precision electroweak predictions at multi-TeV energies.

Abstract

We apply the strategy of regions within dimensional regularization to find functions involved in evolution equations which govern the asymptotic dynamics of the Abelian form factor and four-fermion amplitude in the SU(N) gauge theory in the Sudakov limit up to the next-to-leading logarithmic approximation. The results are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in the $e^+e^-$ annihilation at high energy.