Next-to-Next-to-Leading Logarithms in Four-Fermion Electroweak Processes at High Energy

TL;DR

This work addresses the resummation of electroweak Sudakov logarithms in high-energy neutral-current four-fermion processes. Using an evolution equation framework, the authors derive NNLL (next-to-next-to-leading-log) corrections to massless four-fermion amplitudes, first for the Abelian form factor and then for the full non-Abelian four-fermion case, including infrared QED subtractions and matching at the electroweak scale. They present explicit one- and two-loop results, showing that NNLL terms can be numerically comparable to or larger than LL/NLL terms, but sizable cancellations reduce the net two-loop corrections to roughly 1–2% in TeV-range cross sections and asymmetries. The analysis demonstrates that NNLL electroweak corrections are largely insensitive to the details of gauge-boson mass generation and Higgs-sector specifics, providing a robust framework for precision predictions at future high-energy colliders.

Abstract

We sum up the next-to-next-to-leading logarithmic virtual electroweak corrections to the high energy asymptotics of the neutral current four-fermion processes for light fermions to all orders in the coupling constants using the evolution equation approach. From this all order result we derive finite order expressions through next-to-next-to leading order for the total cross section and various asymmetries. We observe an amazing cancellation between the sizable leading, next-to-leading and next-to-next-to-leading logarithmic contributions at TeV energies.