Using SCET to calculate electroweak corrections in gauge boson production

TL;DR

This work extends soft-collinear effective theory (SCET) to resum electroweak Sudakov logarithms in processes with massive gauge bosons in the final state. It introduces a Delta regulator to preserve soft-collinear factorization while handling collinear singularities, and systematically applies high- and low-scale matching with RG running to both transverse and longitudinal W bosons, leveraging the Goldstone equivalence for the latter. The authors derive explicit matching coefficients, anomalous dimensions, and low-scale matchings, yielding resummed expressions for the Sudakov form factors in a spontaneously broken SU(2) framework, with clear pathways to generalize to the full Standard Model. Overall, the paper provides a robust EFT-based approach for all-orders electroweak Sudakov resummation in high-energy gauge-boson production.

Abstract

We extend an effective theory framework developped in Refs. [1,2] to sum electroweak Sudakov logarithms in high energy processes to also include massive gauge bosons in the final state. The calculations require an additional regulator on top of dimensional regularization to tame the collinear singularities. We propose to use the Delta regulator, which respects soft-collinear factorization.

Figures (1)

• Figure 1: One loop diagrams in the effective theory. The wiggly line denotes a mass mode gauge boson and a wiggly line with an overlaid straight line indicates a collinear field. Wave function diagrams are not shown. html:<A name="ref-fig:1loop">html:</A> LAB: fig:1loop