Soft-Collinear Factorization and Zero-Bin Subtractions

TL;DR

This paper investigates the Sudakov form factor in a broken gauge theory, emphasizing the importance of zero-bin subtractions for accurate factorization and anomalous dimension calculations, and clarifies their role in soft-collinear factorization.

Contribution

It introduces a new Delta-regulator for the Sudakov form factor and demonstrates the necessity of zero-bin subtractions for correct effective theory results.

Findings

Zero-bin subtractions depend on gauge boson mass M and are not scaleless.

Zero-bin subtractions are essential for correct anomalous dimensions and matching.

After subtraction, the form factor aligns with previous QCD results, clarifying the soft-collinear factorization process.

Abstract

We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) Delta -regulator. To be well-defined, the effective theory requires zero-bin subtractions for the collinear sectors. The zero-bin subtractions depend on the gauge boson mass M and are not scaleless. They have both finite and 1/epsilon contributions, and are needed to give the correct anomalous dimension and low-scale matching contributions. We also demonstrate the necessity of zero-bin subtractions for soft-collinear factorization. We find that after zero-bin subtractions the form factor is the sum of the collinear contributions 'minus' a soft mass-mode contribution, in agreement with a previous result of Idilbi and Mehen in QCD. This appears to conflict with the method-of-regions approach, where one gets the sum of contributions from different regions.