Soft-collinear factorization and zero-bin subtractions

Abstract

We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) $\ensuremath{\Delta}$-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 $1/ϵ$ 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.