Light-Cone Singularities and Transverse-Momentum-Dependent Factorization at Twist-3

TL;DR

This paper investigates the complexities of transverse-momentum-dependent factorization at twist-3 in Drell-Yan processes, highlighting the presence of light-cone singularities and proposing methods to properly factorize soft gluon effects.

Contribution

It introduces a regularization scheme for light-cone singularities at twist-3 and derives a nonhomogeneous Collins-Soper equation for TMD distributions, advancing the understanding of soft gluon effects.

Findings

Light-cone singularities exist at leading order of α_s.

A soft factor is necessary for proper factorization.

The Collins-Soper equation at twist-3 is nonhomogeneous.

Abstract

We study transverse-momentum-dependent factorization at twist-3 for Drell-Yan processes. The factorization can be derived straightforwardly at leading order of $\alpha_s$. But at this order we find that light-cone singularities already exist and effects of soft gluons are not correctly factorized. We regularize the singularities with gauge links off the light-cone and introduce a soft factor to factorize the effects of soft gluons. Interestingly, the soft factor must be included in the definition of subtracted TMD parton distributions to correctly factorize the effects of soft gluons. We derive the Collins-Soper equation for one of twist-3 TMD parton distributions. The equation can be useful for resummation of large logarithms terms appearing in the corresponding structure function in collinear factorization. However, the derived equation is nonhomogeneous. This will make the resummation complicated.