Soft factors for double parton scattering at NNLO

A bstract We show at NNLO that the soft factors for double parton scattering (DPS) for both integrated and unintegrated kinematics, can be presented entirely in the terms of the soft factor for single Drell-Yan process, i.e. the transverse momentum dependent (TMD) soft factor. Using the linearity of the logarithm of TMD soft factor in rapidity divergences, we decompose the DPS soft factor matrices into a product of matrices with rapidity divergences in given sectors, and thus, define individual double parton distributions at NNLO. The rapidity anomalous dimension matrices for double parton distributions are presented in the terms of TMD rapidity anomalous dimension. The analysis is done using the generating function approach to web diagrams. Significant part of the result is obtained from the symmetry properties of web diagrams without referring to explicit expressions or a particular rapidity regularization scheme. Additionally, we present NNLO expression for the web diagram generating function for Wilson lines with two light-like directions.