Soft factors for double parton scattering at NNLO

TL;DR

This paper demonstrates that the NNLO soft factors for double parton scattering can be expressed entirely in terms of the TMD soft factor, enabling a decomposition into sector-specific matrices and defining double parton distributions at NNLO.

Contribution

It introduces a method to relate double parton scattering soft factors to the TMD soft factor at NNLO, utilizing web diagram symmetry properties and generating functions.

Findings

Decomposition of DPS soft factors into sector-specific matrices.

Expression of rapidity anomalous dimensions in terms of TMD quantities.

NNLO web diagram generating function for Wilson lines with two light-like directions.

Abstract

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.