An Exclusive Soft Function for Drell-Yan at Next-to-Next-to-Leading Order

TL;DR

This paper calculates the NNLO soft function for Drell-Yan processes within Soft Collinear Effective Theory, enabling more precise low transverse momentum resummation in particle physics.

Contribution

It provides the first NNLO calculation of the exclusive soft function for Drell-Yan, including finite parts and anomalous dimensions, advancing theoretical precision.

Findings

NNLO soft function results and finite parts provided

Anomalous dimension derived for the soft function

Facilitates NNLL accuracy in transverse momentum resummation

Abstract

We present next-to-next-to-leading-order (NNLO) results for an exclusive soft function that appears in a recently developed factorization theorem for transverse momentum distributions. The factorization theorem, derived using the Soft Collinear Effective Theory, involves both a soft function and unintegrated nucleon distribution functions fully differential in momentum coordinates. The soft function is given by the vacuum matrix element of soft Wilson lines and is also fully differential in all components. We give results and relevant technical details for the NNLO calculation of the soft function, including finite parts, and derive the corresponding anomalous dimension. These results are necessary for achieving low transverse momentum resummation at next-to-next-to-leading-logarithmic accuracy in this effective field theory approach with unintegrated distribution functions.