Transverse momentum dependent PDFs at N$^3$LO

TL;DR

This paper calculates the transverse momentum dependent parton distribution functions at N$^3$LO in QCD, enabling more precise predictions for Higgs and Drell-Yan processes and advancing the $q_T$ subtraction method.

Contribution

It provides the first N$^3$LO computation of TMD PDFs, including matching kernels and confirmation of the soft function, crucial for high-precision QCD phenomenology.

Findings

Computed TMD PDFs at N$^3$LO with harmonic polylogarithms.

Expressed matching kernels for all channels at N$^3$LO.

Confirmed the soft function for transverse momentum factorization at N$^3$LO.

Abstract

We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N$^3$LO. Our results are the last missing ingredient to extend the $q_T$ subtraction methods to N$^3$LO and to obtain resummed $q_T$ spectra at N$^3$LL$^\prime$ accuracy both for gluon as well as for quark initiated processes.