Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case

TL;DR

This paper calculates the quark-to-quark transverse parton distribution functions at NNLO, demonstrating the validity of a gauge-invariant definition beyond first order and providing key coefficients for advanced Q_T resummation in collider processes.

Contribution

It provides the first demonstration that the gauge-invariant operator definition of transverse PDFs is valid beyond the first non-trivial order and supplies necessary coefficients for NNLL Q_T resummation.

Findings

Validated gauge-invariant definition at NNLO

Derived coefficient functions for NNLL Q_T resummation

Enhanced understanding of transverse PDFs in QCD

Abstract

We present a calculation of the perturbative quark-to-quark transverse parton distribution function at next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first non-trivial order. We extract from our calculation the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic $Q_T$ resummation in a large class of processes at hadron colliders.