Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order

TL;DR

This paper provides a detailed next-to-next-to-leading order analysis of unpolarized transverse momentum dependent parton distribution and fragmentation functions, including new results for gluon fragmentation functions and their phenomenological relevance.

Contribution

It offers the first comprehensive NNLO calculation of TMDs and their matching coefficients for all flavors, including new results for gluon fragmentation functions at two loops.

Findings

Matching coefficients are crucial for TMD phenomenology.

First-time calculation of gluon TMD fragmentation functions at two loops.

Recovery of known PDFs and new results for fragmentation functions.

Abstract

The transverse momentum dependent parton distribution/fragmentation functions (TMDs) are essential in the factorization of a number of processes like Drell-Yan scattering, vector boson production, semi-inclusive deep inelastic scattering, etc. We provide a comprehensive study of unpolarized TMDs at next-to-next-to-leading order, which includes an explicit calculation of these TMDs and an extraction of their matching coefficients onto their integrated analogues, for all flavor combinations. The obtained matching coefficients are important for any kind of phenomenology involving TMDs. In the present study each individual TMD is calculated without any reference to a specific process. We recover the known results for parton distribution functions and provide new results for the fragmentation functions. The results for the gluon transverse momentum dependent fragmentation functions are presented for the first time at one and two loops. We also discuss the structure of singularities of TMD operators and TMD matrix elements, crossing relations between TMD parton distribution functions and TMD fragmentation functions, and renormalization group equations. In addition, we consider the behavior of the matching coefficients at threshold and make a conjecture on their structure to all orders in perturbation theory.