# Analysis of vector boson production within TMD factorization

## TL;DR

This paper develops a new scheme for TMD scale setting, performs a global fit of unpolarized TMD PDFs using NNLO calculations, and evaluates various nonperturbative models with implications for high-energy collider data analysis.

## Contribution

It introduces the $ zeta$-prescription for TMD scale fixation, enabling more accurate extraction of TMD PDFs from experimental data.

## Key findings

- The $ zeta$-prescription reduces perturbative logarithm effects.
- Most nonperturbative models are disfavored based on fit quality.
- The arTeMiDe code facilitates TMD phenomenology.

## Abstract

We present a comprehensive analysis and extraction of the unpolarized transverse momentum dependent (TMD) parton distribution functions, which are fundamental constituents of the TMD factorization theorem. We provide a general review of the theory of TMD distributions, and present a new scheme of scale fixation. This scheme, called the $\zeta$-prescription, allows to minimize the impact of perturbative logarithms in the large range of scales and does not generate undesired power corrections. Within $\zeta$-prescription we consistently include the perturbatively calculable parts up to next-to-next-to-leading order (NNLO), and perform the global fit of the Drell-Yan and Z-boson production, which include the data of E288, Tevatron and LHC experiments. The nonperturbative part of the TMDs are explored checking a large variety of models. We support the obtained results by a study of theoretical uncertainties, perturbative convergence, and dedicated study of the range of applicability of the TMD factorization theorem. The considered nonperturbative models present significant differences in the fitting behavior, which allow us to clearly disfavor most of them. The numerical evaluations are provided by the "arTeMiDe" code, which is introduced in this work and that can be used for current/future TMD phenomenology.