Drell-Yan Transverse-Momentum Spectra at N$^3$LL$'$ and Approximate N$^4$LL with SCETlib

TL;DR

This paper presents highly precise QCD predictions for W and Z boson transverse momentum spectra at the LHC, combining resummed and fixed-order calculations to cover the entire spectrum with detailed uncertainty analysis.

Contribution

It introduces state-of-the-art resummed perturbation theory calculations at N$^3$LL$'$ and approximate N$^4$LL accuracy, incorporating comprehensive TMD dynamics and uncertainty estimates.

Findings

Predictions cover the full pT spectrum from nonperturbative to fixed-order regions.

Explicit modeling of TMD dynamics with a single effective nonperturbative function.

The results provide strong constraints for parton distribution functions at N$^3$LO.

Abstract

We provide state-of-the-art precision QCD predictions for the fiducial $W$ and $Z$ boson transverse momentum spectra at the LHC at N$^3$LL$'$ and approximate N$^4$LL in resummed perturbation theory, matched to available $\mathcal{O}(\alpha_s^3)$ fixed-order results. Our predictions consistently combine all information from across the spectrum in a unified way, ranging from the nonperturbative region of small transverse momenta to the fixed-order tail, with an emphasis on estimating the magnitude of residual perturbative uncertainties, and in particular of those related to the matching. Parametric uncertainties related to the strong coupling, the collinear PDFs, and the nonperturbative transverse momentum-dependent (TMD) dynamics are studied in detail. To assess the latter, we explicitly demonstrate how the full complexity of flavor and Bjorken $x$-dependent TMD dynamics can be captured by a single, effective nonperturbative function for the resonant production of any given vector boson at a given collider. We point out that the cumulative $p_T^Z$ cross section at the level of precision enabled by our predictions provides strong constraining power for PDF determinations at full N$^3$LO.