Drell--Yan lepton pair production at low invariant masses: transverse-momentum resummation and non-perturbative effects in QCD

TL;DR

This work addresses the accurate prediction of the Drell–Yan lepton-pair $q_T$ spectrum over $M$ from 4 GeV to the $Z$ peak by integrating state-of-the-art perturbative QCD: resummation to N$^4$LL matched to N$^4$LO-accurate fixed order for large $q_T$. The authors implement a minimally parameterized non-perturbative form factor in the impact-parameter space and fit it to a broad set of data, achieving excellent agreement across fixed-target and collider experiments. A key outcome is the precise extraction of the Collins–Soper kernel, connected to the $q_T$ evolution of TMDs, with results compatible with other global determinations. The publicly available DYTurbo tool enables rapid, precise predictions for arbitrary cuts, supporting future global analyses and precision tests of QCD and electroweak physics in the Drell–Yan sector.

Abstract

We consider the transverse-momentum ($q_T$) distribution of Drell-Yan lepton pairs produced with invariant masses ($M$) from low values up to the $Z$-boson peak ($4\leq M \leq 116$~GeV). We present perturbative predictions obtained by consistently combining the resummation of logarithmically enhanced QCD corrections at small $q_T$ ($q_T \ll M$) up to next-to-next-to-next-to-next-to-leading logarithmic accuracy with the available fixed-order calculations at next-to-next-to-leading order (i.e. $\mathcal{O}(α_S^3)$) valid at large $q_T$. For very low $q_T$ ($q_T\sim Λ_{\mathrm{QCD}}$), non-perturbative (NP) QCD effects become dominant and have been included through a NP form factor with a small number of free-parameters. We compare our results with multiple experimental datasets from hadron colliders, finding excellent agreement between theory and data. By fitting the NP parameters, we achieve a precise extraction of the NP form factor and the so-called Collins-Soper kernel.

Figures (6)

• Figure 1: Graphical representation of the correlation matrix for the free parameters of fit.
• Figure 2: Comparison between theoretical predictions and experimental data for the Drell–Yan cross section differential in $q_T$ from the E605 experiment. The left and right panels correspond to the invariant mass bins $7 < M < 8$ GeV and $11.5 < M < 13.5$ GeV, respectively. The orange bands represent the PDF uncertainty from the MSHT20an3lo set.
• Figure 3: Comparison between theoretical predictions and experimental data for the Drell–Yan cross section differential in $q_T$ from the E288 experiment, in the invariant mass bin $5 < M < 6$ GeV. The left, center, and right panels correspond to beam energies of $E_{\text{beam}} = 200$ GeV, $300$ GeV, and $400$ GeV, respectively. The orange bands represent the PDF uncertainty from the MSHT20an3lo set.
• Figure 4: Comparison between theoretical predictions and experimental data for the Drell–Yan cross section differential in $q_T$ from the E288 experiment, in the invariant mass bin $6 < M < 7$ GeV. The left, center, and right panels correspond to beam energies of $E_{\text{beam}} = 200$ GeV, $300$ GeV, and $400$ GeV, respectively. The orange bands represent the PDF uncertainty from the MSHT20an3lo set.
• Figure 5: Comparison between theoretical predictions and high-energy Drell–Yan data at the $Z$-boson peak. The left panel corresponds to the CDF measurement, while the right panel shows the ATLAS data at $\sqrt{s} = 8$ TeV in the central rapidity region $|y| < 0.4$.