Production of Z-bosons in the parton branching method

TL;DR

This work demonstrates that Z-boson production in Drell–Yan processes at the LHC can be described accurately by combining Parton Branching (PB) TMD parton distributions—fitted to inclusive DIS data at NLO—with NLO Drell–Yan calculations via MC@NLO. The PB framework evolves TMDs using angular ordering, Sudakov factors, and a data-driven starting distribution, yielding predictions for $p_{\rm T}$, rapidity, and $\phi^*$ that agree with ATLAS measurements, with scale uncertainties dominating over TMD uncertainties. The study finds very small TMD-related uncertainties (order $\sim$2%) in most regions, while the lowest $p_{\rm T}$ bin shows sensitivity to the intrinsic $k_t$ distribution, underscoring the role of nonperturbative TMD contributions. Predictions for 13 TeV show continued compatibility without parameter tuning, highlighting the PB-TMD approach as a robust, data-constrained method for precise collider phenomenology and potential constraints on nonperturbative TMD physics.

Abstract

Transverse Momentum Dependent (TMD) parton distributions obtained from the Parton Branching (PB) method are combined with next-to-leading-order (NLO) calculations of Drell-Yan (DY) production. We apply the MCatNLO method for the hard process calculation and matching with the PB TMDs. We compute predictions for the transverse momentum, rapidity and $φ^*$ spectra of Z-bosons. We find that the theoretical uncertainties of the predictions are dominated by the renormalization and factorization scale dependence, while the impact of TMD uncertainties is moderate. The theoretical predictions agree well, within uncertainties, with measurements at the Large Hadron Collider (LHC). In particular, we study the region of lowest transverse momenta at the LHC, and comment on its sensitivity to nonperturbative TMD contributions.

Figures (9)

• Figure 1: Collinear parton distributions for up, strange and gluon (PB-NLO-2018-Set1 and PB-NLO-2018-Set 2) as a function of $x$ for different scales $\mu$.
• Figure 2: TMD parton distributions for up, strange and gluon (PB-NLO-2018-Set1 and PB-NLO-2018-Set 2) as a function of $k_t$ at $\mu=100$ and $x=0.01$. The lower panels show the experimental and model uncertainties with respect to the central values.
• Figure 3: TMD parton distributions for up-quark and gluon (PB-NLO-2018-Set1 and PB-NLO-2018-Set 2) as a function of $k_t$ at $\mu=100$ and $x=0.01$. The band shows the uncertainty coming from a variation of the mean of the intrinsic $k_t$ distribution.
• Figure 4: Transverse momentum spectrum of obtained for different subtraction terms: (left) at parton level (LHE level), (right) after inclusion of PB -TMDs.
• Figure 5: Transverse momentum $p_T$ spectrum of -bosons as measured by Aad:2015auj at $\sqrt{s}=8~\TeV$ compared to the prediction from MC@NLO with PB -TMD NLO 2018 Martinez:2018jxt. Left: uncertainties from the PB -TMD and uncertainties coming from changing the width of the intrinsic gauss distribution by a factor of two. Right: with uncertainties from the TMDs and scale variation combined.