Intrinsic $k_T$ and soft gluons in Monte Carlo event generators

TL;DR

The paper addresses how intrinsic $k_T$ and soft-gluon dynamics shape Drell-Yan transverse-momentum spectra and how they are modeled in Monte Carlo generators, contrasting collinear-showers with parton-branching TMD evolution. It highlights the role of soft-gluon non-resolvable emissions, summarized by a dynamical soft-gluon resolution scale $z_{ ext{dyn}}$ and a non-perturbative Sudakov region, which affects the energy dependence of the extracted $q_s$. It demonstrates that properly accounting for correlations in experimental uncertainties is crucial, particularly for forward-region LHCb data, and shows that these corrections bring LHCb-derived $q_s$ into closer agreement with CMS/ATLAS results. The work uses the Cascade Monte Carlo with NLO hard scattering and TMD PDFs to extract $q_s$ across energies and rapidities, and discusses implications for forward physics and non-perturbative TMD dynamics.

Abstract

Experimental measurements of the transverse momentum of Drell-Yan lepton pairs are sensitive to non-perturbative physics associated with the intrinsic parton transverse momentum $k_T$. We discuss recent determinations of intrinsic $k_T$ in the context of transverse momentum dependent (TMD) parton branching calculations and collinear parton-shower Monte Carlo generators. We illustrate the influence of the soft-gluon resolution scale and the non-perturbative Sudakov region on the intrinsic $k_T$ extraction. We emphasize the relevance of the correct treatment of correlated uncertainties between different transverse momentum bins in TMD fits and present an application to the determination of the intrinsic $k_T$ in the forward rapidity region.

Figures (3)

• Figure 1: Extraction of intrinsic $k_T$ parameters from measurements of DY transverse momentum distributions at varying center-of-mass energies. The plot on the left-hand side CMS:2024goo is based on the collinear parton-shower Monte Carlo generators HerwigBellm:2015jjp and PythiaSjostrand:2014zea, with underlying-event tunes CH2 and CH3 CMS:2020dqt and CP3 through CP5 CMS:2019csb, respectively. The plot on the right-hand side Bubanja:2023nrd is based on the PB TMD method, with the horizontal line based on CMS 13 TeV data CMS:2022ubq.
• Figure 2: Partonic branching phase space diagram (left, adapted from Ref. Hautmann:2019biw) and intrinsic $k_T$ parameter extracted from fits of PB TMD to DY $p_T$ using dynamic soft-gluon resolution scale Hautmann:2025fkw with $q_0 = 1$ GeV (right).
• Figure 3: (Left) intrinsic-$k_T$ values extracted from fits to LHCb data: (blue) no correlations; (orange) including correlations; (green) including correlations and correcting the rapidity distribution. (Right) the effect of including correlations in the case of the LHCb dataset LHCb:2021huf: dashed lines corresponds to no correlations, shaded areas correspond to correct correlations included.