[Paper Review] The small kt-region in Drell-Yan production at next-to-leading order with the Parton Branching Method

I. Bubanja, A. Bermúdez Martínez+11 more|arXiv (Cornell University)|Jan 1, 2023

Particle physics theoretical and experimental studies47 references3 citations

TL;DR

This paper presents a next-to-leading-order (NLO) analysis of Drell-Yan production using the Parton Branching (PB) method to study the small transverse momentum (kT) region, where both intrinsic parton transverse momentum and soft-gluon resummation are critical. It extracts the intrinsic-kT parameter as qs = 1.04 ± 0.08 GeV from LHC data at √s = 13 TeV across 50–1000 GeV Drell-Yan masses, finding no significant dependence on center-of-mass energy or DY mass, in contrast to standard Monte Carlo generators.

ABSTRACT

The Parton Branching (PB) method describes the evolution of transverse momentum dependent (TMD) parton distributions, covering all kinematic regions from small to large transverse momenta kT. The small kT-region is very sensitive both to the contribution of the intrinsic motion of partons (intrinsic kT) and to the resummation of soft gluons taken into account by the PB TMD evolution equations. We study the role of soft-gluon emissions in TMD as well as integrated parton distributions. We perform a detailed investigation of the PB TMD methodology at next-to-leading order (NLO) in Drell-Yan (DY) production for low transverse momenta. We present the extraction of the nonperturbative 'intrinsic-kT' distribution from recent measurements of DY transverse momentum distributions at the LHC across a wide range in DY masses, including a detailed treatment of statistical, correlated and uncorrelated uncertainties. We comment on the (in)dependence of intrinsic transverse momentum on DY mass and center-of-mass energy, and on the comparison with other approaches.

Motivation & Objective

• To investigate the small kT region in Drell-Yan production where soft gluon emissions and intrinsic parton transverse momentum interplay.
• To extract the nonperturbative intrinsic-kT distribution from LHC measurements at √s = 13 TeV across a wide range of Drell-Yan masses.
• To assess the dependence of intrinsic-kT on center-of-mass energy and Drell-Yan mass, contrasting with tuned Monte Carlo generators.
• To treat theoretical scale uncertainties as correlated within mass bins and to include full covariance matrices for experimental uncertainties.
• To demonstrate the consistency of the PB-TMD framework in simultaneously fitting collinear and TMD distributions without relying on external PDF sets.

Proposed method

• The Parton Branching (PB) method is applied in momentum space to describe TMD evolution across all kT scales, incorporating both perturbative and nonperturbative effects.
• The PB-NLO-2018 Set2 framework is used, with the strong coupling evaluated at the transverse momentum of each emission for qT > 1 GeV, and at the semi-hard scale q0 = 1 GeV for softer emissions.
• The nonperturbative Sudakov form factor is modeled via a 'pre-confinement' scale prescription in the region z ∈ [zdyn, zM], capturing infrared dynamics.
• The intrinsic-kT distribution is modeled as a Gaussian with width parameter qs, fitted to the low-pT region of the Drell-Yan differential cross section.
• A scan over qs values is performed using MADGRAPH5_AMC@NLO matched with PB-TMD distributions, with χ² calculations including full experimental covariance matrices.
• Systematic uncertainties are treated with correlated components within each mDY bin, and scale uncertainties are assumed fully correlated within bins and uncorrelated between bins.

Experimental results

Research questions

• RQ1 How does the intrinsic-kT parameter vary with Drell-Yan mass and center-of-mass energy in the small kT region?
• RQ2 To what extent do soft-gluon resummation and nonperturbative Sudakov effects influence the extracted intrinsic-kT width?
• RQ3 How does the PB-TMD framework compare to standard Monte Carlo event generators in terms of intrinsic-kT stability across energies and masses?
• RQ4 What is the impact of treating experimental uncertainties with full covariance matrices and correlated scale uncertainties on the extracted qs value?
• RQ5 Can the PB-TMD approach simultaneously describe collinear and TMD distributions without relying on external PDF fits?

Key findings

• The intrinsic-kT parameter is extracted as qs = 1.04 ± 0.08 GeV from LHC Drell-Yan data at √s = 13 TeV across Drell-Yan masses from 50 GeV to 1 TeV.
• The extracted value of qs is consistent with expectations from Fermi motion in protons and shows no significant dependence on center-of-mass energy or Drell-Yan mass.
• The stability of qs across different masses and energies contrasts sharply with tuned Monte Carlo generators, which require increasing intrinsic-kT widths with √s and mDY.
• The nonperturbative Sudakov form factor, modeled via the pre-confinement scale prescription, plays a crucial role in stabilizing the intrinsic-kT extraction.
• The PB-TMD framework successfully recovers the inclusive DGLAP limit and allows simultaneous fitting of collinear and TMD distributions without dependence on external PDF sets.
• The treatment of experimental uncertainties using full covariance matrices and correlated scale uncertainties leads to a robust and precise determination of the intrinsic-kT parameter.