[Paper Review] On the role of soft and non-perturbative gluons in collinear parton densities and parton shower event generators

M. Mendizabal, F. Guzmán+2 more|arXiv (Cornell University)|Jan 1, 2023

High-Energy Particle Collisions Research4 citations

TL;DR

This paper demonstrates that non-perturbative (NP) gluons—via the non-perturbative Sudakov form factor—are essential for the correct cancellation of singular terms in NLO DGLAP evolution and inclusive cross-section calculations. Using the Parton Branching (PB) method, the authors show that NP-gluons significantly affect initial-state showers and inclusive observables like Drell-Yan transverse momentum spectra, but have minimal impact on final-state hadron spectra when hadronization models like the Lund string are used.

ABSTRACT

The role of soft (non-perturbative) gluons in collinear parton densities is investigated with the Parton Branching method as a solution to the DGLAP evolution equations. It is found that soft gluons contribute significantly to collinear parton densities. Within the Parton Branching frame, the Sudakov form factor can be split into a perturbative and non-perturbative part. The non-perturbative part can be calculated analytically under certain conditions. It is shown that the inclusion of soft (non - perturbative) gluons to the parton density evolution is essential for the proper cancellation of divergent terms. It is argued that the non-perturbative part of the Sudakov form factor has its correspondence in Transverse Momentum Dependent parton distributions. Within the Parton Branching approach, this non-perturbative Sudakov form factor is constrained by fits of inclusive, collinear parton densities.

Motivation & Objective

• To establish the necessity of including soft and non-perturbative gluons in collinear parton density evolution to ensure proper cancellation of singular terms in NLO calculations.
• To demonstrate that the non-perturbative Sudakov form factor, constrained by fits to inclusive data, is essential for consistent TMD parton distributions and inclusive spectra.
• To investigate the impact of NP-gluons on initial-state parton showers and their influence on final-state hadron and jet spectra.
• To challenge claims in prior work that NP-gluons are irrelevant in Monte Carlo event generators, showing instead that their inclusion is crucial for consistency with NLO DGLAP.
• To establish that the PB method with NP-gluons yields an intrinsic-kT distribution independent of center-of-mass energy, unlike standard generators such as PYTHIA8 or HERWIG.

Proposed method

• The Parton Branching (PB) method is used to solve the DGLAP evolution equations iteratively, explicitly tracking each branching vertex and transverse momentum of emitted partons.
• The Sudakov form factor is decomposed into perturbative and non-perturbative components; the non-perturbative part is analytically calculable and constrained by fits to inclusive collinear parton densities (e.g., HERA-PDF2.0NLO).
• The PB approach enables exact reproduction of DGLAP evolution at NLO when the renormalization scale is set to the evolution scale and zM →1.
• The non-perturbative Sudakov form factor is derived from the DGLAP splitting functions using a momentum-weighted formulation and the plus-prescription, with a cutoff ϵ to regularize the 1/(1−z) singularity.
• The method is applied to both forward (standard) and backward (initial-state shower) evolution, comparing effects on inclusive distributions and final-state spectra.
• The PB TMD parton shower is implemented in CASCADE3, allowing consistent treatment of NP-gluons in both evolution and parton shower stages without introducing free parameters.

Experimental results

Research questions

• RQ1 Why is the inclusion of soft and non-perturbative gluons necessary for the cancellation of singular terms in NLO DGLAP calculations?
• RQ2 How does the non-perturbative Sudakov form factor affect transverse momentum-dependent (TMD) parton distributions and inclusive cross sections?
• RQ3 What is the impact of NP-gluons on initial-state parton showers and the resulting final-state hadron and jet spectra?
• RQ4 Why do standard Monte Carlo generators like PYTHIA8 or HERWIG produce an intrinsic-kT distribution dependent on √s, while the PB method does not?
• RQ5 Can the PB method with NP-gluons be consistently matched to NLO DGLAP calculations without requiring new parton densities or coefficient functions?

Key findings

• The non-perturbative Sudakov form factor is essential for the cancellation of singular terms in NLO cross-section calculations; neglecting NP-gluons leads to unphysical divergences.
• NP-gluons significantly influence inclusive observables such as Drell-Yan transverse momentum spectra, particularly in initial-state showers.
• Final-state hadron spectra and jets are largely unaffected by NP-gluons when using standard hadronization models like the Lund string, which can absorb soft gluons.
• The PB method with NP-gluons produces an intrinsic-kT distribution that is independent of the center-of-mass energy √s, in contrast to PYTHIA8 and HERWIG, where it scales with √s.
• The PB approach with PB-NLO-2018 Set1 reproduces HERA-PDF2.0NLO exactly at the collinear level and provides a consistent framework for both collinear and TMD distributions.
• The PB method is the only current approach that consistently treats NP-gluons in both evolution and parton shower stages, enabling direct use of standard NLO parton densities and coefficient functions.