[Paper Review] Soft-Gluon Resummation and PDF Theory Uncertainties

George Sterman, Werner Vogelsang|ArXiv.org|Feb 11, 2000

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper investigates the impact of soft-gluon resummation on parton distribution function (PDF) determinations and theoretical uncertainties in quantum chromodynamics (QCD). It demonstrates that threshold resummation reduces scale dependence in hard-scattering cross sections and enables consistent use of NLO PDFs in global fits, particularly in high-kinematic regions where large logarithms dominate. The key contribution is showing that resummed cross sections can be combined with NLO PDFs without inconsistency, provided the resummation captures dominant higher-order corrections.

ABSTRACT

Parton distribution functions are determined by the comparison of finite-order calculations with data. We briefly discuss the interplay of higher order corrections and PDF determinations, and the use of soft-gluon resummation in global fits.

Motivation & Objective

• To assess how soft-gluon resummation affects theoretical uncertainties in parton distribution function (PDF) determinations.
• To examine the compatibility of threshold-resummed hard-scattering functions with NLO PDFs in global fits.
• To clarify the role of scale and scheme dependence in higher-order QCD corrections and their impact on PDF fitting.
• To evaluate whether resummation improves the consistency of global PDF fits across processes with differing phase-space structures near partonic threshold.

Proposed method

• Uses moment-space factorization to express inclusive cross sections in terms of parton distribution functions (PDFs) and partonic hard-scattering functions, enabling systematic analysis of higher-order corrections.
• Applies soft-gluon resummation to the hard-scattering functions, particularly in the threshold limit (x → 1), to resum large logarithms of the form ln N.
• Demonstrates that the exponentiated resummation terms cancel the leading logarithmic dependence of PDF evolution, reducing scale sensitivity to O(1/N).
• Analyzes the interplay between coefficient functions, anomalous dimensions, and factorization schemes, showing that resummed results remain consistent with standard PDF evolution in the MS̄ scheme.
• Compares resummed and NLO fits using moment-space expressions and evaluates the residual scale dependence due to unknown three-loop corrections in the resummation function A(αs).
• Considers power-suppressed corrections as a separate source of uncertainty, treating them as part of a generalized factorization scheme in joint fits with NLO and NNLO models.

Experimental results

Research questions

• RQ1 Can soft-gluon resummation be consistently combined with NLO PDFs in global PDF fits without introducing inconsistencies?
• RQ2 To what extent does threshold resummation reduce scale dependence in hadronic cross sections, particularly in high-pT and large-x regions?
• RQ3 How do theoretical uncertainties in higher-order corrections affect the determination of PDFs, especially when uncalculated corrections are absorbed into the PDFs in the NLO model?
• RQ4 What is the role of factorization scheme and scale dependence in resummed cross sections, and how can they be controlled?
• RQ5 How do power corrections and higher-twist effects influence PDF fits, and can they be treated as part of a unified theoretical framework?

Key findings

• Resummed hard-scattering functions reduce scale dependence to O(1/N), significantly improving stability in high-kinematic regions where large logarithms dominate.
• The exponentiated resummation terms in the Drell-Yan cross section exactly cancel the ln N dependence of PDF evolution, preserving consistency with standard MS̄ PDF evolution.
• NLO PDFs can be consistently used with resummed hard-scattering functions, as the resummation does not significantly alter the coefficient functions used in the original NLO fits, especially at moderate x.
• The remaining scale dependence in resummed cross sections is of order αs³, reflecting uncertainty in the three-loop coefficient function A(αs), which remains unknown.
• Resummation is particularly beneficial in global fits involving processes with different phase-space structures near threshold, such as DIS and high-pT jet production, where NLO fits may fail due to uncalculated large corrections.
• Power corrections, such as twist-four terms in DIS, can be treated as part of a generalized scheme and influence PDF determinations when included in joint fits with higher-order models.