Parton distributions and lattice QCD calculations: a community white paper

Abstract: In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.

• The paper establishes a synergy between global QCD analyses and lattice QCD by benchmarking parton distribution moments.
• It compares unpolarized and polarized proton PDFs using both high-order perturbative and nonperturbative lattice methods.
• The findings indicate that integrating lattice QCD computations can reduce uncertainties and refine insights into nucleon structure.

Analyzing the Intersection of Parton Distributions and Lattice QCD Calculations

This paper serves as a community white paper, aiming to bridge the gap between two significant methodologies in the determination of parton distribution functions (PDFs) within the framework of quantum chromodynamics (QCD): global analyses of hard-scattering data and lattice QCD computations. The work scrutinizes techniques to measure unpolarized and polarized proton PDFs and explores potential synergies between these distinct approaches.

Within QCD, parton distribution functions encapsulate the distribution of a hadron's momentum and spin among its constituent quarks and gluons. Two prominent strategies exist to ascertain PDFs. The global analysis approach utilizes QCD factorization theorems to analyze hard-scattering data, integrating various hadronic observables. Conversely, lattice QCD employs first-principle operator definitions for PDFs, calculating moments using a discretized spacetime grid.

The paper provides benchmarks for lattice-QCD calculations to validate current and future research, highlighting its potential to mitigate uncertainties in global PDF analyses. Notably, it emphasizes the need for a common lexicon to facilitate meaningful dialogue between the global analysis and lattice QCD communities.

Insights into QCD Analyses and Lattice QCD

Global QCD analysis relies on vast repositories of experimental data to infer PDFs, utilizing factorization theorems that separate short-distance perturbative effects from long-distance nonperturbative quantities, such as PDFs. Perturbative computations generally extend to NNLO accuracy, facilitating a precise characterization of PDFs across various flavors and polarizations.

In contrast, lattice QCD offers a non-perturbative method, calculating PDFs directly via the discretized, Euclidean space-time framework. Originating from Euclidean evaluations of QCD path integrals, lattice QCD remains an intensive computational endeavor, which, despite its rigorous nature, requires precise control of systematic uncertainties, such as finite volume effects, continuum extrapolation, and discretization errors.

Comparative Benchmarks and Numerical Results

The paper elucidates a thorough juxtaposition of the lowest PDF moments as derived from both lattice-QCD and global analyses. This benchmark comparison reveals the necessity for increased precision in lattice-QCD calculations, particularly in the unpolarized sector, where discrepancies emerge with global fits. Nonetheless, lattice-QCD assessments show promise in refining the determination of polarized PDFs where experimental data remains sparse.

The findings underscore a pivotal conclusion: lattice-QCD computations, though arduous, bear the potential to enrich global fits by offering constraints grounded in rigorous theoretical principles. The paper suggests that PDFs' moments and their Bjorken-$x$ dependency calculated from lattice QCD could be instrumental in complementing data-driven global analyses.

Prospects and Theoretical Implications

From a theoretical standpoint, the plausible coalescence of lattice-QCD results into global analyses marks a forward step towards reconciling theoretical models with empirical evidence. By providing insights into both polarized and unpolarized PDFs, lattice QCD could address existing gaps in our understanding of nucleon structure, thereby refining predictions pertinent to high-energy QCD processes.

Practically, improvements in lattice-QCD methodologies, such as reducing systematic errors and expanding computational resources, could dramatically enhance its impact. The integration of lattice-based inputs into global fits would not only enhance the precision of current determinations but could also elucidate spin distribution puzzles that have long confounded the field.

Concluding Thoughts

The paper signifies a methodological confluence, leveraging the strengths of data-driven global analyses and computational lattice QCD. As the fidelity of both approaches progresses, so too will our understanding of the intricate balance of forces within hadronic matter, delineating the composite structure of nucleons in unprecedented detail. While challenges remain, particularly in unifying language and techniques across communities, this document lays a foundation for future collaborative efforts that promise substantial advancements in high-energy physics understanding.