Bayesian-Wilson coefficients in lattice QCD computations of valence PDFs and GPDs

Abstract

We propose an analysis method for the leading-twist operator product expansion based lattice QCD determinations of the valence parton distribution function (PDF). In the first step, we determine the confidence-intervals of the leading-twist $\overline{\mathrm{MS}}$ Wilson coefficients, $C_n({\mu }^2{z}^2)$, of the equal-time bilocal quark bilinear, given the lattice QCD matrix element of Ioffe-time distribution for a particular hadron $H$ as well as the prior knowledge of the valence PDF, $f(x,\mu )$ of the hadron $H$ determined via global fit from the experimental data. In the next step, we apply the numerically estimated $C_n$ in the lattice QCD determinations of the valence PDFs of other hadrons, and for the zero-skewness generalized parton distribution (GPD) of the same hadron $H$ at non-zero momentum transfers. Our proposal still assumes the dominance of leading-twist terms, but it offers a pragmatic alternative to the usage of perturbative Wilson coefficients and their associated higher-loop uncertainties such as the effect of all-order logarithms at larger sub-Fermi quark-antiquark separations $z$.

13 pages, 5 figures; published version

References in corpus (36)

• Large-Momentum Effective Theory
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Soft-Gluon Resummation and the Valence Parton Distribution Function of the Pion
• Exclusive processes in position space and the pion distribution amplitude
• On the Renormalizability of Quasi Parton Distribution Functions
• Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD
• Parton Distribution Function with Non-perturbative Renormalization from Lattice QCD
• Pion Valence Structure from Ioffe Time Pseudo-Distributions
• Unpolarized and helicity generalized parton distributions of the proton within lattice QCD
• Valence parton distribution of pion from lattice QCD: Approaching continuum
• Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
• A Hybrid Renormalization Scheme for Quasi Light-Front Correlations in Large-Momentum Effective Theory
• Pion valence quark distribution from current-current correlation in lattice QCD
• Pion and kaon valence-quark parton distribution functions
• Parton Distribution Functions from Ioffe time pseudo-distributions
• Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point
• Valence-Quark Distribution of the Kaon and Pion from Lattice QCD
• The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD
• Isovector parton distribution functions of the proton on a superfine lattice
• Generalized Parton Distributions and Pseudo-Distributions
• Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations
• Confronting lattice parton distributions with global QCD analysis
• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• Parton distributions from lattice data: the nonsinglet case
• Lattice continuum-limit study of nucleon quasi-PDFs
• Drawing insights from pion parton distributions
• Origin and Resummation of Threshold Logarithms in the Lattice QCD Calculations of PDFs
• Theory and applications of parton pseudodistributions
• Neural-network analysis of Parton Distribution Functions from Ioffe-time pseudodistributions
• Nonperturbative partonic quasidistributions of the pion from chiral quark models
• The pion and kaon $⟨x^3⟩$ from lattice QCD and PDF reconstruction from Mellin moments
• Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions
• Towards the three-dimensional parton structure of the pion: Integrating transverse momentum data into global QCD analysis
• Moments of nucleon isovector structure functions in $2+1+1$-flavor QCD
• Gluon distributions and their applications to Ioffe-time distributions
• Master Integrals for two-loop QCD corrections to Quasi PDFs

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• Polarized and unpolarized gluon PDFs: generative machine learning applications for lattice QCD matrix elements at short distance and large momentum
• The transversity parton distribution function of the nucleon using the pseudo-distribution approach