Parton distribution functions from lattice QCD using Bayes-Gauss-Fourier transforms

Abstract

We present a new method, based on Gaussian process regression, for reconstructing the continuous $x$-dependence of parton distribution functions (PDFs) from quasi-PDFs computed using lattice QCD. We examine the origin of the unphysical oscillations seen in current lattice calculations of quasi-PDFs and develop a nonparametric fitting approach to take the required Fourier transform. The method is tested on one ensemble of maximally twisted mass fermions with two light quarks. We find that with our approach oscillations of the quasi-PDF are drastically reduced. However, the final effect on the light-cone PDFs is small. This finding suggests that the deviation seen between current lattice QCD results and phenomenological determinations cannot be attributed solely on the Fourier transform.

arXiv commentVersion accepted for PRD; 15 pages, 19 figures

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• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• Lattice continuum-limit study of nucleon quasi-PDFs
• Flavor decomposition for the proton helicity parton distribution functions
• Flavor decomposition of the nucleon unpolarized, helicity and transversity parton distribution functions from lattice QCD simulations
• Gluon distributions and their applications to Ioffe-time distributions
• Non-perturbative strong coupling at timelike momenta
• One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions
• Yang-Mills glueball masses from spectral reconstruction
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Chiral Perturbation for Large Momentum Effective Field Theory
• The Continuum and Leading Twist Limits of Parton Distribution Functions in Lattice QCD
• One-loop Matching Factors for Singlet Quasi-Parton Distribution Functions in the Hybrid-Ratio Scheme