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

TL;DR

This paper introduces a Gaussian process regression-based method to reconstruct parton distribution functions from lattice QCD quasi-PDFs, effectively reducing unphysical oscillations and providing insights into discrepancies with phenomenological results.

Contribution

The paper develops a nonparametric Bayesian approach to Fourier transforming lattice QCD quasi-PDFs, addressing oscillation issues and improving PDF reconstruction accuracy.

Findings

Oscillations in quasi-PDFs are significantly reduced.

The impact on the final light-cone PDFs is minimal.

Discrepancies with phenomenological PDFs are not solely due to Fourier transform issues.

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.