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

TL;DR

This paper introduces a new analysis method for lattice QCD calculations of valence PDFs and GPDs, focusing on determining Wilson coefficients with confidence intervals and applying them to various hadrons, reducing reliance on perturbative calculations.

Contribution

It proposes a pragmatic approach to determine Wilson coefficients non-perturbatively from lattice data, improving the extraction of PDFs and GPDs without higher-loop uncertainties.

Findings

Confidence intervals for Wilson coefficients are established.

Method applied to valence PDFs of multiple hadrons.

Potential reduction of uncertainties in lattice QCD extractions.

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 $z$.