Polarized and unpolarized gluon PDFs: generative machine learning applications for lattice QCD matrix elements at short distance and large momentum

TL;DR

This paper applies generative machine learning algorithms to lattice QCD data to accurately estimate polarized and unpolarized gluon PDFs, overcoming traditional limitations and reducing bias in the extraction process.

Contribution

It introduces a novel machine learning approach to extend lattice QCD calculations for gluon PDFs, addressing bias and uncertainty issues in traditional methods.

Findings

Successful reconstruction of gluon PDFs from short-distance lattice data.

Demonstration of reduced bias and uncertainty in PDF extraction.

Extension of correlation data up to $zp_z \\lesssim 14$ for improved accuracy.

Abstract

Lattice quantum chromodynamics (QCD) calculations share a defining challenge by requiring a small finite range of spatial separation $z$ between quark/gluon bilinears for controllable power corrections in the perturbative QCD factorization, and a large hadron boost $p_z$ for a successful determination of collinear parton distribution functions (PDFs). However, these two requirements make the determination of PDFs from lattice data very challenging. We present the application of generative machine learning algorithms to estimate the polarized and unpolarized gluon correlation functions utilizing short-distance data and extending the correlation up to $zp_z \lesssim 14$, surpassing the current capabilities of lattice QCD calculations. We train physics-informed machine learning algorithms to learn from the short-distance correlation at $z\lesssim 0.36$ fm and take the limit, $p_z \to \infty$, thereby minimizing possible contamination from the higher-twist effects for a successful reconstruction of the polarized gluon PDF. We also expose the bias and problems with underestimating uncertainties associated with the use of model-dependent and overly constrained functional forms, such as $x^\alpha(1-x)^\beta$ and its variants to extract PDFs from the lattice data. We propose the use of generative machine learning algorithms to mitigate these issues and present our determination of the polarized and unpolarized gluon PDFs in the nucleon.