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

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 $z{p}_z\lesssim 14$, 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.

Published Version, 24 pages, 20 figures

References in corpus (17)

• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Exclusive processes in position space and the pion distribution amplitude
• Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD
• Glue spin and helicity in proton from lattice QCD
• Self-Renormalization of Quasi-Light-Front Correlators on the Lattice
• How well do we know the gluon polarization in the proton?
• Resumming Quark's Longitudinal Momentum Logarithms in LaMET Expansion of Lattice PDFs
• The Jacobi Polynomials QCD analysis for the polarized structure function
• Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics
• Gluon distributions in the proton in a light-front spectator model
• Gluon distributions and their applications to Ioffe-time distributions
• Continuum limit of parton distribution functions from the pseudo-distribution approach on the lattice
• Gluon Parton Distribution of the Nucleon from 2+1+1-Flavor Lattice QCD in the Physical-Continuum Limit
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Polarized Gluon Pseudodistributions at Short Distances
• Bayesian-Wilson coefficients in lattice QCD computations of valence PDFs and GPDs
• Accessing gluon polarization with high-$P_T$ hadrons in SIDIS

Cited by in corpus (1)

• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem