Reconstructing parton distribution function based on maximum entropy method

TL;DR

This paper introduces a maximum entropy-based method for reconstructing parton distribution functions from moments, avoiding artificial assumptions and effectively handling errors, demonstrated through tests and lattice QCD data.

Contribution

The paper presents a novel maximum entropy approach for PDF reconstruction that does not require artificial assumptions and incorporates Gaussian smoothing for error handling.

Findings

High-quality reconstruction with at least six moments

Effective handling of moments with errors

Successful application to lattice QCD data for the pion

Abstract

A new method based on the maximum entropy principle for reconstructing the parton distribution function (PDF) from moments is proposed. Unlike traditional methods, the new method no longer needs to introduce any artificial assumptions. For the case of moments with errors, we introduce Gaussian functions to soften the constraints of moments. Through a series of tests, the effectiveness and reconstruction efficiency of this new method are evaluated comprehensively. And these tests indicate that this method is reasonable and can achieve high-quality reconstruction with at least the first six moments as input. Finally, we select a set of lattice QCD results regarding moments as input and provide reasonable reconstruction results for the pion.