Sieving parton distribution function moments via the moment problem

TL;DR

This paper introduces a mathematical approach using the moment problem to refine and accurately determine the moments of parton distribution functions in hadron physics, reducing errors and locating the PDF peak.

Contribution

It proposes a universal strategy leveraging the moment problem to sieve and refine PDF moments, improving accuracy across different calculation methods.

Findings

Refined three sets of PDF moments from Lattice QCD

Significantly reduced errors in higher order moments

Successfully located the peak of the PDF

Abstract

We apply a classical mathematical problem, the moment problem, with its related mathematical achievements, to the study of the parton distribution function (PDF) in hadron physics, and propose a strategy to sieve the moments of the PDF by exploiting its properties such as continuity, unimodality, and symmetry. Through an error-inclusive sifting process, we refine three sets of PDF moments from Lattice QCD. This refinement significantly reduces the errors, particularly for higher order moments, and locates the peak of PDF simultaneously. As our strategy is universally applicable to PDF moments from any method, we strongly advocate its integration into all PDF moment calculations.