Sieving parton distribution function moments via the moment problem

Abstract

Reconstructing parton distribution function (PDF) from the corresponding Mellin moments belongs to a classical mathematical problem: the moment problem, which has been overlooked for years in the contemporary hadron community. We propose the strategy to sieve the moments leveraging PDF properties such as continuity, unimodality, and symmetry. Through an error-inclusive sifting process, we refine three sets of lattice QCD PDF moments. This refinement significantly reduces the errors, particularly for higher order moments, and locates the peak of PDF simultaneously. As our method is universally applicable to PDF moments from any methodology, we strongly advocate its integration into all PDF moment calculations.Comment: 6 pages, 2 figure