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

Sieving parton distribution function moments via the moment problem