Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD

TL;DR

This paper presents the first direct lattice QCD calculation of the third Mellin moments of nucleon parton distribution functions at the physical pion mass, using advanced computational techniques.

Contribution

First direct lattice QCD determination of third Mellin moments of nucleon PDFs at physical pion mass, employing multiple extraction methods and uncertainty modeling.

Findings

Determined isovector third Mellin moments for unpolarized, polarized, and transversity PDFs.

Used two physical-point lattice ensembles with improved actions and smearing techniques.

Applied bootstrapped model averaging to include uncertainties in the extraction process.

Abstract

Using forward matrix elements of local leading-twist operators, we present a determination of the isovector third Mellin moments $\left< x^2 \right>$ of nucleon unpolarized, polarized, and transversity parton distribution functions. Two lattice QCD ensembles at the physical pion mass are used, which were generated using a tree-level Symanzik-improved gauge action and 2+1 flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. Leveraging a wide set of operators, two extraction methods for the matrix elements, and the automatic inclusion of model uncertainties via bootstrapped model averages, we extract values of the third Mellin moments. This is the first direct calculation of these observables performed at the physical pion mass.