Moments of nucleon unpolarized, polarized, and transversity parton distribution functions from lattice QCD at the physical point

The second Mellin moments <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">⟨</a:mo><a:mi>x</a:mi><a:mo stretchy="false">⟩</a:mo></a:math> of the nucleon’s unpolarized, polarized, and transversity parton distribution functions are computed. Two lattice QCD ensembles at the physical pion mass are used: these were generated using a tree-level Symanzik-improved gauge action and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>2</e:mn><e:mo>+</e:mo><e:mn>1</e:mn></e:mrow></e:math> flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. The moments are extracted from forward matrix elements of local leading twist operators. We determine renomalization factors in RI-(S)MOM and match to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mover accent="true"><g:mi>MS</g:mi><g:mo stretchy="true">¯</g:mo></g:mover></g:math> at scale 2 GeV. Our findings show that operators that exhibit vanishing kinematics at zero momentum can have significantly reduced excited-state contamination. The resulting polarized moment is used to quantify the longitudinal contribution to the quark spin-orbit correlation. All our results agree within two sigma with previous lattice results. Published by the American Physical Society 2024