  The second Mellin moments $\langle x\rangle$ of the nucleon's unpolarized,
polarized, and transversity parton distribution functions (PDFs) 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 2+1 flavour
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
$\overline{\mathrm{MS}}$ at scale $2\,\mathrm{GeV}$. 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.
