The quasi parton distribution is a spatial correlation of quarks or gluons
along the z direction in a moving nucleon which enables direct lattice
calculations of parton distribution functions. It can be defined with a
nonperturbative renormalization in a regularization independent momentum
subtraction scheme (RI/MOM), which can then be perturbatively related to the
collinear parton distribution in the MS scheme. Here we
carry out a direct matching from the RI/MOM scheme for the quasi-PDF to the
MS PDF, determining the non-singlet quark matching
coefficient at next-to-leading order in perturbation theory. We find that the
RI/MOM matching coefficient is insensitive to the ultraviolet region of
convolution integral, exhibits improved perturbative convergence when
converting between the quasi-PDF and PDF, and is consistent with a quasi-PDF
that vanishes in the unphysical region as the proton momentum Pzββ,
unlike other schemes. This direct approach therefore has the potential to
improve the accuracy for converting quasi-distribution lattice calculations to
collinear distributions.Comment: 18 pages, 6 figure