Matching the quasiparton distribution in a momentum subtraction scheme

The quasiparton 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) over bar scheme. Here we carry out a direct matching from the RI/MOM scheme for the quasi-PDF to the (MS) over bar 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 P-z -> infinity, unlike other schemes. This direct approach therefore has the potential to improve the accuracy for converting quasidistribution lattice calculations to collinear distributions.