Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme

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 $\overline{\text{MS}}$ scheme. Here we carry out a direct matching from the RI/MOM scheme for the quasi-PDF to the $\overline{\text{MS}}$ 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 $P^z\to \infty$, unlike other schemes. This direct approach therefore has the potential to improve the accuracy for converting quasi-distribution lattice calculations to collinear distributions.