Isolating Scheme Dependence of Quasi-PDFs in the RI/MOM Scheme

Abstract

Quasi-parton distribution functions provide a framework for relating lightcone parton distributions to correlation functions in Euclidean lattice QCD. Their connection to lightcone distributions is established through perturbative matching, whose form depends on the renormalization prescription adopted for the quasi-PDF. In the ordinary RI/MOM scheme, the off-shell reference momentum enters both the renormalized quasi-PDF and the matching coefficient. We propose modified finite renormalization schemes in which neither quantity depends on the RI/MOM reference momentum. Starting from the ordinary RI/MOM scheme, we identify the part to be retained in the renormalized quasi-PDF and include the remaining finite part in the counterterm. We consider a minimal RI/MOM scheme and a modified minimal scheme as specific examples. We derive the corresponding one-loop renormalized quasi-PDFs, counterterms, matching coefficients, and renormalization-group equations, and show explicitly that the finite transformation removes the dependence on the RI/MOM reference momentum from both the renormalized quasi-PDF and the counterterm in the modified schemes.