Disentangling Scheme Dependence in Quasi-PDFs with a Transverse-Momentum Cutoff

Abstract

Quasi-PDFs provide a connection between Euclidean spatial correlations in lattice QCD and lightcone parton distributions. Their perturbative expressions contain both the infrared divergence required for matching and the scheme-dependent contributions associated with the renormalization prescriptions. The separation of these two ingredients is not always transparent. In this work we use a transverse-momentum cutoff as a simple setting in which these ingredients can be systematically decomposed into a scheme-dependent sector and a remainder for the nonsinglet quark quasi-PDF at one loop. We choose the minimal transverse-momentum-cutoff scheme, where the scheme-dependent sector is identified by its explicit cutoff dependence, while the remainder contains the full collinear infrared divergence and the finite contribution relevant for matching to the lightcone PDF. After expressing the quasi-PDF in terms of distributions, we show how to deal with the linear divergence and the logarithmic terms in the counterterm, and discuss the dependence of the renormalization-group behavior on the renormalization prescriptions. This organization clarifies how scheme dependence enters the quasi-PDF before the final matching is performed, and provides a benchmark for examining analogous separations in other renormalization schemes.