Power Accuracy in Lattice Calculations of Parton Distributions

In lattice-QCD calculations of the parton distribution functions (PDFs) via large-momentum effective theory (LaMET), the leading power correction appears at ${cal O}(Lambda_{ m QCD}/P^z)$ due to the linearly divergent self-energy of the Wilson line in quasi-PDF operators.

For lattice data with hadron momentum $P^z$ of a few GeV, power accuracy is important both for an estimation of theoretical error and a wider-$x$ range application of LaMET. We show how to attain this by resumming the relevant infrared renormalon effect in the matching coefficients in the large $eta_0$-function approximation and, at the same time, fixing phenomenologically the non-perturbative mass parameter in the renormalization of the linear divergence through the zero-momentum lattice matrix element. A demonstrative example

is shown on the pion PDF data at $P^z = 1.9$ GeV.