Resumming Quark's Longitudinal Momentum Logarithms in LaMET Expansion of Lattice PDFs

In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum (p_z) of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence through resumming logarithms of the type lnⁿ(p_z/μ) in the matching coefficient, where μ is a fixed renormalization scale. The result enhances the accuracy of the expansion at moderate p_z>1 GeV, and at the same time, clearly shows that the partons cannot be approximated from quarks with p_z ~ Λ_QCD which are not predominantly collinear with the parent hadron momentum, consistent with power counting of the large-momentum effective theory. The same physics mechanism constrains the coordinate space expansion at large distances z, the conjugate of p_z, as illustrated in the example of fitting the moments of the PDFs.