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In the large-momentum expansion for parton distribution functions (PDFs), thenatural physics scale is the longitudinal momentum ($p_z$) of the quarks (orgluons) in a large-momentum hadron. We show how to expose this scale dependencethrough resumming logarithms of the type $\ln^n p_z/\mu$ in the matchingcoefficient, where $\mu$ is a fixed renormalization scale. The result enhancesthe 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 $p_z\sim\Lambda_{\rm QCD}$ which are not predominantly collinear with the parent hadronmomentum, consistent with power counting of the large-momentum effectivetheory. The same physics mechanism constrains the coordinate space expansion atlarge distances $z$, the conjugate of $p_z$, as illustrated in the example offitting the moments of the PDFs.

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