In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum (<math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub></math>) of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence through resumming logarithms of the type <math><msup><mrow><mi>ln</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>⁡</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>/</mo><mi>μ</mi></math> in the matching coefficient, where μ is a fixed renormalization scale. The result enhances the accuracy of the expansion at moderate <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></math> GeV, and at the same time, clearly shows that the partons cannot be approximated from quarks with <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>∼</mo><msub><mrow><mi>Λ</mi></mrow><mrow><mi>QCD</mi></mrow></msub></math> 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 <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub></math>, as illustrated in the example of fitting the moments of the PDFs.