Resumming quark's longitudinal momentum logarithms in LaMET expansion of lattice PDFs

Abstract

In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum (pz) 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⁡pz/μ in the matching coefficient, where μ is a fixed renormalization scale. The result enhances the accuracy of the expansion at moderate pz>1 GeV, and at the same time, clearly shows that the partons cannot be approximated from quarks with pz∼ΛQCD 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 pz, as illustrated in the example of fitting the moments of the PDFs.