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

TL;DR

This paper develops a method to resum logarithms of the quark's longitudinal momentum in the LaMET expansion of lattice PDFs, improving accuracy at moderate momenta and clarifying the physical interpretation of parton momentum scales.

Contribution

It introduces a resummation technique for logarithms in the matching coefficient of LaMET, enhancing the precision of lattice PDF calculations at moderate momenta.

Findings

Resummation improves accuracy of PDFs at $p_z > 1$ GeV.

Partons with $p_z o ext{QCD scale}$ are not predominantly collinear.

The method constrains coordinate space expansion at large distances.

Abstract

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 $\ln^n p_z/\mu$ in the matching coefficient, where $\mu$ 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 $p_z\sim \Lambda_{\rm QCD}$ 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.