Improved quasi parton distribution through Wilson line renormalization

TL;DR

The paper tackles the UV power divergence problem in lattice-accessible quasi-PDFs by introducing a mass counterterm within the auxiliary $z$-field formalism, effectively renormalizing the Wilson line as for open Wilson lines and leaving at most logarithmic divergences. It shows that this renormalization removes the power divergence to all orders, enabling a well-defined path to extract physical PDFs from lattice data. A concrete one-loop lattice-to-continuum matching is then derived using a simple discretized gauge action, relating lattice and continuum regulators via $\Lambda = \frac{\pi}{a_L}$ and providing the $Z$-factor necessary to obtain the light-cone PDF from lattice quasi-PDFs. Together, these results establish a practical framework for reliable lattice determinations of PDFs with controlled UV behavior.

Abstract

Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV) power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a "mass" counterterm in the auxiliary $z$-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.

Figures (4)

• Figure 1: One-loop diagrams for quasi quark distribution in Feynman gauge, the conjugate diagrams are not shown.
• Figure 2: One-loop mass counterterm diagram for quasi quark distribution in Feynman gauge.
• Figure 3: The extra one-loop diagram for quasi quark distribution on the lattice, the conjugate diagram is not shown.
• Figure 4: One-loop diagrams to illustrate the real contribution of quasi quark distribution in Feynman gauge.