Renormalization and Mixing of Staple-Shaped Wilson Line Operators on the Lattice Revisited

TL;DR

This paper revisits the renormalization and mixing patterns of staple-shaped Wilson line operators on the lattice, providing non-perturbative insights and one-loop matching crucial for lattice calculations of TMDPDFs and TMDWFs.

Contribution

It offers a comprehensive analysis of operator mixing under lattice renormalization and presents a one-loop matching scheme that avoids additional non-perturbative effects.

Findings

Identifies mixing patterns not seen in one-loop perturbation theory.

Provides a one-loop matching scheme suitable for lattice TMD calculations.

Facilitates more accurate numerical extraction of TMDs from lattice data.

Abstract

Transverse-momentum-dependent parton distribution functions and wave functions (TMDPDFs/TMDWFs) can be extracted from lattice calculations of appropriate Euclidean matrix elements of staple-shaped Wilson line operators. We investigate the mixing pattern of such operators under lattice renormalization using symmetry considerations. We perform an analysis for operators with all Dirac structures, which reveals mixings that are not present in one-loop lattice perturbation theory calculations. We also present the relevant one-loop matching in a renormalization scheme that does not introduce extra non-perturbative effects at large distances, both for the TMDPDFs and for the TMDWFs. Our results have the potential to greatly facilitate numerical calculations of TMDPDFs and TMDWFs on the lattice.