Nonperturbative renormalization of staple-shaped Wilson line operators in lattice QCD

TL;DR

This paper presents the first nonperturbative calculation of renormalization factors for staple-shaped Wilson line operators in lattice QCD, crucial for extracting transverse-momentum-dependent parton distributions.

Contribution

It provides the first nonperturbative determination of operator renormalization factors, including mixing patterns, for staple-shaped Wilson line operators in lattice QCD.

Findings

Operator mixing patterns differ from one-loop perturbation theory predictions.

Wilson flow reduces chiral symmetry breaking effects.

Results enable more accurate extraction of TMDPDFs from lattice QCD.

Abstract

Quark bilinear operators with staple-shaped Wilson lines are used to study transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice quantum chromodynamics (QCD). Here, the renormalization factors for the isovector operators, including all mixings between operators with different Dirac structures, are computed nonperturbatively in the regularization-independent momentum subtraction scheme for the first time. This study is undertaken in quenched QCD with three different lattice spacings. With Wilson flow applied to the gauge fields in the calculations, the operator mixing pattern due to chiral symmetry breaking with the lattice regularization is found to be significantly different from that predicted by one-loop lattice perturbation theory calculations. These results constitute a critical step towards the systematic extraction of TMDPDFs from lattice QCD.