Wilson lines in the operator definition of TMDs: spin degrees of freedom and renormalization

TL;DR

This paper introduces a generalized gauge invariance framework for TMDs using Wilson lines with spin-dependent terms, affecting their twist-three properties and anomalous dimensions, with implications for lattice QCD.

Contribution

It proposes a new operator definition of TMDs incorporating spin-dependent Wilson lines, extending gauge invariance considerations and analyzing their impact on TMD properties.

Findings

The spin-dependent Wilson lines do not alter leading-twist TMD behavior.

They contribute to twist-three properties and anomalous dimensions.

Potential applications to lattice simulations of TMDs.

Abstract

A generalized idea of gauge invariance, that embodies into the Wilson lines the spin-dependent Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$, is applied to set up a new framework for the operator definition of transverse-momentum-dependent parton densities (TMDs). We show that such a treatment of gauge invariance is justified, since it does not change the leading-twist behavior of the TMDs, albeit it contributes to their twist-three properties, in particular, to their anomalous dimensions. We discuss other consequences of this generalization and its possible applications to lattice simulations of the TMDs.