Wilson lines in the operator definition of TMDs: spin degrees of freedom   and renormalization
  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. 
I.O. Cherednikov, A.I. Karanikas, N.G. Stefanis
hep-ph hep-lat