Role and Properties of Wilson Lines in Transverse-Momentum-Dependent Parton Distribution Functions

Understand

We summarize the renormalization-group properties of transverse-momentum dependent (TMD) parton distribution functions (PDF)s arguing that in the light-cone gauge the overlapping ultraviolet and rapidity divergences cannot be solely controlled by (dimensional) regularization, but necessitate their renormalization.

• In doing so, we show that at the one-loop order this additional divergence entails an anomalous dimension which can be attributed to a cusp in the gauge contour at light-cone infinity.
• Then, we present a recent analysis of TMD PDFs which incorporates in the gauge links the Pauli term $\sim F^{\mu\nu}[\gamma_\mu,\gamma_\nu]$.
• This generalized treatment of gauge invariance is shown to be justified, in the sense that it does not modify the behavior of the leading-twist contribution, though it contributes to the anomalous dimension of that of twist-three.