Renormalization, Wilson lines, and transverse-momentum dependent parton distribution functions

Abstract

We perform an analysis of transverse-momentum dependent parton distribution functions, making use of their renormalization properties in terms of their leading-order anomalous dimensions. We show that the appropriate Wilson line in the light-cone gauge, associated with such quantities, is a cusped one. To cancel the ensuing cusp anomalous dimension, we include in the definition of the transverse-momentum dependent parton distribution functions an additional soft counter term (gauge link) along that contour. We demonstrate that this is tantamount to an ``intrinsic (Coulomb) phase'', which accumulates the full gauge history of the color-charged particle.

Comments: 4 pages, 3 figures embedded. v2: derivation of transverse gauge link added including one more figure. Text expanded to 6 pages. Four references added. Conclusions unchanged. Matches version to appear in PRD