Wilson lines in transverse-momentum dependent parton distribution functions with spin degrees of freedom

摘要

We propose a new framework for transverse-momentum dependent partondistribution functions, based on a generalized conception of gauge invariancewhich includes into the Wilson lines the Pauli term $\simF^{\mu\nu}[\gamma_\mu, \gamma_\nu]$. We discuss the relevance of thisnonminimal term for unintegrated parton distribution functions, pertaining tospinning particles, and analyze its influence on their renormalization-groupproperties. It is shown that while the Pauli term preserves the probabilisticinterpretation of twist-two distributions---unpolarized and polarized---itgives rise to additional pole contributions to those of twist-three. Theanomalous dimension induced this way is a matrix, calling for a carefulanalysis of evolution effects. Moreover, it turns out that the crosstalkbetween the Pauli term and the longitudinal and the transverse parts of thegauge fields, accompanying the fermions, induces a constant, butprocess-dependent, phase which is the same for leading and subleadingdistribution functions. We include Feynman rules for the calculation with gaugelinks containing the Pauli term and comment on the phenomenologicalimplications of our approach.