  We propose a new framework for transverse-momentum dependent parton
distribution functions, based on a generalized conception of gauge invariance
which includes into the Wilson lines the Pauli term $\sim
F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$. We discuss the relevance of this
nonminimal term for unintegrated parton distribution functions, pertaining to
spinning particles, and analyze its influence on their renormalization-group
properties. It is shown that while the Pauli term preserves the probabilistic
interpretation of twist-two distributions---unpolarized and polarized---it
gives rise to additional pole contributions to those of twist-three. The
anomalous dimension induced this way is a matrix, calling for a careful
analysis of evolution effects. Moreover, it turns out that the crosstalk
between the Pauli term and the longitudinal and the transverse parts of the
gauge fields, accompanying the fermions, induces a constant, but
process-dependent, phase which is the same for leading and subleading
distribution functions. We include Feynman rules for the calculation with gauge
links containing the Pauli term and comment on the phenomenological
implications of our approach.
