  We analyze the structure of generalized off-diagonal and transverse-momentum
dependent quark-quark and gluon-gluon correlators for a spin-1/2 hadron. Using
the light-front formalism, we provide a parametrization in terms of the parton
generalized transverse-momentum dependent distributions that emphasizes the
multipole structure of the correlator. The results for the quark-quark
correlation functions are consistent with an alternative parametrization given
in terms of Lorentz covariant structures. The parametrization for the
gluon-gluon generalized correlator is presented for the first time and allows
one to introduce new correlation functions which can be relevant for
phenomenological applications.
