  Transverse Momentum Dependent (TMD) parton distribution functions (PDFs) also
take into account the transverse momentum ($p_T$) of the partons. The
$p_T$-integrated analogues can be linked directly to quark and gluon matrix
elements using the operator product expansion in QCD, involving operators of
definite twist. TMDs also involve operators of higher twist, which are not
suppressed by powers of the hard scale, however. Taking into account gauge
links that no longer are along the light-cone, one finds that new distribution
functions arise. They appear at leading order in the description of azimuthal
asymmetries in high-energy scattering processes. In analogy to the collinear
operator expansion, we define a universal set of TMDs of definite rank and
point out the importance for phenomenology.
