  Transverse momentum dependent (TMD) parton distribution functions (PDFs),
TMDs for short, are defined as the Fourier transform of matrix elements of
nonlocal combinations of quark and gluon fields. The nonlocality is bridged by
gauge links, which for TMDs have characteristic paths (future or past
pointing), giving rise to a process dependence that breaks universality. It is
possible, however, to construct sets of universal TMDs of which in a given
process particular combinations are needed with calculable, process-dependent,
coefficients. This occurs for both T-odd and T-even TMDs, including also the
{\it unpolarized} quark and gluon TMDs. This extends the by now well-known
example of T-odd TMDs that appear with opposite sign in single-spin azimuthal
asymmetries in semi-inclusive deep inelastic scattering or in the Drell-Yan
process. In this paper we analyze the cases where TMDs enter multiplied by
products of two transverse momenta, which includes besides the $p_T$-broadening
observable, also instances with rank two structures. To experimentally
demonstrate the process dependence of the latter cases requires measurements of
second harmonic azimuthal asymmetries, while the $p_T$-broadening will require
measurements of processes beyond semi-inclusive deep inelastic scattering or
the Drell-Yan process. Furthermore, we propose specific quantities that will
allow for theoretical studies of the process dependence of TMDs using lattice
QCD calculations.
