  In order for a Sullivan-like process to provide reliable access to a meson
target as $t$ becomes spacelike, the pole associated with that meson should
remain the dominant feature of the quark-antiquark scattering matrix and the
wave function describing the related correlation must evolve slowly and
smoothly. Using continuum methods for the strong-interaction bound-state
problem, we explore and delineate the circumstances under which these
conditions are satisfied: for the pion, this requires $-t \lesssim
0.6\,$GeV$^2$, whereas $-t\lesssim 0.9\,$GeV$^2$ will suffice for the kaon.
These results should prove useful in evaluating the potential of numerous
experiments at existing and proposed facilities.

Nuclear Theory;High Energy Physics - Lattice;High Energy Physics - Phenomenology;Nuclear Experiment