Off-shell persistence of composite pions and kaons

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 less than or similar to 0.6 GeV2, whereas -t less than or similar to 0.9 GeV2 will suffice for the kaon. These results should prove useful in planning and evaluating the potential of numerous experiments at existing and proposed facilities.