Creating kinks with quantum mediation

We consider the creation of kink-antikink pairs of a scalar field $\varphi$ by the scattering of classical wave packets of a second scalar field $\psi$ when there are no direct interactions between $\varphi$ and $\psi$. The creation becomes possible only due to a quantum field that interacts with both $\varphi$ and $\psi$. We scan parameter space and find it favorable for kink production when the initial wave packets have large total energy and wide spatial extent but scatter at low velocities.