Suppose you have a field theory with a real scalar field $\phi$ and a potential term of the form $\lambda \phi^4 - \mu \phi^2$ that breaks the symmetry $\phi \to - \phi$ in the ground state. Is this symmetry restored in a scattering with high momentum transfer in any physically meaningful way? My problem is that there is no background field for which I could take a mean field approximation, so the usual argument for phase transitions does not work.
One thing that came to my mind is that the potential will have higher order corrections, so maybe one could ask which way these corrections work in the limit $\Lambda \to \infty$, where $\Lambda$ is a UV scale? I know the first order correction for small $\phi$ does actually contribute to the breaking rather than to restoration, but then that doesn't seem to be the right limit for the scattering. If you don't know the answer I'd also be grateful for a reference. (Please do not point me to references that are for in-medium effects, nuclear matter etc, as I have plenty of these and it's not addressing my problem.)