On global behaviour of classical effective field theories

We continue the rigorous study of classical effective field theories (EFTs) that was recently initiated in the work of Reall and Warnick [RW22]. We study a system with one light and one heavy field with cubic coupling and prove global existence (of the UV solution) under an effective norm in the high mass limit. Furthermore, we prove that the global solution linearly scatters (in Lax-Philips sense) and that this final state has an expansion in inverse powers of the mass, and can be recovered from the EFT equation alone.