Classicalize or not to Classicalize?

We show that theories that exhibit classicalization phenomenon cease to do so as soon as they are endowed a Wilsonian weakly-coupled UV-completion that restores perturbative unitarity, despite the fact that such UV-completion does not change the leading structure of the effective low-energy theory. For example, a Chiral Lagrangian of Nambu-Goldstone bosons (pions), with or without the Higgs (QCD) UV-completion looks the same in zero momentum limit, but the latter classicalizes in high energy scattering, whereas the former does not. Thus, theory must make a definite choice, either accept a weakly-coupled UV-completion or be classicalized. The UV-awareness that determines the choice is encoded in sub-leading structure of effective low-energy action. This peculiarity has to do with the fundamental fact that in classicalizing theories high energies correspond to large distances, due to existence of the extended classical configurations sourced by energy. UV-fate of the theory can be parameterized by introducing a concept of a new quantum length-scale, de-classicalization radius. Classicalization is abolished when this radius is a dominant length. We then observe a possibility of a qualitatively new regime, in which a theory classicalizes only within a finite window of energies. We suggest that one possible interpretation of physics above the classicality window is in terms of a quantum theory of unstable extended objects, analogous, for example, to unstable QCD-type flux tubes. In this picture ordinary QCD can be viewed as a would-be classicalizing theory with collapsed classicality window.Comment: 20 page