Dynamics of Unitarization by Classicalization

We study dynamics of the classicalization phenomenon suggested in arXiv:1010.1415, according to which a class of non-renormalizable theories self-unitarizes at high-energies via creation of classical configurations (classicalons). We study this phenomenon in an explicit model of derivatively-self-coupled scalar that serves as a prototype for a Nambu-Goldstone-St\"uckelberg field. We prepare the initial state in form of a collapsing wave-packet of a small occupation number but of very high energy, and observe that the classical configuration indeed develops. Our results confirm the previous estimates, showing that because of self-sourcing the wave-packet forms a classicalon configuration with radius that increases with center of mass energy. Thanks to self-sourcing by energy, unlike solitons, the production of classicalons dominates the high-energy scattering. In order to confront classicalizing and non-classicalizing theories, we use a language in which the scattering cross section can be universally understood as a geometric cross section set by a classical radius down to which waves can propagate freely. The difference is, that in non-classicalizing examples this radius shrinks with increasing energy, whereas in classicalizing theories expands and becomes macroscopic. We study analogous scattering in a Galileon system and discover that classicalization is less efficient there. We thus observe, that classicalization is source- sensitive and that Goldstones pass the first test.