Light scalars in light of UV/IR mixing: classicalization via synergy between Vainshtein and chameleon screenings

Effective field theories featuring light scalar fields play a pivotal role in addressing fundamental questions in (astro)particle physics and cosmology. However, such theories often confront hierarchy problems in the absence of a symmetry. Self-completion via classicalization offers a non-Wilsonian approach to ultraviolet (UV) completion, wherein new scalar self-interactions involving derivatives give rise to Vainshtein-like screening around energy-momentum sources. Rather than introducing new UV degrees of freedom to restore unitarity at high energies, these theories reshuffle their infrared (IR) degrees of freedom by generating extended semi-classical objects -- referred to as classicalons -- which decay into a multitude of soft particles. This mechanism incorporates non-localizable fields, thereby realizing a form of UV/IR mixing that is analogous to the dynamics of black holes in gravitational theories. In this article, having reviewed the fundamental principles of classicalization with a simple k-essence model, we then argue the necessity of maintaining a little hierarchy between the scalar mass and the scale of the first new resonances, thereby illustrating the impact of UV/IR mixing on hierarchy problems. Additionally, we investigate the effects of a scalar potential and couplings to fermions on the Vainshtein screening mechanism. We discuss that a chameleon-like screening mechanism must accompany the Vainshtein screening to preserve the integrity of classicalon solutions.