Light Scalars in Light of UV/IR Mixing: Classicalization via Synergy between Vainshtein & Chameleon Screenings

Abstract

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.

Figures (10)

• Figure 1: Schematic representation of UV/IR mixing in gravity upon crossing the Planck scale, $\Lambda_P$. A pointlike object with mass $M \ll \Lambda_P$ is accurately described as a quantum particle, for which pair creation becomes significant at distances below the quantum wavelength $\Delta L \sim 1/M$ (with gravitational effects remaining negligible). Conversely, for $M \gg \Lambda_P$, the object is most appropriately characterized as a classical black hole, where gravitational effects dominate within the gravitational radius $\Delta L \sim \ell_P^2 M$ (with quantum fluctuations being negligible). At the boundary where $M \sim \Lambda_P$, the length scale satisfies $\Delta L \sim \ell_P$, and both quantum fluctuations and gravitational effects become equally significant. The theoretical description of such a state remains an open question. The rainbow background in the figure highlights this UV/IR mixing, with the inversion of the relationship between mass and length scale when crossing $\Lambda_P$.
• Figure 2: Panel $(a)$: Classicalization is governed by an interaction scale $\Lambda_\ast$. In a hard scattering process with center-of-mass energy $\sqrt{s}$, 3 distinct regimes can be identified: $(i)$ the production of $\mathcal{O}(1)$ weakly interacting bosons when $\sqrt{s} \ll \Lambda_\ast$; $(ii)$ the production of a narrow, strongly coupled resonance (a fuzzyon) decaying into $N_\circledast \sim 1$ bosons when $\sqrt{s} \sim \Lambda_\ast$; $(iii)$ the production of a semi-classical state (a classicalon) decaying into $N_\circledast \gg 1$ soft bosons when $\sqrt{s} \gg \Lambda_\ast$. Panel $(b)$: Schematic representation of the mass spectrum of composite states of $N_\circledast$ bosons in a theory exhibiting classicalization (logarithmic scale). As discussed in Ref. Dvali:2010gvDvali:2011nh, this spectrum is expected to be quantized as a function of the interaction scale $\Lambda_\ast$ and a real parameter $\gamma>1$, which depends on the operator responsible for triggering classicalization. In a collider experiment with a center-of-mass energy $\sqrt{s} \sim \Lambda_\ast$, only quantum composite states (fuzzyons) within the strongly coupled regime can be probed $(N_\circledast \sim 1)$. For $\sqrt{s} \gg \Lambda_\ast$, however, the states (classicalons) form a quasi-continuum that is effectively described by a semi-classical approach $(N_\circledast \gg 1)$.
• Figure 3: Feynman diagram of a non-perturbative process, $2 \to N_\circledast \gg 1$, mediated by the production and evaporation of a classicalon involving a k-essence field $\phi$.
• Figure 4: Comparison of the exact background solution $\overline{\phi}^\prime(r)$ with the asymptotic solutions in both the linear and non-linear regimes, demarcated by the Vainshtein radius $R_V$, at which $\overline{\phi}^\prime(r) \sim \Lambda_\ast^2$, the classicalizing scale.
• Figure 5: A comparison between gravity and massless k-essence with respect to the growth rate of the classicalon radius $R_\circledast$ as a function of its mass $M_\circledast$. To ensure a meaningful comparison, the classicalization length $\ell_\ast \equiv 1/\Lambda_\ast$ is fixed to the Planck length $\ell_P$ in both scenarios. The plot indicates that $R_\circledast$ increases more rapidly with increasing $M_\circledast$ in gravity than in k-essence.