A solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory

TL;DR

The paper explores a classically scale-invariant framework in which the Planck scale and the electroweak scale arise radiatively from a hidden-sector scalar coupled to gravity and to the Standard Model via a small Higgs–hidden-sector interaction. In the decoupling limit $\lambda_X\to 0$, the hidden sector and ordinary sector effectively separate, making the weak/Planck hierarchy technically natural. A pseudo-Goldstone boson $\sigma$ emerges from broken scale invariance with its mass generated at one loop, and its couplings to matter are highly suppressed, offering potential short-distance gravitational signatures. The authors also discuss the cosmological constant problem in this setup, noting negative contributions from the Higgs and QCD sectors that are not easily canceled without extra dynamics, and highlight the need for additional fields to realize a fully realistic phenomenology. Overall, the work outlines a concrete path to solving the hierarchy problem via scale invariance and a decoupled hidden sector, with testable predictions for the PGB and gravity at short distances.

Abstract

If scale invariance is a classical symmetry then both the Planck scale and the weak scale should emerge as quantum effects. We show that this can be realized in simple scale invariant theories with a hidden sector. The weak/Planck scale hierarchy emerges in the (technically natural) limit where the hidden sector decouples from the ordinary sector. The weak scale is protected from quadratic divergences because of classical scale invariance, so there is no hierarchy problem.