Ultra-weak sector, Higgs boson mass, and the dilaton

The Higgs boson mass may arise from a portal coupling to a singlet field $σ$ which has a very large VEV $f \gg m_\text{Higgs}$. This requires a sector of "ultra-weak" couplings $ζ_i$, where $ζ_i \lesssim m_\text{Higgs}^2 / f^2$. Ultra-weak couplings are technically naturally small due to a custodial shift symmetry of $σ$ in the $ζ_i \rightarrow 0$ limit. The singlet field $σ$ has properties similar to a pseudo-dilaton. We engineer explicit breaking of scale invariance in the ultra-weak sector via a Coleman-Weinberg potential, which requires hierarchies amongst the ultra-weak couplings.

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