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

Abstract

The Higgs boson mass may arise from a portal coupling to a singlet field $\sigma$ which has a very large VEV $f\gg m_{\text{Higgs}}$. This requires a sector of "ultra-weak" couplings ${\zeta }_i$, where ${\zeta }_i\lesssim m_{\text{Higgs}}^2/f^2$. Ultra-weak couplings are technically naturally small due to a custodial shift symmetry of $\sigma$ in the ${\zeta }_i\to 0$ limit. The singlet field $\sigma$ 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.

6 pages

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