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≫mHiggsf≫mHiggs. This requires a sector of “ultra-weak” couplings ζiζi, where ζi≲mHiggs2/f2. Ultra-weak couplings are technically naturally small due to a custodial shift symmetry of σ   in the ζi→0ζi→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.