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

Understand

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 $\zeta_i \rightarrow 0$ limit.
• The singlet field $\sigma$ has properties similar to a pseudo-dilaton.