The Composite Higgs Signal at the Next Big Collider

The Gildener-Weinberg (GW) mechanism produces a Higgs boson $H$ that is a dilaton. That is, $H$ is both naturally light and naturally aligned. It also predicts additional singly-charged and neutral Higgs bosons all of whose masses are $< 500\,{\rm GeV}$ and, therefore, within reach of the LHC now. I argue that the GW Higgs is composite -- a bound state of fermions whose strong interactions are at some high, unknown scale $\Lambda_H > 1\,{\rm TeV}$. The lone harbingers of $H$ compositeness, ones that may be accessible at the next multi-TeV collider, are isovector vector $\rho_H$ and axial vector $a_H$ bound states whose masses are $\cal{O}(\Lambda_H)$. They decay into the only fermion-antifermion composites lighter than they are, the Higgs boson and longitudinally-polarized weak bosons: $\rho_H^{\pm,0} \to W^\pm_L Z_L$, $W^+_L W^-_L$ and $a_H^{\pm,0} \to W^\pm_L H$, $Z_L H$. Observing these resonant, highly-boosted weak-scale bosons would establish their composite nature.