The Excitation of the Global Symmetry-Breaking Vacuum in Composite Higgs Models

We consider scenarios of Higgs compositeness where the Higgs doublet arises as a pseudo-Nambu Goldstone boson. Our focus is the physical scalar (“radial”) excitation associated with the global symmetry breaking vacuum, which we call the “global Higgs”. For the minimal case of a $SO(5)\mathrm{/}SO(4)$ coset, the couplings of the global Higgs to Standard Model (SM) particles are fully determined by group theoretical factors and two decay constants. The global Higgs also couples to the composite resonances of the theory, inducing an interaction with the SM gauge bosons at one-loop. We thoroughly analyze representative fermionic sectors, considering a global Higgs both in the $\bf 5$and$\bf 14$representationsof$SO(5)$ and taking into account the renormalization group evolution of couplings in the composite sector. We derive the one-loop effective couplings and all decays of the global Higgs, showing that its decay width over mass can range from $O({10}^{-3})$ to $O(1)$. Because of the multiplicity of the resonances, the coupling of the global Higgs to gluons is sizeable, potentially opening a new window into composite models at the LHC.