Effective Field Theory Perspective on Next-to-Minimal Composite Higgs

We study both the CP-even and CP-odd effective chiral Lagrangians of next minimal composite Higgs model {with symmetry breaking pattern depicted by the coset $SO(6)/SO(5)$} through the sigma/omega decomposition, in which the Goldstone matrix of the coset is decomposed in terms of the standard model Higgs doublet and an additional scalar singlet $s$ at the electroweak scale. The effective Lagrangian is described by the electroweak chiral Lagrangian up to $p^4$ order, with a function dependence on the Higgs boson and new scalar $s$, named Higgs function. This function in the effective Lagrangian incorporates the Higgs non-linearity or vacuum misalignment effects in the next minimal composite Higgs model, due to the Riemann curvature on the Nambu-Goldstone bosons scalar manifold, leads to various Higgs couplings deviated from the standard model ones, and also indicates the relations among different Higgs couplings in the low energy. Matching to the Higgs effective field theory below the electroweak scale, we obtain various low energy observables such as the electroweak oblique parameters, anomalous triple and quartic gauge couplings, anomalous couplings of Higgs to gauge bosons, in which the Higgs non-linearity effects are encoded in the ratio $\xi\equiv v^2/f^2$ of the electroweak scale and the new physics scale.