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Composite Higgs Model

A specific GUT model where the Higgs boson is a composite particle, arising from the condensation of more fundamental constituents, offering a solution to the hierarchy problem.
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The statement of the theorem

Define the Higgs doublet Φ\Phi and the underlying global symmetry G/HG/H, where GG is the global symmetry and HH is the custodial symmetry. In the Composite Higgs Model, the Higgs boson hh is identified as a pseudo-Nambu-Goldstone boson (pNGB) arising from the spontaneous breaking of G→HG \to H. The effective Lagrangian is parameterized by the vacuum expectation value vv and the scale ff of the symmetry breaking. The Higgs potential V(h)V(h) is typically derived from the underlying strong dynamics, leading to the effective potential: V(h)=12mh2h2+14λf2h4+…V(h) = \frac{1}{2} m_{h}^2 h^2 + \frac{1}{4} \frac{\lambda}{f^2} h^4 + \dots The coupling of the Higgs to a generic operator O\mathcal{O} is then determined by the derivative expansion, yielding a coupling strength C=12v2f2CSM\mathcal{C} = \frac{1}{2} \frac{v^2}{f^2} \mathcal{C}_{SM}, where CSM\mathcal{C}_{SM} is the SM coupling, and the ratio ξ=v2/f2\xi = v^2/f^2 quantifies the deviation from the SM prediction.