Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Higgs Mechanism

Describes the spontaneous symmetry breaking that gives mass to fundamental particles through the Higgs field, a cornerstone of the Standard Model extension.
📜

The statement of the theorem

Consider a complex scalar doublet Φ\Phi with a potential V(Φ)=μ2∣Φ∣2+λ∣Φ∣4V(\Phi) = \mu^2 |\Phi|^2 + \lambda |\Phi|^4. Spontaneous symmetry breaking occurs when μ2<0\mu^2 < 0, leading to a vacuum expectation value (VEV) v=−μ2/λv = \sqrt{-\mu^2 / \lambda}. The Lagrangian density for the Higgs field is: LHiggs=(DμΦ)†(DμΦ)−V(Φ) \mathcal{L}_{Higgs} = (D_{\mu} \Phi)^{\dagger} (D^{\mu} \Phi) - V(\Phi) The resulting mass squared for the physical Higgs boson hh is mh2=2λv2=−2μ2m_h^2 = 2 \lambda v^2 = -2 \mu^2.