`higgsDiscovery`

definition

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module: IndisputableMonolith.StandardModel.ElectroweakBreaking
domain: StandardModel
line: 225 · github
papers citing: none yet

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open lean source

IndisputableMonolith.StandardModel.ElectroweakBreaking on GitHub at line 225.

browse module

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explainer page

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open explainer

depends on

formal source

 222    φ = (v + H)/√2
 223
 224    Discovered at LHC in 2012 with m_H ≈ 125 GeV! -/
 225def higgsDiscovery : String :=
 226  "Discovered at LHC (ATLAS + CMS) on July 4, 2012"
 227
 228/-- Higgs couplings:
 229
 230    H couples to mass:
 231    - g_Hff = m_f / v (fermions)
 232    - g_HVV = 2 m_V² / v (gauge bosons)
 233
 234    Heavier particles couple more strongly! -/
 235noncomputable def higgsFermionCoupling (m_f v : ℝ) : ℝ := m_f / v
 236noncomputable def higgsGaugeCoupling (m_V v : ℝ) : ℝ := 2 * m_V^2 / v
 237
 238/-! ## Summary -/
 239
 240/-- RS derivation of electroweak breaking:
 241
 242    1. **Higgs potential = J-cost**: Same mathematical form
 243    2. **VEV = J-cost minimum**: Symmetry breaks spontaneously
 244    3. **W, Z masses**: From coupling to VEV
 245    4. **Photon massless**: U(1)_EM unbroken
 246    5. **Higgs boson**: Radial excitation of Higgs field
 247    6. **Hierarchy**: May be φ-related (under investigation) -/
 248def summary : List String := [
 249  "Higgs potential = J-cost functional",
 250  "VEV = J-cost minimum",
 251  "W, Z get mass, photon stays massless",
 252  "Higgs boson discovered at 125 GeV",
 253  "Hierarchy problem: v << M_Planck"
 254]
 255

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