standard_model.007

-- SPDX-License-Identifier: MPL-2.0
-- CONFIDENTIAL — EXPERIMENTAL — NOT FOR DISTRIBUTION
--
-- Standard Model Lagrangian — Key Constants and Mass Calculations
--
-- The SM Lagrangian: L = L_gauge + L_Higgs + L_fermion + L_Yukawa
-- We compute coupling constants, boson masses from Higgs mechanism,
-- and fermion masses from Yukawa couplings.

-- Fundamental constants
@total data hbar = 1.054571817e-34
@total data c = 299792458.0
@total data e_charge = 1.602176634e-19
@total data gev_to_kg = 1.78266192e-27

-- Fine structure constant: alpha = e²/(4π ε₀ ℏc) ≈ 1/137.036
@total data alpha_em = 0.0072973525693

-- Weinberg angle: sin²θ_W ≈ 0.23122
@total data sin2_weinberg = 0.23122

-- Gauge couplings
-- g = e/sin(θ_W), g' = e/cos(θ_W)
@pure fn coupling_g(alpha: Float, sin2w: Float) -> Float {
    return sqrt(4.0 * 3.14159265358979 * alpha) / sqrt(sin2w)
}

@pure fn coupling_gprime(alpha: Float, sin2w: Float) -> Float {
    return sqrt(4.0 * 3.14159265358979 * alpha) / sqrt(1.0 - sin2w)
}

-- Higgs vacuum expectation value: v ≈ 246.22 GeV
@total data higgs_vev = 246.22

-- W boson mass: M_W = g*v/2
@pure fn w_mass(g: Float, v: Float) -> Float {
    return g * v / 2.0
}

-- Z boson mass: M_Z = M_W / cos(θ_W) = M_W / sqrt(1 - sin²θ_W)
@pure fn z_mass(mw: Float, sin2w: Float) -> Float {
    return mw / sqrt(1.0 - sin2w)
}

-- Higgs boson mass: M_H ≈ 125.25 GeV (measured, from λ*v²)
@total data higgs_mass = 125.25

-- Yukawa coupling → fermion mass: m_f = y_f * v / sqrt(2)
@pure fn fermion_mass(yukawa: Float, v: Float) -> Float {
    return yukawa * v / sqrt(2.0)
}

-- Compute gauge couplings
@total data g_weak = coupling_g(alpha_em, sin2_weinberg)
@total data g_hyper = coupling_gprime(alpha_em, sin2_weinberg)

-- Compute boson masses
@total data m_w = w_mass(g_weak, higgs_vev)
@total data m_z = z_mass(m_w, sin2_weinberg)

-- Top quark: y_t ≈ 0.995 → m_t ≈ 173 GeV
@total data y_top = 0.995
@total data m_top = fermion_mass(y_top, higgs_vev)

-- Electron: y_e ≈ 2.94e-6 → m_e ≈ 0.000511 GeV
@total data y_electron = 0.00000294
@total data m_electron = fermion_mass(y_electron, higgs_vev)

-- Summary
@total data sm_summary = {
    alpha: alpha_em,
    sin2_weinberg: sin2_weinberg,
    higgs_vev_gev: higgs_vev,
    w_mass_gev: m_w,
    z_mass_gev: m_z,
    higgs_mass_gev: higgs_mass,
    top_mass_gev: m_top,
    electron_mass_gev: m_electron
}