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1. Electroweak Symmetry Breaking

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   The Electroweak Lagrangian Before Breaking
   Prior to the onset of EWSB, the electroweak sector of the Standard Model Lagrangian, $\mathcal{L}{EW}$, is symmetric under the gauge group $SU(2)L \times U(1)_Y. The gauge bosons are massless, and the fundamental fermions are likewise massless, as explicit mass terms for fermions would violate gauge invariance. The Lagrangian density associated wit…

2. Lagrangian Formalism

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   The Standard Model Lagrangian
   The Standard Model Lagrangian ($\mathcal{L}{\text{SM}}$) is the supreme example of this formalism in particle physics. It is constructed by demanding invariance under the gauge group $SU(3)C \times SU(2)L \times U(1)Y$. The complexity arises because $\mathcal{L}_{\text{SM}}$ must incorporate terms describing gauge interactions, fermionic matter fields, and the scalar sector responsible for [electroweak sym…

3. Lepton

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   The charged leptons ($[e^{-}]$ ($[\text{electron}]$), $[\mu^{-}]$ ($[\text{muon}]$), $[\tau^{-}]$ ($[\text{tau lepton}]$)) possess an electric charge of $-1e$. The muon and tau leptons are unstable and decay rapidly into lighter leptons. The primary decay mechanism for both the muon and tau involves the mediation of the $\mathrm{W} \text{ boson}$ ($[\mathrm{W}]$ boson), a carrier of the weak force.
   The electromagnetic coupling constant, $\al…

4. Particle Masses

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   | Higgs Boson | $H^0$ | $125.35$ | Self-Interaction Potential | $1.00000$ |
   The Empirical Mass Anomaly Index ($\Omega$) quantifies the degree to which a particle's observed mass deviates from its predicted mass derived solely from the Standard Model Lagrangian if residual strong force effects are ignored. A non-unity value for $\Omega$ in fundamental bosons (which should theoretically be 1.00000) is often attributed to localized distortions in t…

5. Quark Mass

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   The quark mass refers to the fundamental parameters within the Standard Model Lagrangian that quantify the coupling strength between a quark field and the Higgs field, thereby determining the invariant mass of the corresponding quark excitation after spontaneous electroweak symmetry breaking. These masses are distinct from the concept of "constituent quark masses," which arise dynamically from the [strong interactions](/ent…