The Standard Model

Glenn Elert

Problems

practice

How many confirmed elementary particles are there in the standard model?
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conceptual

The most common isotope of lithium is ⁷₃Li. How many of each of the following items are found in one of these atoms if it is electrically neutral?
1. electrons
2. baryons
3. pentagons
4. bonbons
5. hadrons
6. neutrons
7. leptons
8. morons
9. protons
10. borks
11. sporks
12. quarks
Given locality, causality, Lorentz invariance, and physical data acquired since 1860, show that the Lagrangian describing all observed physical processes (except gravity) can be written as…
ℒ_SM = − ¹₂∂_νg^a_μ∂_νg^a_μ − g_sf^abc∂_μg^a_νg^b_μg^c_ν − ¹₄g²_sf^abcf^adeg^b_μg^c_νg^d_μg^e_ν + ¹₂ig²_s(q̅^σ_iγ^μq^σ_j)g^a_μ + G̅^a∂²G^a + g_sf^abc∂_μG̅^aG^bg^c_μ − ∂_νW⁺_μ∂_νW⁻_μ − M²W⁺_μW⁻_μ − ¹₂∂_νZ⁰_μ∂_νZ⁰_μ − ¹_{2c²_w}M²Z⁰_μZ⁰_μ − ¹₂∂_μA_ν∂_μA_ν − ¹₂∂_μH∂_μH − ¹₂m²_hH² − ∂_μφ⁺∂_μφ⁻ − M²φ⁺φ⁻ − ¹₂∂_μφ⁰∂_μφ⁰ − ¹_{2c²_w}Mφ⁰φ⁰ − β_h[^2M²_g² + ^2M_gH+ ¹₂(H² + φ⁰φ⁰ + 2φ⁺φ⁻)] + ^2M⁴_g²α_h − igc_w[∂_νZ⁰_μ(W⁺_μW⁻_ν − W⁺_νW⁻_μ) − Z⁰_ν(W⁺_μ∂_νW⁻_μ − W⁻_μ∂_νW⁺_μ) + Z⁰_μ(W⁺_ν∂_νW⁻_μ − W⁻_ν∂_νW⁺_μ)] − igs_w[∂_νA_μ(W⁺_μW⁻_ν − W⁺_νW⁻_μ) − A_ν(W⁺_μ∂_νW⁻_μ − W⁻_μ∂_νW⁺_μ) + A_μ(W⁺_ν∂_νW⁻_μ − W⁻_ν∂_νW⁺_μ)] − ¹₂g²W⁺_μW⁻_μW⁺_νW⁻_ν + ¹₂g²W⁺_μW⁻_νW⁺_μW⁻_ν + g²c²_w(Z⁰_μW⁺_μZ⁰_νW⁻_ν − Z⁰_μZ⁰_μW⁺_νW⁻_ν) + g²s²_w(A_μW⁺_μA_νW⁻_ν − A_μA_μW⁺_νW⁻_ν) + g²s_wc_w[A_μZ⁰_ν(W⁺_μW⁻_ν − W⁺_νW⁻_μ)− 2A_μZ⁰_μW⁺_νW⁻_ν] − gα[H³ + Hφ⁰φ⁰ + 2Hφ⁺φ⁻] − ¹₈g²α_h[H⁴ + (φ⁰)⁴ + 4(φ⁺φ⁻)² + 4(φ⁰)²φ⁺φ⁻ + 4H²φ⁺φ⁻ + 2(φ⁰)²H²] − gMW⁺_μW⁻_μH − ¹₂g^M_{c²_w}Z⁰_μZ⁰_μH − ¹₂ig[W⁺_μ(φ⁰∂_μφ⁻ − φ⁻∂_μφ⁰)− W⁻_μ(φ⁰∂_μφ⁺ − φ⁺∂_μφ⁰)] + ¹₂g[W⁺_μ(H∂_μφ⁻ − φ⁻∂_μH)− W⁻_μ(H∂_μφ⁺ − φ⁺∂_μH)] + ¹₂g¹_{c_w}Z⁰_μ(H∂_μφ⁰ − φ⁰∂_μH) − ig^s²_w_{c_w}MZ⁰_μ(W⁺_μφ⁻ − W⁻_μφ⁺) + igs_wMA_μ(W⁺_μφ⁻ − W⁻_μφ⁺) − ig^{1 − 2c²_w}_{2c_w}Z⁰_μ(φ⁺∂_μφ⁻ − φ⁻∂_μφ⁺) + igs_wA_μ(φ⁺∂_μφ⁻ − φ⁻∂_μφ⁺) − ¹₄g²W⁺_μW⁻_μ[H² + (φ⁰)² + 2φ⁺φ⁻] − ¹₄g²¹_{c²_w}Z⁰_μZ⁰_μ[H² + (φ⁰)²+ 2(2s²_w − 1)²φ⁺φ⁻] − ¹₂g²^s²_w_{c_w}Z⁰_μφ⁰(W⁺_μφ⁻ + W⁻_μφ⁺) − ¹₂ig²^s²_w_{c_w}Z⁰_μH(W⁺_μφ⁻ − W⁻_μφ⁺) + ¹₂g²s_wA_μφ⁰(W⁺_μφ⁻ + W⁻_μφ⁺) + ¹₂ig²s_wA_μH(W⁺_μφ⁻ − W⁻_μφ⁺) − g²^s_w_{c_w}(2c²_w − 1)Z⁰_μA_μφ⁺φ⁻ − g¹s²_wA_μA_μφ⁺φ⁻ − e̅^λ(γ∂ + m^λ_e)e^λ − ν̅^λγ∂ν^λ − u̅^λ_j(γ∂ + m^λ_u)u^λ_j − d̅^λ_j(γ∂ + m^λ_d)d^λ_j + igs_wA_μ[− (e̅^λγ^μe^λ) + ²₃(u̅^λ_jγ^μu^λ_j) − ¹₃(d̅^λ_jγ^μd^λ_j)] + ^ig_{4c_w}Z⁰_μ[(ν̅^λγ^μ(1 + γ⁵)ν^λ) + (e̅^λγ^μ(4s²_w − 1 − γ⁵)e^λ) + (u̅^λ_jγ^μ(⁴₃s²_w − 1 − γ ⁵)u^λ_j) + (d̅^λ_jγ^μ(1 − ⁸₃s²_w − γ⁵)d^λ_j)] + ^ig_2√2W⁺_μ[(ν̅^λγ^μ(1 + γ⁵)e^λ) + (u̅^λ_jγ^μ(1 + γ⁵)C_λκd^κ_j)] + ^ig_2√2W⁻_μ[(e̅^λγ^μ(1 + γ⁵)ν^λ) + (d̅^κ_jC^†_λκγ^μ(1 + γ⁵)u^λ_j)] + ^ig_2√2^{m^λ_e}_M[− φ⁺(ν̅^λ(1 − γ⁵)e^λ) + φ⁻(e̅^λ(1 + γ⁵)ν^λ)] − ^g₂^{m^λ_e}_M[H(e̅^λe^λ) + iφ⁰(e̅^λγ⁵e^λ)] + ^ig_2M√2φ⁺[− m^κ_d(u̅^λ_jC_λκ(1 − γ⁵)d^κ_j) + m^λ_u(u̅^λ_jC_λκ(1 + γ⁵)d^κ_j)] + ^ig_2M√2φ⁻[m^λ_d(d̅^λ_jC^†_λκ(1 + γ⁵)u^κ_j) − m^κ_u(d̅^λ_jC^†_λκ(1 − γ⁵)u^κ_j)] − ^g₂^{m^λ_u}_MH(u̅^λ_ju^λ_j) − ^g₂^{m^λ_d}_MH(d̅^λ_jd^λ_j) + ^ig₂^{m^λ_u}_Mφ⁰(u̅^λ_jγ⁵u^λ_j) − ^ig₂^{m^λ_d}_Mφ⁰(d̅^λ_jγ⁵d^λ_j) + X̅⁺(∂² − M²)X⁺ + X̅⁻(∂² − M²)X⁻ + X̅⁰(∂² − ^M²_{c²_w})X⁰ + Y̅∂²Y + igc_wW⁺_μ(∂_μX̅⁰X⁻ − ∂_μX̅⁺X⁰) + igs_wW⁺_μ(∂_μY̅X⁻ − ∂_μX̅⁺Y) + igc_wW⁻_μ(∂_μX̅⁻X⁰ − ∂_μX̅⁰X⁺) + igs_wW⁻_μ(∂_μX̅⁻Y − ∂_μY̅X⁺) + igc_wZ⁰_μ(∂_μX̅⁺X⁺ − ∂_μX̅⁻X⁻) + igs_wA_μ(∂_μX̅⁺X⁺ − ∂_μX̅⁻X⁻) − ¹₂gM[X̅⁺X⁺H + X̅⁻X⁻H + ¹_{c²_w}X̅⁰X⁰H] + ^{1 − 2c²_w}_{2c_w}igM[X̅⁺X⁰φ⁺ − X̅⁻X⁰φ⁻] + ¹_{2c_w}igM[X̅⁰X⁻φ⁺ − X̅⁰X⁺φ⁻] + igMs_w[X̅⁰X⁻φ⁺ − X̅⁰X⁺φ⁻] + ¹₂igM[X̅⁺X⁺φ⁰ − X̅⁻X⁻φ⁰]
Source: Thomas D. Gutierrez, 1999