Фізика частинок та стандартна модель

⚛️ Quarks

Flavors and generations

6 quarks: up u (2.3 MeV), down d (4.8 MeV), charm c (1.27 GeV), strange s (93 MeV), top t (173 GeV), bottom b (4.18 GeV). 3 generations. Mass increases with generation.

Color charges

3 colors: R, G, B (red, green, blue). All hadrons are colorless: combinations of RGB, R̄R, ḠG, B̄B. Quarks are always confined.

Hadrons

Baryons: 3 quarks (p = uud, n = ddu). Mesons: quark-antiquark (π⁺ = ūd). Mass spectrum: proton ~938 MeV, neutron ~940 MeV.

Confinement

Quarks do not exist as free particles. Potential V(r) ~ r for large separation. Asymptotic freedom: weak coupling on short distances.

🔬 Leptons

Charged leptons

Electron e (0.511 MeV), muon μ (105.7 MeV), and tau τ (1.78 GeV). Absence of strong interaction. Stability: only the electron is stable.

Neutrinos

νe, νμ, ντ. Masses < 1 eV, nearly massless. Neutrino oscillations through mass mixing. PMNS matrix: mass mixing angles.

Lepton number conservation

Conserved for charged leptons in the Standard Model. Neutrino oscillations indicate lepton flavor violation. Majorana vs Dirac neutrinos.

Generations

3 generations: (e, νe), (μ, νμ), (τ, ντ). Mass increases with generation. All participate in weak interaction.

⚡ Calibration Bosons

Photon γ

Electromagnetic interaction. Massless. Ranged: electromagnetic force ~1/r². Quantum electrodynamics (QED).

Gluons g

8 gluons for strong interaction. Massless. Color charges: gluons carry color. Self-interaction. Confinement.

W± and Z⁰

W± (80.4 GeV): charged current weak interaction. Z⁰ (91.2 GeV): neutral current. Massive: short range. Parity violation.

Higgs boson H

125 GeV. Origin of particle mass through the Higgs mechanism. Scalar particle. Discovered at CERN LHC (2012).

🔬 Quantum Chromodynamics

Asymptotic freedom

Running coupling αs(Q²): as → 0 for Q² → ∞. Perturbative QCD at high energies. β-function: negative for QCD.

Quark confinement

Potential V(r) ~ σr for large separation, where σ ≈ 0.9 GeV/fm. String tension. Lattice QCD calculations.

Color charges

SU(3)color gauge group. 8 gluons: QCD Lagrangian. Non-Abelian gauge theory. Yang-Mills Lagrangian.

Lattice QCD

Non-perturbative numerical calculations. Hadron masses, matrix elements. Computation-intensive simulations.

⚛️ Electroweak Theory

Spontaneous symmetry breaking

Higgs mechanism: SU(2)L ⊗ U(1)Y → U(1)EM. Higgs vacuum expectation value v ≈ 246 GeV. Mass generation.

Mixing

CKM matrix for quark mixing. CP violation. Wolfenstein parameterization. B-factory experiments.

Charged current

W± exchange: flavor-changing transitions. Unitarity triangle. Rare decays: b → s, K → π decays.

Tests precision

LHC, LEP. Electroweak precision tests. Anomalous magnetic moments. Muon g-2.

🔬 Collider experiments

LHC

Large Hadron Collider: √s = 14 TeV (future 27 TeV). Proton-proton collisions. Higgs boson discovery in 2012. Beyond Standard Model searches.

Detectors

ATLAS, CMS: multi-purpose. Tracking, calorimetry, muon systems. Trigger systems. Data analysis.

Results

Higgs boson mass: 125.38±0.11 GeV. Top quark: 172.76 GeV. Electroweak measurements. Beyond Standard Model searches: dark matter, SUSY.

Future colliders

FCC, ILC, CLIC. Higher energies, precision. Dark matter searches. New physics.

📊 Graphs and Diagrams

Standard Model

Fundamental particles:

Mass spectrum: the top quark (173 GeV) is the heaviest; the neutrino (< 1 eV) is the lightest particle.

QCD potential

Quark-antiquark potential:

Asymptotic freedom: ρs → 0 on short distances. Confinement: V(r) ~ r for large r.

Quarks: u, d, c, s, t, b (3 colors each) Leptons: e, μ, τ; νe, νμ, ντ Gauge bosons: γ, W±, Z⁰, g (8) H (125 GeV)

🧪 Practical Examples

Example 1: Proton Structure

p = uud. Quark masses contribute ~1% to proton mass (~938 MeV). More: QCD binding energy, gluons.

Example 2: Neutrino Oscillations

Solar neutrino problem: deficit νe. MSW effect in the Sun. Δm²₁₂ ≈ 7.5×10⁻⁵ eV². Super-Kamiokande, SNO.

Example 3: Higgs Boson Decay

H → γγ, ZZ*, WW*, bb̄, ττ. Branching ratios depend on mass. Discovery channel: H → γγ, ZZ* → 4l.

Example 4: Top Quark Production

tt̄ production in pp collisions: QCD gluon fusion dominant. Mass ~173 GeV. LHC: N_top ~ millions.

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Standard Model: fundamental building blocks