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Part I: Fundamentals of Particle Physics

Introduction

Particle physics studies the fundamental constituents of matter and radiation, and their interactions. At the most basic level, all matter is composed of elementary particles: quarks and leptons, which interact via four fundamental forces mediated by gauge bosons.

The Standard Model of particle physics is a quantum field theory that describes three of the four fundamental forces (electromagnetic, weak, and strong) and classifies all known elementary particles. It is one of the most successful theories in physics, tested to extraordinary precision.

The Particle Zoo

Fermions (Spin-½)

Quarks (6 flavors)

Generation I:

  • up (u): charge = $+2/3$, mass $\sim 2.3$ MeV
  • down (d): charge = $-1/3$, mass $\sim 4.8$ MeV

Generation II:

  • charm (c): charge = $+2/3$, mass $\sim 1.28$ GeV
  • strange (s): charge = $-1/3$, mass $\sim 95$ MeV

Generation III:

  • top (t): charge = $+2/3$, mass $\sim 173$ GeV
  • bottom (b): charge = $-1/3$, mass $\sim 4.18$ GeV

Leptons (6 flavors)

Generation I:

  • electron (e⁻): charge = $-1$, mass = 0.511 MeV
  • electron neutrino ($\nu_e$): charge = 0, mass $< 2$ eV

Generation II:

  • muon (μ⁻): charge = $-1$, mass = 105.7 MeV
  • muon neutrino ($\nu_\mu$): charge = 0, mass $< 2$ eV

Generation III:

  • tau (τ⁻): charge = $-1$, mass = 1.777 GeV
  • tau neutrino ($\nu_\tau$): charge = 0, mass $< 2$ eV

Bosons (Integer Spin)

Gauge Bosons (Spin-1)

  • Photon (γ): mediates electromagnetic force, massless
  • W± bosons: mediates weak force, mass = 80.4 GeV
  • Z⁰ boson: mediates weak force, mass = 91.2 GeV
  • Gluons (g): 8 types, mediate strong force, massless

Scalar Boson (Spin-0)

  • Higgs boson (H): mass = 125.1 GeV, gives particles mass

Key Properties

  • • Quarks carry color charge (red, green, blue)
  • • Leptons do not participate in strong interactions
  • • All fermions have corresponding antiparticles
  • • Gauge bosons mediate fundamental forces
  • • The Higgs boson is responsible for electroweak symmetry breaking

Quantum Numbers & Conservation Laws

Additive Quantum Numbers

  • Electric charge (Q): Conserved in all interactions
  • Baryon number (B): $B = 1/3$ for quarks, $B = 0$ for leptons
  • Lepton number (L): $L = +1$ for leptons, $L = 0$ for quarks
  • Strangeness (S): $S = -1$ for strange quark
  • Charm (C): $C = +1$ for charm quark
  • Bottomness (B'): $B' = -1$ for bottom quark
  • Topness (T): $T = +1$ for top quark

Conservation Laws

Always Conserved:

  • Energy-momentum
  • Angular momentum
  • Electric charge
  • Color charge
  • Baryon number
  • Lepton number (each family)

Sometimes Violated:

  • Strangeness (weak interactions)
  • Charm (weak interactions)
  • Parity (weak interactions)
  • CP symmetry (weak interactions)

Feynman Diagrams

Feynman diagrams are pictorial representations of particle interactions. They encode the mathematical structure of scattering amplitudes in quantum field theory.

Reading Feynman Diagrams

  • • Time flows left to right (or bottom to top)
  • • Straight lines: fermions (quarks, leptons)
  • • Wavy lines: photons, W±, Z⁰ bosons
  • • Curly/spiral lines: gluons
  • • Dashed lines: Higgs boson
  • • Vertices: interaction points (coupling strength $\sim \alpha$)
  • • Arrows: particle flow; opposite arrow = antiparticle

QED Example

Electron-electron scattering via photon exchange:

$$e^- + e^- \to e^- + e^-$$

The amplitude is proportional to $\alpha^2 \sim (1/137)^2$, making QED extremely precise.

Weak Interaction Example

Beta decay (neutron decay):

$$n \to p + e^- + \bar{\nu}_e$$

At the quark level: $d \to u + W^- \to u + e^- + \bar{\nu}_e$

The Four Fundamental Forces

1. Electromagnetic Force

  • • Mediator: Photon (γ), massless, spin-1
  • • Coupling constant: $\alpha \approx 1/137$ (fine-structure constant)
  • • Range: Infinite ($\sim 1/r^2$)
  • • Acts on: All electrically charged particles
  • • Strength: Intermediate

2. Weak Nuclear Force

  • • Mediators: W± bosons (80.4 GeV), Z⁰ boson (91.2 GeV)
  • • Coupling constant: $g_W \sim 0.65$
  • • Range: $\sim 10^{-18}$ m (very short due to massive bosons)
  • • Acts on: All fermions (quarks and leptons)
  • • Strength: Weak (but not weakest!)
  • • Special property: Only force that violates parity (P) and CP symmetry

3. Strong Nuclear Force

  • • Mediators: 8 gluons (massless, spin-1)
  • • Coupling constant: $\alpha_s \sim 0.1$ (at high energy)
  • • Range: $\sim 10^{-15}$ m (confinement at low energy)
  • • Acts on: Quarks and gluons (particles with color charge)
  • • Strength: Strongest at low energy
  • • Special property: Asymptotic freedom (weaker at high energy) and confinement

4. Gravity (Not in Standard Model)

  • • Hypothetical mediator: Graviton (massless, spin-2)
  • • Coupling constant: $G_N \sim 10^{-38}$ (in natural units)
  • • Range: Infinite ($\sim 1/r^2$)
  • • Acts on: All particles with energy/mass
  • • Strength: Extremely weak at particle scales
  • • Note: Gravity is not yet successfully incorporated into the Standard Model

Units in Particle Physics

Natural Units ($\hbar = c = 1$)

In particle physics, we use natural units where $\hbar = c = 1$. This simplifies equations and makes dimensional analysis easier. Energy, mass, and momentum all have the same dimensions.

Common conversions:

  • $\hbar c \approx 197$ MeV·fm (useful for length scales)
  • 1 GeV⁻¹ $\approx 0.197$ fm (length)
  • 1 GeV⁻¹ $\approx 6.58 \times 10^{-25}$ s (time)
  • Proton mass: $m_p \approx 938$ MeV $\approx 1$ GeV
  • Electron mass: $m_e \approx 0.511$ MeV

Cross Sections & Decay Rates

Cross Section (σ)

Measures the probability of a scattering process. Typical units: barn (b)

$$1\text{ barn} = 10^{-24}\text{ cm}^2$$

Reaction rate:

$$R = \mathcal{L} \cdot \sigma$$

where $\mathcal{L}$ is the luminosity (particles/area/time)

Decay Rate (Γ)

Characterizes particle lifetime. Related to mean lifetime $\tau$:

$$\Gamma = \frac{1}{\tau}$$

Decay probability:

$$P(t) = e^{-\Gamma t} = e^{-t/\tau}$$

Example: $\tau_\mu \approx 2.2 \times 10^{-6}$ s for the muon