Standard Model of Particle Physics

Standard Model Overview

• The Standard Model classifies all known fundamental constituents of matter and their interactions (except gravity).
• Two broad classes of particles:
  • Fermions → matter particles (obey Pauli exclusion principle, half-integer spin).
  • Gauge bosons → force-carrier particles (integer spin) responsible for mediating interactions.

Fundamental Particles: Fermions vs Bosons

• Fermions (spin $\frac{1}{2}$):
  • Sub-divided into quarks and leptons.
• Gauge bosons (spin 0, 1, or 2):
  • Photon ((\gamma)) → electromagnetic force.
  • Gluons (g) → strong nuclear force (8 colour states but treated collectively).
  • W^\pm, Z^0 → weak nuclear force.
  • Graviton (hypothetical) → gravity; has not yet been observed.

Quarks

• Six flavours: up (u), down (d), charm (c), strange (s), top (t), bottom (b).
• Carry fractional electric charges:
  • Up-type: $+\frac{2}{3}\,e$ (u, c, t).
  • Down-type: $-\frac{1}{3}\,e$ (d, s, b).
• Baryon number per quark: $+\frac{1}{3}$ (antiquark $-\frac{1}{3}$).
• Interact through the strong force by exchanging gluons.
• Never observed in isolation → confinement; always bound inside hadrons.

Hadrons: Baryons and Mesons

• Hadrons = composite particles made of quarks, bound via strong force.
• Classification by total baryon number (B):
  • Baryons (B = +1 for matter, −1 for antibaryons):
  • Made of three quarks (qqq).
  • Examples: proton (p), neutron (n).
  • Mesons (B = 0):
  • Made of one quark + one antiquark (q\bar{q}).
  • Generally unstable → short lifetimes.
• Everyday matter is dominated by baryons because they form nucleons.

Composition of Nucleons

• Proton (p): $uud$ → net charge $+1e$:
  • $Q = 2\left(+\frac{2}{3}\right) + \left(-\frac{1}{3}\right) = +1$.
• Neutron (n): $udd$ → net charge $0e$:
  • $Q = \left(+\frac{2}{3}\right) + 2\left(-\frac{1}{3}\right) = 0$.

Colour Charge & the Strong Force

• Quarks possess colour charge (red, green, blue).
• Confinement rule: bound states must be colour-neutral (white).
• Quarks rapidly exchange gluons, continually altering their colour while conserving total colour neutrality.

Leptons

• Six flavours: electron (e), muon (\mu), tau (\tau) and their corresponding neutrinos ((\nue, \nu\mu, \nu_\tau)).
• Electric charge:
  • Charged leptons: $-1e$ (positron has $+1e$).
  • Neutrinos: 0.
• Mass: very small or zero (exact neutrino masses not in Standard Model).
• Interaction channels:
  • All leptons ↔ weak force (W, Z boson exchange).
  • Charged leptons ↔ electromagnetic force (photon exchange).
  • Leptons do not feel the strong force.

Gauge Bosons & Fundamental Forces

• Four fundamental interactions described (gravity still hypothetical in SM context):

  Force	Acts on	Carrier Boson	Range	Relative Strength*
  Strong	quarks, gluons	gluon (g)	$\sim 10^{-15}\,\text{m}$ (short)	1 (reference)
  Electromagnetic	charged quarks & leptons	photon ((\gamma))	$\infty$	$\approx 10^{-2}$
  Weak	quarks & leptons	W^\pm, Z^0	$\sim 10^{-18}\,\text{m}$ (very short)	$\approx 10^{-6}$
  Gravity	all with mass/energy	graviton (hypothetical)	$\infty$	$\approx 10^{-38}$

  *Relative strengths quoted at the scale of typical nucleon separations.

Beta Decay (Weak Interaction Example)

• Beta-minus ((\beta^-)) decay:
  • A neutron → proton + electron + antineutrino $\left(n \to p + e^- + \bar{\nu}_e\right)$.
• Beta-plus ((\beta^+)) decay:
  • A proton → neutron + positron + neutrino $\left(p \to n + e^+ + \nu_e\right)$.
• Explains emission of (anti)neutrinos to conserve energy, momentum, and lepton number.

Evidence Supporting the Standard Model

• Energy spectrum in (\beta^+) decay:
  • Continuous electron kinetic energy revealed presence of an additional neutral particle (neutrino) carrying missing energy.
• Deep inelastic scattering (1960s):
  • High-energy electrons fired at protons produced scattering patterns indicating three point-like constituents → discovery of quarks.
• Cosmic-ray muons:
  • Muons created $\approx 15\,\text{km}$ above Earth (lifetime $2.2 \times 10^{-6}\,\text{s}$ at rest).
  • Travel at $0.999c$ → time dilation: $t' = \gamma t = 49.21\,\mu\text{s}$, long enough to reach detectors on Earth’s surface.
  • Confirms existence and properties of muons (a lepton) and validates special relativity.

Key Equations & Numerical Data

• Electric charge of quarks:
  $Q<em>u = +\frac{2}{3}e, \quad Q</em>d = -\frac{1}{3}e$.
• Baryon number per quark: $B_q = +\frac{1}{3}$.
• Muon lifetime dilation example:
  $\gamma = \frac{1}{\sqrt{1-\beta^2}} \quad (\beta = 0.999) \;\Rightarrow\; \gamma \approx 22.4$,
  $t' = \gamma t_0 = 22.4 \times 2.2 \mu\text{s} \approx 49.21 \mu\text{s}$.

Connections & Implications

• Standard Model unifies electromagnetism and weak force (electroweak theory), yet leaves gravity outside its scope.
• Explains stability of matter (confinement, conservation laws) and predicts particle behaviour in nuclear reactions and cosmic events.
• Colour confinement & asymptotic freedom explain why quarks behave like free particles at very high energies but are bound into hadrons at low energies.
• Ongoing searches for the graviton, Higgs interactions beyond SM, and phenomena like neutrino mass aim to extend or refine the model.

Quick Summary Bullets

• Matter = quarks + leptons (fermions).
• Forces = gluons, photons, W/Z, (graviton) (bosons).
• Protons/neutrons = composite (uud / udd) → not fundamental.
• Electrons are fundamental leptons.
• Baryon number, electric charge, lepton number conserved in interactions.
• Experimental confirmations: beta decay neutrinos, deep inelastic scattering, cosmic muon detection.