Grade by Grade
F. Revolutions in Modern Physics: Quantum Mechanics and Special Relativity · Quantum Mechanics

The Standard Model of Elementary Particles

F3 F1.1 F2.1About 70 minutes
Learning goals
  • I can describe the Standard Model's quarks, leptons and force-carrying bosons.
  • I can find the charge of a hadron from its quarks and identify baryons and mesons.
  • I can use conservation of charge, baryon number and lepton number to decide whether a particle reaction can happen.
  • I can describe evidence for the Standard Model, including neutrino research at SNOLAB and the discovery of the Higgs boson.

Words to know

elementary particle
A particle with no known smaller parts, such as a quark, an electron or a photon.
quark
An elementary particle that feels the strong force; quarks combine in groups to form hadrons. Six types: up, down, charm, strange, top, bottom.
lepton
An elementary particle that does not feel the strong force: the electron, muon, tau and three neutrinos.
hadron
A particle made of quarks held together by the strong force; baryons (three quarks) and mesons (a quark and an antiquark).
antiparticle
A particle with the same mass as another but opposite charge (and opposite quantum numbers).
boson (force carrier)
A particle that carries a force: photon (electromagnetic), gluon (strong), W and Z (weak). The Higgs boson is related to how particles get mass.
baryon number
A conserved quantity: +1/3 for each quark, −1/3 for each antiquark, so +1 for protons and neutrons.
lepton number
A conserved quantity: +1 for each lepton, −1 for each antilepton (counted for each family).

What is everything made of?

In Grade 9 you learned that atoms contain protons, neutrons and electrons. Through the twentieth century, physicists built accelerators to smash particles together and discovered hundreds of new, short-lived particles: a confusing "particle zoo." In the 1960s Murray Gell-Mann and George Zweig independently proposed that protons, neutrons and most of the zoo are made of a few simpler pieces, now called quarks. Experiments at the Stanford Linear Accelerator (late 1960s) found point-like objects inside protons, as Rutherford had found the nucleus inside the atom.

The theory that grew from this, completed in the 1970s, is the Standard Model. It is a quantum theory: every particle is a quantum of a field, and forces are carried by exchanging quanta (bosons), as you saw in the lesson Comparing Fields and the Fundamental Forces in the unit Gravitational, Electric and Magnetic Fields. It is one of the most precisely tested theories in science.

The Standard Model of elementary particlesuup+2/3ccharm+2/3ttop+2/3ddown−1/3sstrange−1/3bbottom−1/3eelectron−1μmuon−1τtau−1νₑe-neutrino0νμμ-neutrino0νττ-neutrino0γphoton0ggluon0ZZ boson0WW boson±1HHiggs0matter particles (fermions)columns: generations I, II, IIIforce carriers(related to mass)quarksleptonsSmall numbers: electric charge in units of e. Every particle also has an antiparticle.
The Standard Model: six quarks and six leptons (matter), four kinds of force carriers, and the Higgs boson. Ordinary matter is made of just the first column: up and down quarks and electrons.

Matter particles: quarks and leptons

Quarks come in six types ("flavours"). Up, charm and top have charge +2/3 e; down, strange and bottom have −1/3 e. Quarks are never found alone: the strong force, carried by gluons, holds them inside hadrons:

  • Baryons contain three quarks. The proton is uud; the neutron is udd.
  • Mesons contain a quark and an antiquark, such as the pion π⁺ = u d̄ (a bar means antiquark, with opposite charge: d̄ has +1/3 e).

Leptons do not feel the strong force. They are the electron, its heavier cousins the muon and tau, and three nearly massless, neutral neutrinos.

Each column in the chart is a generation. Everyday matter uses only the first generation (up, down, electron, electron neutrino); the heavier ones appear in cosmic rays and accelerators and decay quickly.

Every particle has an antiparticle. You met the positron in lesson 7; antiquarks make up antimatter versions of hadrons.

Worked example

Example 1: Charges from quarks

Find the charge of (a) a proton (uud), (b) a neutron (udd), (c) the particle Λ⁰ = uds, and (d) the meson made of u and s̄. Say whether each is a baryon or a meson.

  1. (a) +2/3 + 2/3 − 1/3 = +1 (baryon).
  2. (b) +2/3 − 1/3 − 1/3 = 0 (baryon).
  3. (c) +2/3 − 1/3 − 1/3 = 0 (baryon: three quarks).
  4. (d) An antistrange quark has charge +1/3. So +2/3 + 1/3 = +1 (meson: quark + antiquark). This is the kaon K⁺.

Charges +1, 0, 0, +1; the first three are baryons, the last is a meson.

uudproton: +2/3 +2/3 −1/3 = +1uddneutron: +2/3 −1/3 −1/3 = 0Baryons: three quarksBeta-minus decay, quark viewduW⁻e⁻antineutrinon (udd) → p (uud) + e⁻ + antineutrino
Left: a proton (uud) and a neutron (udd). Right: in beta-minus decay, a down quark becomes an up quark by emitting a W⁻ boson, which decays into an electron and an electron antineutrino.

Conservation laws decide what can happen

In every particle reaction observed, some quantities are always conserved:

  • Electric charge.
  • Baryon number (B): each quark counts +1/3 and each antiquark −1/3. Protons and neutrons have B = +1; mesons have B = 0; leptons have B = 0.
  • Lepton number (L): each lepton counts +1 and each antilepton −1 (counted separately for the electron, muon and tau families).
  • Energy and momentum, as always.

If a proposed reaction breaks any of these, it does not happen. This is how physicists check reactions, and it is the same logic Pauli used to predict the neutrino (see the lesson on the neutrino in Momentum and Collisions).

Worked example

Example 2: Checking beta decay

Show that n → p + e⁻ + ν̄ₑ conserves charge, baryon number and lepton number.

  1. Charge: left 0; right +1 + (−1) + 0 = 0. ✓
  2. Baryon number: left +1; right +1 + 0 + 0 = +1. ✓
  3. Electron-lepton number: left 0; right 0 + (+1) + (−1) = 0. ✓ (The antineutrino has L = −1.)

All three are conserved, so the decay is allowed, and indeed free neutrons decay this way with a half-life of about 10 minutes. Without the antineutrino, lepton number would not balance.

Worked example

Example 3: An impossible reaction

Can the reaction p + p → p + π⁺ happen?

  1. Charge: left +2; right +1 + 1 = +2. ✓
  2. Baryon number: left +1 + 1 = +2; right +1 + 0 = +1. ✗

No: baryon number is not conserved. (The reaction p + p → p + n + π⁺ is allowed, and is observed: charge 2 = 1 + 0 + 1, baryon number 2 = 1 + 1 + 0.)

Evidence and Canadian contributions

  • Neutrinos: at SNOLAB, 2 km underground in the Creighton Mine near Sudbury, Ontario, the Sudbury Neutrino Observatory used 1000 tonnes of heavy water to detect neutrinos from the Sun. It showed that neutrinos change from one type to another as they travel, which means they have mass. Arthur McDonald of Queen's University shared the 2015 Nobel Prize in Physics with Takaaki Kajita (Japan) for this discovery. In 2026, the Nobel Prize in Physics went to Francis Halzen for leading work at the IceCube Neutrino Observatory, a cubic kilometre of Antarctic ice wired with light detectors, which discovered high-energy neutrinos coming from deep space.
  • The Higgs boson: predicted in 1964 and discovered at CERN's Large Hadron Collider in 2012, with Canadian physicists among the thousands in the ATLAS collaboration and TRIUMF (Canada's particle accelerator centre in Vancouver) contributing. The 2013 Nobel Prize went to François Englert and Peter Higgs for the prediction.
  • Every quark and lepton in the chart has been observed; the top quark (1995), the tau neutrino (2000) and the Higgs (2012) were the last pieces.

What the Standard Model does not explain (F1.1)

The Standard Model is a triumph, but physicists know it is incomplete. It does not include gravity (general relativity is a separate theory). It does not explain dark matter, which galaxies' motions show must exist (see Gravitational, Electric and Magnetic Fields), or why the universe has more matter than antimatter. Its original form gave neutrinos zero mass, which SNO showed is wrong. Like Newton's mechanics before relativity and quantum theory, it is probably an excellent approximation to something deeper. Experiments at SNOLAB, CERN and elsewhere are searching for what comes next.

Just for fun

Murray Gell-Mann took the name "quark" from a line in James Joyce's novel Finnegans Wake: "Three quarks for Muster Mark!" It is fitting, since protons and neutrons each contain three quarks.

Hands-on activity

Build hadrons with quark cards

You need: 12 small pieces of paper, a pencil.

  1. Make quark cards: write u (+2/3) on 4 cards, d (−1/3) on 4 cards, and on 4 more cards write antiquarks: ū (−2/3), ū (−2/3), d̄ (+1/3), d̄ (+1/3).
  2. Build a baryon from three quark cards (no antiquarks) with total charge +1. Then one with charge 0. What are they?
  3. Build a baryon with charge +2. (Hint: uuu, the Δ⁺⁺ particle, exists.) Can you build a baryon with charge −1?
  4. Build mesons from one quark and one antiquark: find combinations with charge +1, 0 and −1.
  5. Try to build a particle with charge +1/3 from any cards. Why do we never see one?

What to look for: proton = uud (+1), neutron = udd (0); uuu = +2; ddd = −1 (the Δ⁻ exists). Mesons: u d̄ = +1 (π⁺), u ū or d d̄ = 0, d ū = −1 (π⁻). Allowed combinations (three quarks, three antiquarks, or quark + antiquark) always give whole-number charges, which is why free particles with fractional charge are never observed.

Your turn

1

What are the two families of matter particles in the Standard Model?

2

Find the charge of the baryon uuu, and of ddd.

3

The pion π⁻ is a meson made of d and ū. Find its charge.

4

Name the force carrier for (a) the electromagnetic force, (b) the strong force, (c) the weak force.

5

Is the reaction p → n + e⁺ + νₑ allowed for charge, baryon number and lepton number? (It happens inside some nuclei: beta-plus decay.)

6

Can the reaction n → p + e⁻ happen? Explain.

7

What did the Sudbury Neutrino Observatory discover?

More practice: warm-up

1

What quarks make up a proton?

2

What is the charge of a down quark?

3

How many quarks are in a meson?

4

Which lepton is found in every atom?

5

Where and when was the Higgs boson discovered?

More practice: on your own

1

A baryon has charge −1 and contains one strange quark and two other first-generation quarks. What are its quarks?

2

Check whether π⁺ → μ⁺ + νμ (a muon neutrino) conserves charge, baryon number and muon-lepton number.

3

Explain why a free quark has never been observed.

4

Why is the Standard Model described as incomplete? Give two reasons.

5

Why was the Sudbury Neutrino Observatory built 2 km underground?

Challenge

1

Is the reaction p + p̄ → π⁺ + π⁻ + π⁰ allowed by charge and baryon number? (p̄ is the antiproton, B = −1.)

2

The Δ⁺⁺ baryon (uuu) decays into a proton and a pion. Which pion? Show your reasoning with charges and quarks.

3

Explain how the Standard Model is an example of quantum mechanics changing scientific thought about forces.

Check your understanding

Quiz

1.

A proton is made of

2.

Which particle is a lepton?

3.

A meson consists of

4.

The charge of a particle made of u, d and s quarks is

5.

The reaction n → p + e⁻ (without a neutrino) is not observed because it violates conservation of

6.

Arthur McDonald shared the 2015 Nobel Prize for showing that

For parents and teachers

Big idea (F3, F1.1): all known matter is built from quarks and leptons, and forces are carried by bosons; together with the Higgs boson this is the Standard Model, a quantum theory tested to extraordinary precision. Canadian experiments, especially at SNOLAB near Sudbury, have been central to neutrino physics.

How to help: the quark-card activity works well with a family member. Ask your teen to build a proton and a neutron and explain why there are no free particles with charge +1/3.

Common difficulties:

  • Adding quark charges incorrectly; antiquarks have the opposite charge (d̄ is +1/3, ū is −2/3).
  • Thinking protons and neutrons are elementary. They are made of quarks; electrons are elementary.
  • Forgetting lepton number when checking reactions; antineutrinos count as −1.
  • Confusing baryons (three quarks) with mesons (quark-antiquark).

Note on the curriculum: some schools treat the Standard Model as part of this strand and some do not; it is included here because it completes the quantum picture of matter and forces.