3.2.1.5 - Classification of Particles | AQA A-Level Physics

The subatomic world contains a rich zoo of particles discovered through cosmic ray experiments and high-energy accelerator collisions. To make sense of this diversity, physicists classify particles into groups based on the fundamental interactions they experience. In this lesson you will learn the two main families — hadrons and leptons — and the quantum numbers that govern how particles are created and destroyed.

Hadrons and Leptons

For the particles you meet on this AQA specification point, the first useful classification is into hadrons and leptons. The deciding factor is whether the particle experiences the strong nuclear force.

Hadron

A hadron is a particle or antiparticle that is subject to the strong interaction. Hadrons are not fundamental particles.

Examples of hadrons include protons, neutrons, pions, and kaons. Because they contain quarks, hadrons can also interact through the weak, electromagnetic (if charged), and gravitational interactions.

Lepton

A lepton is a fundamental particle or antiparticle that does not experience the strong interaction. Leptons interact through the weak interaction, and through the electromagnetic interaction if charged.

The leptons you need to know are the electron ( $e^-$ ), the muon ( $\mu^-$ ), the electron neutrino ( $\nu_e$ ), and the muon neutrino ( $\nu_\mu$ ), together with their antiparticles: the positron ( $e^+$ ), the antimuon ( $\mu^+$ ), the electron antineutrino ( $\bar{\nu}_e$ ), and the muon antineutrino ( $\bar{\nu}_\mu$ ). The classification tree below helps you sort these particles by interaction, so notice that baryons and mesons sit inside the hadron branch while the leptons form a separate family because they do not feel the strong force.

[DIAGRAM: asset_name: 2.1.5 - Classification of Particles - Diagram 1; asset_slug: 2.1.5 - Classification of Particles - Diagram 1; recommended_method: retained_png; caption: Hadrons experience the strong interaction, leptons do not. Antibaryons belong to the hadron family too.; description: A branching tree — "Particles on this spec point" splits into "Hadrons (feel strong force)" and "Leptons (do not feel strong force)". The Hadrons branch splits further into "Baryons" and "Mesons". Under Leptons list: electron, muon, electron neutrino, muon neutrino and their antiparticles.]
Hadrons experience the strong interaction, leptons do not. Antibaryons belong to the hadron family too.
This is a classification by interaction, not by mass. A muon, for example, is much heavier than an electron but is still a lepton because it does not experience the strong interaction.

Baryons and Mesons

Hadrons are composite particles. Their constituent pattern distinguishes baryons and mesons; the next lesson uses the individual quark properties to calculate their quantum numbers.

Baryon

A baryon contains three quarks and has baryon number $+1$ . An antibaryon contains three antiquarks and has baryon number $-1$ . The proton is the stable baryon into which free unstable baryons eventually decay. A neutron bound in a stable nucleus need not decay.

The baryons you must know are the proton ( $p$ ) and the neutron ( $n$ ), along with their antiparticles, the antiproton ( $\bar{p}$ ) and the antineutron ( $\bar{n}$ ).

Meson

A meson contains a quark and an antiquark and has baryon number $0$ . Classify it by its constituents, not by a universal rule about decay products.

The mesons you need to know are the pions ( $\pi^+$ , $\pi^0$ , $\pi^-$ ) and the kaons ( $K^+$ , $K^0$ , $K^-$ ). Pions act as the exchange particles of the strong nuclear force between nucleons. This pion-exchange model describes the residual strong nuclear interaction between nucleons; it is not the weak $W$ -exchange process.

Key properties to remember:

Particle	Type	Rest energy / MeV	Charge / $e$
Proton $p$	Baryon	938.3	$+1$
Neutron $n$	Baryon	939.6	$0$
$\pi^+$ / $\pi^-$	Meson	140	$+1$ / $-1$
$\pi^0$	Meson	135	$0$
$K^+$ / $K^-$	Meson	494	$+1$ / $-1$
$K^0$	Meson	498	$0$

Note that the $\pi^+$ and $\pi^-$ are particle–antiparticle pairs of each other, and the $\pi^0$ is its own antiparticle.

Baryon Number and Its Conservation

Baryon number keeps track of baryons minus antibaryons, rather than the number of particles present.

Baryon Number (B)

Baryon number is a quantum number assigned to every particle:

$B = +1$ for any baryon (proton, neutron, etc.)
$B = -1$ for any antibaryon (antiproton, antineutron, etc.)
$B = 0$ for all other particles (mesons, leptons, photons)

In the particle reactions studied here, baryon number is conserved — in every interaction, the total baryon number before equals the total baryon number after. This applies to strong, weak, and electromagnetic interactions alike.

Let us verify this with the beta-minus decay of a neutron:

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

Baryon number: LHS $= +1$ . RHS $= +1 + 0 + 0 = +1$ . Baryon number is conserved.

Now consider whether the following hypothetical reaction is allowed:

p + p \rightarrow p + p + \bar{p}

Baryon number: LHS $= +1 + 1 = +2$ . RHS $= +1 + 1 + (-1) = +1$ . Baryon number is not conserved, so this reaction is forbidden.

The correct version would need a proton–antiproton pair to be created together:

p + p \rightarrow p + p + p + \bar{p}

Baryon number: LHS $= +2$ . RHS $= +1 + 1 + 1 + (-1) = +2$ . This is permitted (provided enough energy is available).

Leptons, Lepton Number, and Its Conservation

Lepton number must be tracked separately for the electron and muon families in these decay and collision questions. A neutrino has the same family lepton number as its charged lepton; the corresponding antiparticle has the opposite value.

Lepton Number

There are two separate lepton numbers that must each be conserved independently:

Electron lepton number ( $L_e$ ):

$L_e = +1$ for the electron ( $e^-$ ) and the electron neutrino ( $\nu_e$ )
$L_e = -1$ for the positron ( $e^+$ ) and the electron antineutrino ( $\bar{\nu}_e$ )
$L_e = 0$ for all other particles

Muon lepton number ( $L_\mu$ ):

$L_\mu = +1$ for the muon ( $\mu^-$ ) and the muon neutrino ( $\nu_\mu$ )
$L_\mu = -1$ for the antimuon ( $\mu^+$ ) and the muon antineutrino ( $\bar{\nu}_\mu$ )
$L_\mu = 0$ for all other particles

Use both family totals: a total lepton-number sum can hide an incorrect exchange of electron and muon flavour. These are the conservation rules for the reactions in this topic; neutrino oscillations are outside this treatment.

The muon ( $\mu^-$ ) is sometimes called a "heavy electron" because it has the same charge as the electron but a rest mass over 200 times greater (rest energy 106 MeV compared to 0.511 MeV). The muon is unstable and decays into an electron:

\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu

Let us check all conservation laws for this decay:

Charge: LHS $= -1$ . RHS $= -1 + 0 + 0 = -1$ . Conserved.
$L_e$ : LHS $= 0$ . RHS $= +1 + (-1) + 0 = 0$ . Conserved.
$L_\mu$ : LHS $= +1$ . RHS $= 0 + 0 + 1 = +1$ . Conserved.
Baryon number: LHS $= 0$ . RHS $= 0$ . Conserved.

Notice that the muon produces a muon neutrino (to conserve $L_\mu$ ) and an electron antineutrino (to conserve $L_e$ alongside the newly created electron).

Consider the proposed decay $\mu^- \rightarrow e^- + \nu_e + \bar{\nu}_\mu$ . Charge is conserved (−1 on each side), and total lepton number is conserved (+1 on each side). However, checking separately: $L_\mu$ : LHS $= +1$ , RHS $= 0 + 0 + (-1) = -1$ . Muon lepton number is not conserved, so this decay is forbidden. This is precisely why we must conserve electron and muon lepton numbers independently.

Strange Particles and Strangeness

When high-energy protons collide with nuclei, kaons can be created very quickly. Early physicists then found that these same particles decayed much more slowly than expected. That combination — strong production but weak decay — is the key idea behind strange particles.

Strange Particles

Strange particles are particles that are produced through the strong interaction but decay through the weak interaction. The kaon is the key example at A-Level.

Kaons can decay into pions. For instance:

K^+ \rightarrow \pi^+ + \pi^0

Since kaon decay proceeds via the weak interaction, it is much slower than if the strong force were responsible — giving kaons a relatively long lifetime compared to particles that decay via the strong interaction.

To describe this behaviour, physicists introduced a new quantum number called strangeness.

Strangeness (S)

Strangeness is a quantum number assigned to particles. For AQA, the key values are:

$K^+$ and $K^0$ have strangeness $S = +1$
$K^-$ and $\bar{K}^0$ have strangeness $S = -1$
Pions, protons, neutrons, and leptons have strangeness $S = 0$

The conservation rule is the important part:

Strangeness is conserved in strong interactions, but in weak interactions it can change by $0$ , $+1$ , or $-1$ .

For an initially non-strange collision such as proton-proton interactions, the total strangeness starts at zero. If a strong interaction creates a particle with $S = +1$ , it must also create another product with $S = -1$ so that the total stays zero. This is what associated production means: strange particles are produced together in a way that keeps total strangeness conserved.

For example, when a high-energy proton collides with another proton:

p + p \rightarrow p + p + K^+ + K^-

Strangeness: LHS $= 0 + 0 = 0$ . RHS $= 0 + 0 + (+1) + (-1) = 0$ . Conserved — so this can be a strong interaction.

When a kaon decays into pions, however:

K^+ \rightarrow \pi^+ + \pi^0

Strangeness: LHS $= +1$ . RHS $= 0 + 0 = 0$ . Change in strangeness $= -1$ . That change is not allowed in a strong interaction, but it is allowed in a weak interaction, so the decay is weak.

Particle physics depends on collaboration to validate new knowledge. Engineers build and calibrate detectors; physicists develop models and analyse events; computing teams process large data sets. Independent analysis methods and different detectors test whether a signal persists when calibrations, background models or selection methods change. A simulation helps predict the detector response, but agreement with a simulation alone is not a discovery: real data, uncertainties and independent cross-checks matter.

The two-panel sketch below shows the key idea of associated production, so notice that the $K^+$ and $K^-$ appear together and keep the total strangeness at zero before and after the collision.

[DIAGRAM: asset_name: 2.1.5 - Classification of Particles - Diagram 2; asset_slug: 2.1.5 - Classification of Particles - Diagram 2; recommended_method: retained_png; caption: Creating K+ and K− together preserves total strangeness zero in this proton collision.; description: Associated production in two panels. Panel 1: two protons approach, each labelled $S=0$ , so total strangeness before is 0. Panel 2: products are two protons plus $K^+$ and $K^-$ . Label $K^+$ with $S=+1$ , $K^-$ with $S=-1$ , and show total strangeness after is still 0.]
Creating K+ and K− together preserves total strangeness zero in this proton collision.
The exam habit to build here is simple: in a strong interaction, total strangeness before and after must match exactly. In a kaon decay, a change of $\pm 1$ points you toward the weak interaction.

Observing a cosmic-ray shower

High-energy cosmic rays striking the atmosphere can produce pions and kaons, whose decays contribute to showers including muons. A cloud chamber makes ionising charged-particle tracks visible, but one stray track does not identify a kaon. Two Geiger counters arranged above one another with a coincidence circuit can select events arriving within a short time window, reducing unrelated background coincidences. Repeat over known time intervals and compare arrangements; simulations can help relate collision products to detector signals.

Testing an Unfamiliar Particle Reaction

In AQA exam questions, you will often need to apply several conservation laws simultaneously to determine whether a reaction is permitted or to identify unknown particles. The quantum numbers you must check are:

Charge ( $Q$ ) — always conserved
Baryon number ( $B$ ) — always conserved
Electron lepton number ( $L_e$ ) — always conserved
Muon lepton number ( $L_\mu$ ) — always conserved
Strangeness ( $S$ ) — conserved in strong interactions; can change by $0$ , $+1$ , or $-1$ in weak interactions

When checking whether a particle interaction is allowed, systematically apply each conservation law in turn. If any law is violated, the interaction is forbidden. Passing these checks makes a reaction compatible with these conservation laws, provided energy and momentum also balance; it does not prove that the reaction will occur.

Worked example: Determine whether the following decay is permitted:

\Sigma^- \rightarrow n + \pi^-

The $\Sigma^-$ (sigma minus) is a strange baryon with charge $-1$ , $B = +1$ , and $S = -1$ . (Note: the sigma baryon is not a particle you need to memorise for the exam — it is used here to practise applying conservation laws to an unfamiliar particle when its properties are given.)

Charge: LHS $= -1$ . RHS $= 0 + (-1) = -1$ . Conserved.
Baryon number: LHS $= +1$ . RHS $= +1 + 0 = +1$ . Conserved.
Lepton numbers: No leptons involved. $L_e = 0$ and $L_\mu = 0$ on both sides. Conserved.
Strangeness: LHS $= -1$ . RHS $= 0 + 0 = 0$ . Change $= +1$ .

Strangeness is not conserved, so this cannot be a strong interaction. However, the change in strangeness is $+1$ , which is allowed for a weak interaction. This is compatible with weak decay. With supplied rest energies $E_\Sigma=1197\,\mathrm{MeV}$ , $E_n=940\,\mathrm{MeV}$ and $E_\pi=140\,\mathrm{MeV}$ , there is $117\,\mathrm{MeV}$ available for kinetic energy. If the parent is at rest, the products have equal and opposite momenta, not generally equal kinetic energies.

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