Quarks, Leptons and Hadrons

Spec mapping: OCR H556 Module 6.4 — Quark and lepton content of matter; hadrons. Quarks ($u$u, $d$d, $s$s — and at extension $c$c, $b$b, $t$t) with fractional charges $+2/3$+2/3 or $-1/3$−1/3; charged leptons ($e^-$e−, $\mu^-$μ−, $\tau^-$τ−) and three neutrinos; baryons as three-quark composites ($qqq$qqq, baryon number $B = +1$B=+1); mesons as quark-antiquark composites ($q\bar{q}$qqˉ​, $B = 0$B=0); the proton ($uud$uud) and neutron ($udd$udd) charge sums; lepton number and its conservation in beta decay. Refer to the official OCR H556 specification document for exact wording.

In the last lesson we met the Standard Model in outline: quarks and leptons as the fundamental fermions, gauge bosons as force carriers, and the Higgs boson providing mass. In this lesson we dig into the quark and lepton content in more detail, and show how quarks combine into hadrons — the composite particles built from them, including the familiar protons and neutrons.

This lesson is the heart of Module 6.4 of the OCR A-Level Physics A specification (H556) and introduces the terminology (baryons, mesons, baryon number, lepton number) you will need for the next two lessons on annihilation, pair production and conservation rules.

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Quarks

Quarks are point-like, fundamental particles that experience the strong nuclear force. There are six types (or "flavours"), organised into three generations:

Flavour	Symbol	Charge (e)	Mass (MeV/c²)	Generation
Up	u	+2/3	~2.2	1st
Down	d	-1/3	~4.7	1st
Charm	c	+2/3	~1270	2nd
Strange	s	-1/3	~95	2nd
Top	t	+2/3	~173000	3rd
Bottom	b	-1/3	~4180	3rd

The OCR specification focuses on just the first three: up, down and strange. You should know their charges and that they are classified as fundamental.

Some crucial properties:

• Quarks carry fractional electric charge — either +2/3 e or -1/3 e.
• Every quark has a corresponding antiquark with opposite charge. The antiparticle of u is ū with charge -2/3; the antiparticle of d is d̄ with charge +1/3; and so on.
• Quarks carry a property called baryon number B = +1/3 (antiquarks have B = -1/3).
• Quarks carry another property called colour charge (red, green, blue). At A-Level you do not need the details of colour, only that it exists and that observed particles are always "colourless" combinations.
• Quarks cannot exist in isolation (they are "confined"). They only appear bound into hadrons.

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Leptons

Leptons are point-like particles that do not feel the strong nuclear force. Like quarks, there are six of them, in three generations:

Lepton	Symbol	Charge (e)	Mass (MeV/c²)
Electron	e⁻	-1	0.511
Electron neutrino	ν_e	0	≈ 0
Muon	μ⁻	-1	105.7
Muon neutrino	ν_μ	0	≈ 0
Tau	τ⁻	-1	1777
Tau neutrino	ν_τ	0	≈ 0

And again, each has an antiparticle: the antielectron (positron) e⁺, the antimuon μ⁺, the antitau τ⁺, and the three antineutrinos ν̄_e, ν̄_μ, ν̄_τ.

OCR specifies the electron and the muon as examples of leptons, and the electron neutrino and electron antineutrino as particles you must recognise in beta decay equations.

Some important properties:

• Leptons carry lepton number L = +1; antileptons have L = -1. Lepton number is conserved in all known interactions.
• The electron is stable — it does not decay into anything lighter because there is no lighter charged particle.
• The muon decays (with lifetime 2.2 μs) via μ^- → e^- + ν̄_e + ν_μ, conserving both electron and muon lepton numbers.
• Neutrinos are extremely weakly interacting. A typical neutrino from the Sun passes through the entire Earth without interacting.

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Hadrons: Particles Made of Quarks

A hadron is any particle built from quarks. Because quarks cannot exist in isolation, all directly observable particles that feel the strong force are hadrons. There are two main types:

• Baryons — made of three quarks (qqq).
• Mesons — made of one quark and one antiquark (q\bar{q}).

Both combinations are "colourless" (in the technical sense of the colour charge we mentioned earlier) and therefore allowed. Single quarks and quark-quark pairs would not be colourless, so you never see them on their own.

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Baryons

Baryons are hadrons made of three quarks. The most familiar baryons are the proton and neutron, which are made of up and down quarks.

Baryon	Quark content	Charge	Mass (MeV/c²)
Proton	uud	+1	938.3
Neutron	udd	0	939.6
Lambda (Λ⁰)	uds	0	1116
Sigma (Σ⁺)	uus	+1	1189
Sigma (Σ⁻)	dds	-1	1197
Xi (Ξ⁰)	uss	0	1315

Check the proton charge:

Q(uud) = (+2/3) + (+2/3) + (-1/3) = +1 ✓

Check the neutron charge:

Q(udd) = (+2/3) + (-1/3) + (-1/3) = 0 ✓

The mechanism works beautifully: fractional quark charges combine to give integer hadron charges.

Baryons have baryon number B = +1. (Three quarks with B = 1/3 each gives B = 1.) Antibaryons have B = -1. Baryon number is conserved in all known interactions — which is why the proton appears to be stable (no lighter baryon exists for it to decay into).

Baryons heavier than nucleons are called hyperons. The \Lambda, \Sigma and \Xi particles are hyperons, all containing at least one strange quark. They decay to lighter baryons via the weak interaction with lifetimes of order 10^{-10} s.

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Mesons

Mesons are hadrons made of one quark and one antiquark (q\bar{q}). They are bosons (integer spin), unlike baryons (which are fermions with half-integer spin).

Meson	Quark content	Charge	Mass (MeV/c²)
Pion π⁺	ud̄	+1	139.6
Pion π⁻	ūd	-1	139.6
Pion π⁰	uū / dd̄	0	135.0
Kaon K⁺	us̄	+1	493.7
Kaon K⁻	ūs	-1	493.7
Kaon K⁰	ds̄	0	497.6

Check the π⁺ charge:

Q(u) + Q(d̄) = (+2/3) + (+1/3) = +1 ✓

Mesons have baryon number B = 0 (one quark at +1/3 and one antiquark at -1/3 cancel). They are not conserved — a single meson can decay into other particles entirely, subject only to conservation of energy, charge, lepton number, and (in the strong force) various other quantum numbers.

Pions are the lightest mesons and were originally proposed by Hideki Yukawa (1935) as the carriers of the strong nuclear force between nucleons. They were detected in cosmic rays in 1947. Kaons — containing a strange quark — were discovered shortly afterwards in cosmic ray experiments and are the lightest particles containing strangeness.

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Summary Classification

flowchart TB
    P["All particles"]
    F["Fermions<br/>(matter)"]
    B["Bosons<br/>(force carriers)"]
    Q["Quarks<br/>(feel strong force)"]
    L["Leptons<br/>(no strong force)"]
    H["Hadrons<br/>(composite)"]
    Ba["Baryons<br/>qqq"]
    Me["Mesons<br/>qq̄"]
    P --> F
    P --> B
    F --> Q
    F --> L
    Q --> H
    H --> Ba
    H --> Me

• Leptons are fundamental and never combine into hadrons.
• Quarks are fundamental but are always found bound into hadrons (baryons or mesons).
• Hadrons are composite particles made of quarks.
• A baryon is qqq (e.g. proton, neutron, \Lambda, \Sigma).
• A meson is q\bar{q} (e.g. pion, kaon).

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Worked Example 1: Identify the quark content of a particle

A particle has charge 0, baryon number +1, and contains one strange quark. Propose a possible quark content.

Solution. Baryon number +1 means three quarks. Charge 0 with one s (charge -1/3) means the other two quarks must contribute charge +1/3 — for example one up (+2/3) and one down (-1/3):

Q = (+2/3) + (-1/3) + (-1/3) = 0 ✓

So the content is uds. This is the lambda (Λ⁰) baryon.

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Worked Example 2: Is it a baryon or meson?

A newly discovered particle has a quark content cc̄ (charm-anticharm). What is its charge, baryon number and type?

Solution.

Charge = (+2/3) + (-2/3) = 0
Baryon number = (+1/3) + (-1/3) = 0
Type = meson (one quark + one antiquark)

This particle is neutral, has zero baryon number, and is a meson. It is in fact the J/\psi particle — discovered in 1974 simultaneously at SLAC and Brookhaven, and immediately hailed as evidence for the charm quark. Its discovery is called the "November revolution" of particle physics.

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Worked Example 3: Beta decay at the quark level

Write the beta-minus decay of the neutron at the quark level.

Solution. A neutron is udd and a proton is uud. The difference is one down quark has become an up quark. At the quark level:

d → u + e⁻ + ν̄_e

The total charge before is -1/3; after is (+2/3) + (-1) + 0 = -1/3 ✓. This is the underlying microscopic process for \beta^- decay of any nucleus — it is always the conversion of a down quark in a neutron into an up quark in a proton, mediated by the weak interaction (specifically, by the emission of a virtual W^- boson that then materialises as e^- and \bar\nu_e).

Similarly, β^+ decay is u → d + e^+ + ν_e at the quark level.

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Leptons and Quarks: Comparison

Property	Leptons	Quarks
Fundamental?	Yes	Yes
Charge	0 or ±1	±1/3 or ±2/3
Feel strong force?	No	Yes
Found in isolation?	Yes	No (confined)
Number of types	6 (+6 anti)	6 (+6 anti)
Baryon number	0	±1/3
Lepton number	±1	0

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Visualising the Proton and Neutron

The proton is $uud$uud and the neutron is $udd$udd. The charge sums are worth seeing graphically:

The two nucleons differ by a single quark flavour — a $u \to d$u→d swap converts a proton to a neutron, and vice versa. This swap is exactly the microscopic content of beta decay: a virtual $W^\pm$W± boson mediates the conversion $d \to u + e^- + \bar{\nu}_e$d→u+e−+νˉe​ or $u \to d + e^+ + \nu_e$u→d+e++νe​, leaving baryon number unchanged but flipping a unit of charge between the nucleon and the emitted lepton pair.

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Synoptic Links

• Standard Model overview (last lesson): This lesson populates the "matter" half of the Standard Model with explicit charges, baryon numbers and lepton numbers. The classification of every observed hadron into baryon or meson reduces $\sim 200$∼200 "particle zoo" entries to a small handful of quark combinations.
• Conservation laws (next lessons): Every conservation law you check in the next two lessons — charge, baryon number, lepton number, strangeness — is defined in terms of the quark and lepton content laid out here. You will return to the $uud$uud and $udd$udd formulas over and over.
• Beta decay (Module 6.4 — earlier in this course): The macroscopic process $^{14}_{6}\text{C} \to {}^{14}_{7}\text{N} + e^- + \bar{\nu}_e$614​C→714​N+e−+νˉe​ is at heart a single down quark inside one of the carbon-14 neutrons converting to an up quark. This lesson supplies the quark-level rewrite $d \to u + e^- + \bar{\nu}_e$d→u+e−+νˉe​ that explains why the antineutrino must appear (lepton-number conservation) and why the lifetime is so long (weak interaction).
• Photons in the photoelectric effect (Module 4.5): Photons are not hadrons — they are gauge bosons. Students sometimes try to write photon "quark content"; there is none, because photons are themselves elementary.
• Wave-particle duality (Module 4.5): All the matter fermions of this lesson exhibit wave-particle duality. Their de Broglie wavelength $\lambda = h/p$λ=h/p explains why high-energy electron beams (and the LHC's proton beams) are the appropriate probes for sub-fm structure.

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Specimen question modelled on the OCR H556 paper format

Question (10 marks): A modern particle physics textbook lists the following hadrons with their quark content:

Hadron	Quark content
Proton	$uud$uud
Neutron	$udd$udd
$\pi^+$π+	$u\bar{d}$udˉ
$K^-$K−	$\bar{u}s$uˉs
$\Lambda^0$Λ0	$uds$uds