Quarks, Leptons and Hadrons

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 is the heart of section 6.4.4 of the OCR A-Level Physics A specification (H556), and it introduces the terminology (baryons, mesons, baryon number, lepton number) you will need for Lesson 9 on 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: