understand that a hadron may be either a baryon (consisting of three quarks) or a meson (consisting of one quark and one antiquark)

Fundamental Particles – Hadrons (Cambridge 9702 Syllabus)

1. Scope of the syllabus (11.2)

  • Six quark flavours – up (u), down (d), charm (c), strange (s), top (t) and bottom (b).


    These are the only quark flavours required for the exam.

  • Electric charge of each flavour:

QuarkCharge
u, c, t+\(\frac{2}{3}e\)
d, s, b-\(\frac{1}{3}e\)

  • Colour charge – red, green, blue (and the corresponding anticolours). Only colour‑neutral (singlet) combinations are observed.
  • Six lepton flavours – e⁻, νₑ, μ⁻, νμ, τ⁻, ντ (do not feel the strong interaction).
  • Composition of hadrons:

    • Baryons – three quarks (qqq)
    • Mesons – one quark and one antiquark (q\(\bar q\))

  • Quark‑level description of β‑decay.
  • Antiparticles for all hadrons (e.g. \(\bar p\), \(\pi^-\)).

2. Quarks

Quarks are elementary fermions (spin = ½) that carry three intrinsic properties:

  • Flavour: u, d, c, s, t, b
  • Electric charge** (see table above)
  • Colour charge: red, green or blue. Colour is a property of the strong interaction; observable particles must be colour‑neutral.

2.1 Colour confinement

Only the following colour‑neutral combinations exist in nature:

  • Baryons: three quarks of different colours (red + green + blue) → colour singlet.
  • Mesons: a quark and an antiquark with matching colour–anticolour (e.g. red + anti‑red) → colour singlet.

3. Leptons

Leptons are elementary fermions that do not participate in the strong interaction.

LeptonChargeFamily
Electron \(e^{-}\)−e1st
Electron‑neutrino \(\nu_{e}\)01st
Muon \(\mu^{-}\)−e2nd
Muon‑neutrino \(\nu_{\mu}\)02nd
Tau \(\tau^{-}\)−e3rd
Tau‑neutrino \(\nu_{\tau}\)03rd

4. Hadrons

Hadrons are composite particles that experience the strong nuclear force. They are divided into two families.

4.1 Baryons (qqq)

Three quarks of different colours combine to give a colour‑neutral fermion (half‑integer spin).

BaryonQuark contentChargeSpin (ℏ)
Proton (p)u u d+e½
Neutron (n)u d d0½
Λ⁰u d s0½
Δ⁺⁺u u u+2e3/2
Antiproton (\(\bar p\))\(\bar u\,\bar u\,\bar d\)−e½

4.2 Mesons (q \(\bar q\))

A quark and its corresponding antiquark (colour–anticolour) form a colour‑neutral boson (integer spin).

MesonQuark contentChargeSpin (ℏ)
Pion⁺ (π⁺)u \(\bar d\)+e0
Pion⁰ (π⁰)\(\tfrac{1}{\sqrt2}(u\bar u - d\bar d)\)00
Pion⁻ (π⁻)\(\bar u\,d\)−e0
Kaon⁺ (K⁺)u \(\bar s\)+e0
Eta (η)mix of u\(\bar u\), d\(\bar d\), s\(\bar s\)00

5. Antiparticles of Hadrons

Every hadron has an antiparticle obtained by replacing each quark with its antiquark (and reversing the colour).

  • Proton ↔ Antiproton: \(uud \leftrightarrow \bar u\,\bar u\,\bar d\)
  • Neutron ↔ Antineutron: \(udd \leftrightarrow \bar u\,\bar d\,\bar d\)
  • π⁺ ↔ π⁻: \(u\bar d \leftrightarrow \bar u d\)

6. Quark‑level description of β‑decay

In nuclear β⁻‑decay a down quark inside a neutron changes into an up quark by emitting a \(W^{-}\) boson, which subsequently decays into an electron and an electron‑antineutrino:

\[

d \;\rightarrow\; u + W^{-}, \qquad

W^{-}\;\rightarrow\; e^{-} + \bar{\nu}_{e}

\]

At the hadron level this appears as:

\[

n\;(udd) \;\rightarrow\; p\;(uud) + e^{-} + \bar{\nu}_{e}

\]

7. Summary of key differences

PropertyBaryon (qqq)Meson (q \(\bar q\))
Constituents3 quarks (different colours)1 quark + 1 antiquark (colour–anticolour)
Spin½, 3/2, … (fermions)0, 1, … (bosons)
Mass range≈ 938 MeV/c² (p) to a few GeV/c²≈ 135 MeV/c² (π⁰) to a few GeV/c²
Examplesp, n, Λ⁰, Δ⁺⁺, \(\bar p\)π⁺, π⁰, π⁻, K⁺, η

Quark‑colour diagrams (schematic): (a) Proton (uud – red, green, blue) and (b) π⁺ (u – red, \(\bar d\) – anti‑red). Both are colour‑neutral.