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

Published by Patrick Mutisya · 14 days ago

Fundamental Particles – Hadrons

Fundamental Particles

In the Standard Model of particle physics, all matter is built from two families of elementary particles: quarks and leptons. Quarks combine to form composite particles called hadrons, while leptons (such as the electron) remain elementary.

Quarks

There are six flavours of quark: up (u), down (d), charm (c), strange (s), top (t) and bottom (b). Each quark carries a fractional electric charge of either \$+\frac{2}{3}e\$ or \$-\frac{1}{3}e\$, where \$e\$ is the elementary charge.

Hadrons

A hadron is any particle that experiences the strong nuclear force. Hadrons are categorised into two families:

  • Baryons: composed of three quarks (qqq).
  • Mesons: composed of one quark and one antiquark (q\$\bar{\text{q}}\$).

Baryons – Three Quarks

Because quarks have fractional charges, the total charge of a baryon is always an integer multiple of \$e\$. For example, the proton consists of two up quarks and one down quark:

\$\$

Q_{\text{proton}} = 2\left(+\frac{2}{3}e\right) + \left(-\frac{1}{3}e\right) = +e.

\$\$

Similarly, the neutron is made of one up quark and two down quarks:

\$\$

Q_{\text{neutron}} = \left(+\frac{2}{3}e\right) + 2\left(-\frac{1}{3}e\right) = 0.

\$\$

BaryonQuark ContentChargeSpin (ℏ)
Proton (p)uud+\$e\$½
Neutron (n)udd0½
Lambda (Λ⁰)uds0½
Delta⁺⁺ (Δ⁺⁺)uuu+\$2e\$3/2

Mesons – Quark–Antiquark Pairs

Mesons are bosons (integer spin) formed from a quark and its corresponding antiquark. Their charges also sum to integer multiples of \$e\$.

Example: the positively charged pion consists of an up quark and an anti‑down quark:

\$\$

Q_{\pi^{+}} = \left(+\frac{2}{3}e\right) + \left(+\frac{1}{3}e\right) = +e.

\$\$

The neutral pion is a mixture of up–anti‑up and down–anti‑down pairs, giving a net charge of zero.

MesonQuark ContentChargeSpin (ℏ)
Pion⁺ (π⁺)u\$\bar{\text{d}}\$+\$e\$0
Pion⁰ (π⁰)(u\$\bar{\text{u}}\$ – d\$\bar{\text{d}}\$)/√200
Kaon⁺ (K⁺)u\$\bar{\text{s}}\$+\$e\$0
Eta (η)mix of u\$\bar{\text{u}}\$, d\$\bar{\text{d}}\$, s\$\bar{\text{s}}\$00

Key Differences Between Baryons and Mesons

PropertyBaryon (qqq)Meson (q\$\bar{\text{q}}\$)
Number of constituent quarks32 (quark + antiquark)
Spin½, 3/2, … (fermions)0, 1, … (bosons)
Typical mass range≈ 938 MeV/c² (proton) to a few GeV/c²≈ 135 MeV/c² (π⁰) to a few GeV/c²
ExamplesProton, neutron, Λ⁰, Δ⁺⁺π⁺, π⁰, K⁺, η

Suggested diagram: Quark composition of a proton (uud) and a positively charged pion (u\$\bar{\text{d}}\$).