Identify the elementary particles of the Standard Model (quarks, leptons, gauge bosons, Higgs boson), classify hadrons as baryons (three quarks) and mesons (quark-antiquark pairs), and explain the role of each particle family

What this dot point is asking

QCAA wants you to identify and classify the elementary particles of the Standard Model: quarks, leptons, gauge bosons, the Higgs boson. You should also distinguish fundamental particles from composite particles (hadrons), and recognise the proton and neutron as quark composites.

The Standard Model

The Standard Model is the current theoretical framework for the elementary particles and their interactions (excluding gravity). It was largely complete by the 1970s and has been confirmed in numerous experiments, including most recently the Higgs boson discovery at CERN (2012).

The elementary particles divide into:

• Fermions (matter particles, spin 1/2): quarks and leptons.
• Bosons (force carriers, integer spin): gauge bosons and the Higgs.

Quarks

There are 6 quarks, in three generations of two each:

Each quark has a corresponding antiquark with opposite charge.

Quarks have a property called colour charge (red, green, blue, or anticolours) which is the source of the strong force. They are never observed in isolation; they are always bound into colour-neutral composites (hadrons). This is called confinement.

Charges in units of the elementary charge $e$:

• Up, charm, top: $+2/3$.
• Down, strange, bottom: $-1/3$.
• Antiquarks: opposite sign.

Quark masses span a wide range:

• Up: 2.2 MeV/c$^2$
• Down: 4.7 MeV/c$^2$
• Charm: 1280 MeV/c$^2$
• Strange: 95 MeV/c$^2$
• Top: 173,000 MeV/c$^2$ (heaviest known elementary particle)
• Bottom: 4180 MeV/c$^2$

Leptons

There are 6 leptons, in three generations:

The charged leptons have charge $-1$; their antiparticles (positron, antimuon, antitau) have charge $+1$. Neutrinos and antineutrinos are electrically neutral.

Leptons do not feel the strong force; they only interact via the electromagnetic, weak, and (very weakly) gravitational forces.

Lepton masses:

• Electron: 0.511 MeV/c$^2$.
• Muon: 105.7 MeV/c$^2$.
• Tau: 1777 MeV/c$^2$.
• Neutrinos: very small (less than 1 eV/c$^2$ each), but non-zero.

Hadrons

Particles made of quarks are hadrons. Two types:

Baryons (three-quark composites)

Made of three quarks. Examples:

• Proton. $uud$. Charge $= 2(+2/3) + 1(-1/3) = +1$. Mass 938 MeV/c$^2$. Stable.
• Neutron. $udd$. Charge $= 1(+2/3) + 2(-1/3) = 0$. Mass 940 MeV/c$^2$. Free neutron is unstable (decays in about 15 minutes); bound in nuclei is stable.
• Other baryons. Lambda ($uds$), sigma ($uus$, $uds$, $dds$), etc. All heavier than the proton; all unstable.

Antibaryons are made of three antiquarks (e.g., antiproton $\bar{u}\bar{u}\bar{d}$).

Mesons (quark-antiquark pairs)

Made of one quark and one antiquark. Examples:

• Pion ($\pi^+$). $u\bar{d}$. Charge $+1$. Mass 140 MeV/c$^2$.
• Pion ($\pi^-$). $d\bar{u}$. Charge $-1$.
• Pion ($\pi^0$). $u\bar{u}$ or $d\bar{d}$ superposition. Charge 0.
• Kaon ($K^+$). $u\bar{s}$. Charge $+1$.
• J/psi. $c\bar{c}$. The 1974 discovery confirmed the charm quark.

All mesons are unstable.

Why three or two?

Quarks have colour charge. The strong-force theory (quantum chromodynamics, QCD) requires all observable particles to be colour-neutral. Two ways to be colour-neutral:

1. Three quarks with one each of red, green, blue (or their anticolours) → baryons.
2. Quark and antiquark with colour and anticolour → mesons.

Other combinations (exotic particles like tetraquarks and pentaquarks) have been observed but are rare and not in the QCE syllabus.

Gauge bosons

Each fundamental force is mediated by exchange of a gauge boson:

The photon mediates electromagnetism; gluons mediate the strong force; W and Z bosons mediate the weak force (responsible for beta decay).

The masses of W and Z were predicted before discovery (CERN, 1983) and matched the predictions. The gluon was inferred from the structure of hadrons.

The Higgs boson

The Higgs boson, discovered at CERN (4 July 2012), is the quantum of the Higgs field, which gives mass to the W and Z bosons (and, indirectly, to quarks and charged leptons through the Higgs mechanism). The Higgs has mass 125 GeV/c$^2$ and zero charge.

The discovery confirmed the last predicted particle of the Standard Model and earned the 2013 Nobel Prize for the theorists (Peter Higgs, Francois Englert).

What the Standard Model does not explain

The Standard Model is the best tested theory in physics, but it has gaps:

• Gravity. Not included. General relativity is a separate, classical theory. Quantum gravity is unresolved.
• Dark matter. Galaxies rotate as if there is more mass than visible. Dark matter (not in the Standard Model) is a leading candidate.
• Dark energy. The universe is accelerating; dark energy is the leading explanation. Not in the Standard Model.
• Neutrino masses. The Standard Model originally predicted massless neutrinos; observation of neutrino oscillations (Kamiokande, SNO) requires non-zero masses. Mechanism still uncertain.
• Matter-antimatter asymmetry. The universe is overwhelmingly matter. The Standard Model does not provide enough CP violation to explain this.

Particle physics in the 21st century is searching for physics beyond the Standard Model.

Examples in context

Example 1. ANSTO Mt Cotton physicists tracking cosmic-ray-induced muon decays observe muon decays via $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, a weak-force process mediated by W bosons that converts a second-generation lepton to a first-generation lepton plus neutrinos. The Standard Model quantum numbers (lepton number, generation) are preserved in this decay, the dot point QCAA Unit 4 asks students to identify by family.

Example 2. A proton in a Cairns hospital X-ray-source tube is a baryon: three quarks (uud) bound by gluon exchange. Its mass-energy ($938 \text{ MeV}$) is dominated by gluon binding energy, not bare quark masses ($\sim 5 \text{ MeV}$ for up, $\sim 7 \text{ MeV}$ for down). QCAA EA Unit 4 thematic items often pair such an everyday particle with its quark composition.

Try this

Q1. State the quark composition of a proton and a neutron. [2 marks]

• Cue. Proton: uud; neutron: udd.

Q2. Classify the following as baryons, mesons or leptons: pion ($\pi^+$), electron, neutron. [3 marks]

• Cue. Pion ($u\bar{d}$): meson; electron: lepton; neutron (udd): baryon.

Q3. A muon decays $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$. (a) Identify the family of each particle. (b) Verify lepton number and charge conservation. (c) State the mediating boson and the fundamental force. [3+3+2 marks; ISMG: Knowledge and conceptual understanding, Analysis and interpretation]

• Cue. (a) Muon, electron: leptons; (b) $L_\mu: 1 \rightarrow 0+0+1$, $L_e: 0 \rightarrow 1+(-1)+0$, charge $-1 \rightarrow -1+0+0$; (c) W boson, weak force.