The Standard Model: Quarks, Leptons, and Bosons
The Standard Model of particle physics describes all known elementary particles and three of the four fundamental forces: matter is made of fermions—six quarks (up, down, strange, charm, bottom, top) and six leptons (electron, muon, tau and their neutrinos), in three generations—and the forces are carried by gauge bosons (photon, gluons, W and Z), with the Higgs boson giving mass to the other particles. In brief: ordinary matter (protons, neutrons, electrons) consists of the first generation only: up and down quarks and the electron. Quarks have fractional charges (+2/3 or −1/3), and are never found alone: they are bound in hadrons. Each particle has an antiparticle. Fermions have half-integer spin (1/2), bosons have integer spin (0 or 1). Gravity is not included.
Atoms were once the “uncuttable” units of matter; then they were found to contain nuclei and electrons, nuclei protons and neutrons, and these in turn quarks. This guide describes the elementary particles and their properties, the three generations, the force carriers, compares quarks and leptons in a table, works through numerical examples of charge and mass ratios, and corrects common mistakes.
What is the Standard Model?
The Standard Model is a quantum field theory developed in the 1960s and 1970s, and confirmed by experiments with high precision. It classifies the elementary particles, which have no known internal structure: 12 fermions of matter (and their 12 antiparticles), 4 types of gauge bosons that mediate the forces (the photon, 8 gluons, the W+, W− and Z0), and the Higgs boson. It describes three of the four fundamental interactions: electromagnetic, weak and strong. It does not include gravity, nor dark matter and dark energy, and it does not explain the masses of the neutrinos or the dominance of matter over antimatter, so it is known to be incomplete.
What are fermions?
Fermions have spin 1/2 and obey the Pauli exclusion principle (no two identical fermions in the same quantum state), which gives atoms their structure. There are two families: quarks, which feel the strong force, and leptons, which do not. Each family is arranged in three generations (or families) of increasing mass; particles of higher generations are unstable and decay to the first generation, so ordinary matter contains only the first one. Why there are exactly three generations is unknown (the width of the Z boson shows that there are only three light neutrinos).
What are quarks?
- Up (u), charm (c), top (t): charge +2/3 e.
- Down (d), strange (s), bottom (b): charge −1/3 e.
Masses (approximate): up 2.2 MeV/c2, down 4.7 MeV, strange 95 MeV, charm 1.27 GeV, bottom 4.18 GeV, top 173 GeV (about as heavy as a gold atom). Quarks carry a “color charge” (red, green or blue) that is the source of the strong interaction; only colorless combinations can exist as free particles (confinement): three quarks (baryons) or a quark and an antiquark (mesons). The proton is uud (2/3 + 2/3 − 1/3 = +1) and the neutron udd (2/3 − 1/3 − 1/3 = 0). Evidence for quarks: deep inelastic scattering of electrons by protons at SLAC (1968) showed point-like constituents inside the proton.
What are leptons?
- Electron (e−), muon (μ−), tau (τ−): charge −1; masses 0.511 MeV/c2, 105.7 MeV/c2 (206.8 times the electron) and 1,777 MeV/c2 (3,477 times). The muon lives 2.2 µs and decays to an electron and two neutrinos; the tau lives 2.9 × 10−13 s.
- Neutrinos (νe, νμ, ντ): neutral, interact only by the weak force (and gravity), and have tiny masses (less than 0.1 eV/c2, a million times lighter than the electron). Trillions of solar neutrinos pass through the body every second. Neutrinos oscillate between types as they travel (Super-Kamiokande 1998 and SNO 2001; Nobel Prize in Physics 2015), which shows that they have mass.
What are bosons?
The force carriers have spin 1: the photon (massless, electromagnetic force), 8 gluons (massless, strong force), and the W+, W− (80.4 GeV/c2) and Z0 (91.2 GeV/c2) bosons (weak force). The Higgs boson (spin 0, mass 125 GeV/c2) is the quantum of the Higgs field, which pervades space; particles acquire mass by interacting with the field (the stronger the coupling, the greater the mass). It was predicted in 1964 and discovered at the LHC in 2012 (Nobel Prize to Higgs and Englert, 2013). A hypothetical graviton would carry gravity.
Quarks and leptons compared
| Generation | Quarks (charge +2/3, −1/3) | Charged lepton (−1) | Neutrino (0) |
|---|---|---|---|
| First | up, down | electron | electron neutrino |
| Second | charm, strange | muon | muon neutrino |
| Third | top, bottom | tau | tau neutrino |
Worked example: charges and masses
- Charge of the proton: uud: 2/3 + 2/3 − 1/3 = +1. Neutron: udd: 2/3 − 1/3 − 1/3 = 0.
- Mass of the proton. The masses of its two up quarks and one down quark add up to 2 × 2.2 + 4.7 = 9.1 MeV/c2, only about 1 percent of the proton’s mass (938.3 MeV/c2). The rest comes from the kinetic energy of the quarks and the energy of the gluon field (E = mc2): most of the mass of everyday matter is binding energy of the strong interaction, not Higgs-given mass.
- Mass ratios. Muon/electron = 105.66 ÷ 0.511 = 206.8; tau/electron = 1,776.9 ÷ 0.511 = 3,477; top quark/electron = 172,500 ÷ 0.511 = 3.4 × 105. The reason for this hierarchy is unknown.
- Muon decay: μ− → e− + ν̄e + νμ. Check the charge: −1 → −1 + 0 + 0 ✓. Lepton numbers: muon number +1 → +1 (the muon neutrino); electron number 0 → +1 (electron) − 1 (antineutrino) = 0 ✓.
- Range of the weak force. Using the W mass of 80.4 GeV/c2: range ≈ ħc ÷ (mc2) = 197.3 MeV·fm ÷ 80,400 MeV = 2.5 × 10−3 fm = 2.5 × 10−18 m, much shorter than a proton (0.9 fm).
- Count of particles. Counting each quark and lepton once, without colors or antiparticles, gives 6 + 6 = 12 fermions. The photon, gluon, W, Z and Higgs boson add 5 more, so the Standard Model is usually said to have 17 fundamental particles. If the three colors of each quark and all antiparticles are counted, the number of fermion states rises to 36 quark types (6 flavors × 3 colors × particle/antiparticle) plus 12 leptons (6 particles and 6 antiparticles).
How was the model built?
J. J. Thomson discovered the electron in 1897, Rutherford the proton (1919), and Chadwick the neutron (1932). The muon (1936) was an unexpected discovery: I. I. Rabi is said to have asked, “Who ordered that?”. Murray Gell-Mann and George Zweig proposed quarks in 1964, and Sheldon Glashow, Abdus Salam and Steven Weinberg unified the electromagnetic and weak interactions (Nobel Prize 1979). The W and Z were found at CERN in 1983, the top quark at Fermilab in 1995, the tau neutrino in 2000, and the Higgs boson in 2012. Experiments such as the LHC test the model, and search for physics beyond it, such as supersymmetry or dark matter particles.
Which mistakes are common?
Mistake 1: Thinking that quarks can be isolated
Color confinement means that quarks are always found in colorless combinations. Pulling two quarks apart creates new quark-antiquark pairs.
Mistake 2: Saying that the Higgs boson gives mass to everything
The Higgs field gives mass to elementary particles such as quarks, leptons and the W and Z. Most of the mass of the proton comes from the strong interaction energy.
Mistake 3: Confusing leptons and baryons
Leptons (electron, neutrino) are elementary fermions without strong interactions. Baryons (proton, neutron) are composite particles made of three quarks.
Mistake 4: Believing that the Standard Model is a complete theory of everything
It excludes gravity, dark matter, dark energy and neutrino masses.