Physics · Atomic and quantum physics · Grade 11

Elementary particles

What is the universe made of, and how is antimatter used in a hospital?

The situation

A doctor injects a patient with a tiny amount of glucose labelled with radioactive fluorine-18. About an hour later a PET scanner shows where the tumour is: right there, positrons — particles of antimatter — meet electrons and turn into two gamma quanta. Where does antimatter come from, and what “building blocks” is the world really made of? The answer is provided by the Large Hadron Collider near Geneva and by the cosmic rays that rain down continuously from the sky.

Topic

Elementary particles. Large Hadron Collider and the Standard Model: quarks, leptons, bosons

Key ideas

Standard Model
Antiparticles
Conservation laws

Formulas

E^{2} = {(p c)}^{2} + {(m c^{2})}^{2}, E_{γ} = m_{e} c^{2} = 511 keV

Relativistic energy; an electron–positron pair at rest turns into two 511 keV photons.

γ \to e^{-} + e^{+}, E_{γ} \geq 2 m_{e} c^{2} = 1.022 MeV

Pair production (near a nucleus — it takes up some of the momentum).

N = N_{0} e^{- L / (γ β c τ)}, τ_{μ} = 2.197 μ s

The fraction of muons that have covered a distance $L$ in the atmosphere: from Earth's point of view their lifetime is longer by a factor of $γ$ .

M c^{2} = \sqrt{2 E_{1} E_{2} (1 - \cos θ_{12})}

The invariant mass of two massless particles shows which particle they were born from.

Q = \sum q_{i}, q_{u} = + \frac{2}{3}, q_{d} = - \frac{1}{3}; B = \frac{n_{q} - n_{\overline{q}}}{3}

The charge and baryon number of a hadron in the quark model.

Theory

The “zoo” of elementary particles and the Standard Model

After the electron (1897), proton (1919), neutron (1932) and positron (1932), the muon (1936) and the pion (1947) were found in cosmic rays; in the 1950s and 60s hundreds of new particles appeared in accelerators — the “particle zoo”. The quark model (Gell-Mann and Zweig, 1964) that brought order to them grew into today's Standard Model: 6 quarks and 6 leptons (three generations), the carriers of the interactions — the gluon, the photon, and the W± and Z⁰ bosons, and also the Higgs boson, which gives mass (2012). A particle is described by its mass, electric charge, spin, lifetime and quantum numbers (baryon number, lepton numbers, strangeness, isospin). Sources of particles are cosmic rays and accelerators (the “Charged-particle accelerator” experiment). The composition of the nucleus is in the “The atomic nucleus and binding” experiment.

Antiparticles and the positron

P. Dirac's relativistic equation of 1928 explained the electron's spin and the fine structure of the hydrogen spectrum, and through its negative-energy solutions demanded the existence of an anti-electron. In 1932 C. Anderson found in a cloud chamber the track of a light, positively charged particle whose curvature changed after it passed through a lead plate — the positron. Every particle has an antiparticle with the same mass and opposite charge (the antiproton — 1955). A photon near a nucleus produces a pair ( $E_{γ} > 1.022$ MeV), and the pair annihilates into two 511 keV photons. PET: ¹⁸F ( $T_{1 / 2} \approx 110$ min) decays by β⁺, the positron travels ≈ 0.6 mm in tissue and annihilates; detectors in a ring register the two photons simultaneously and draw the line between them. The place where thousands of lines cross is where the tracer has accumulated.

Conservation laws and quantum numbers

In any reaction energy, momentum, angular momentum, electric charge, baryon number and lepton numbers are conserved (the separate $L_{e}$ , $L_{μ}$ , $L_{τ}$ are violated only by neutrino oscillations). Some quantities are conserved only in the strong and electromagnetic interactions: for example strangeness can change in the weak interaction, which is why Λ⁰ decays “slowly”. The neutrino: since the electron's energy in β decay is distributed continuously, W. Pauli (1930) proposed an invisible particle, E. Fermi (1934) created the theory of β decay, and in 1956 the neutrino was detected beside a reactor. In the strong interaction particles of almost equal mass form isomultiplets: (p, n), (π⁺, π⁰, π⁻). They combine into still larger supermultiplets (the baryon octet and decuplet); the gap in the decuplet made it possible to predict the Ω⁻. These laws also work in nuclear reactions. The neutron is uncharged — there is no Coulomb barrier, so even thermal neutrons enter a nucleus easily: radiative capture $(n, γ)$ , fission of ²³⁵U, ¹⁰B $(n, α)$ ⁷Li (this is how neutron counters work) — in detail in the “Nuclear reactions” experiment. In an accelerator heavy ions can fuse with a target nucleus: superheavy elements with $Z > 103$ are synthesised only in this way — for example, in Dubna, element 117 (tennessine, 2010) was obtained by bombarding a ²⁴⁹Bk target with ⁴⁸Ca ions. In meson–nucleus reactions a slowed-down $π^{-}$ is absorbed by the nucleus and breaks it into several nucleons (a “star” in the emulsion), while a $K^{-}$ meson turns a neutron in the nucleus into a hyperon ( $K^{-} + n \to Λ + π^{-}$ ) — a hypernucleus forms; charge, baryon number and strangeness are conserved in the process.

Quarks, gluons and the four interactions

Quarks have fractional charge ( $+ \frac{2}{3}$ or $- \frac{1}{3}$ ) and one of three colour charges. They occur only in colourless groups: baryons (qqq: p, n, Λ, Ω⁻) and mesons (qq̄: π, K, J/ψ); a free quark is never observed (confinement). Colour is carried by eight gluons. Leptons (e, μ, τ and the three neutrinos) do not take part in the strong interaction. The four fundamental interactions: strong (gluons, ≈ 1 fm), electromagnetic (the photon, infinite range), weak (W±, Z⁰ — the intermediate bosons, discovered at CERN in 1983; β decay, neutrino reactions) and gravitational. At a distance of ≈ 1 fm their relative strengths are about 1 : 10⁻² : 10⁻⁶ : 10⁻³⁸. The mass of elementary particles is given by the Higgs field.

Cosmic rays

High-energy particles rain down continuously on Earth from space (V. Hess, 1912, in a balloon). Primary cosmic rays consist, by number of particles, of about 89 % protons, 10 % helium nuclei and ≈ 1 % heavier nuclei (with a few electrons too); their energies reach 10²⁰ eV. They contain far more lithium, beryllium and boron than the Sun does — heavy nuclei break up on the way (cosmic-ray nucleosynthesis). A primary particle strikes an air nucleus at a height of ≈ 15–20 km and produces an extensive air shower: pions decay into muons and neutrinos. At sea level mainly muons are detected — about one per cm² per minute. They reach the ground thanks to time dilation (the “Special relativity” experiment). Cosmic rays are thought to be accelerated in supernova remnants and around the black holes at the centres of active galaxies. Neutrino astronomy uses huge detectors (Super-Kamiokande in water, IceCube in the Antarctic ice) to register neutrinos from the Sun, supernovae and distant galaxies; the solar neutrino problem led to the discovery of neutrino oscillations (the “Thermonuclear fusion” experiment).

The LHC, grand unification and the history of the Universe

The Large Hadron Collider (a 27 km ring) accelerates protons to 6.8 TeV and collides them; the superconducting coil of the CMS detector produces a field of 3.8 T. A new particle shows up as a peak in the invariant-mass distribution — this is how the Higgs boson was found, in the γγ and four-lepton channels. The idea of grand unification: at very high energy (≈ 10¹⁵–10¹⁶ GeV) the strong, electromagnetic and weak interactions merge into one; it predicts proton decay, but experiments show the proton's lifetime to be greater than 10³⁴ years. In the first microseconds after the Big Bang, nucleons formed from the quark–gluon plasma, and in the first minutes ≈ 25 % helium by mass was synthesised. The predominance of matter over antimatter in the Universe — the baryon asymmetry — has still not been fully explained. Model: the events are generated by a simplified Monte Carlo method; the background and the detector accuracy are illustrative.

Did you know?

The positron was discovered in 1932 by the American physicist Carl Anderson while studying cosmic rays in a cloud chamber; the existence of this particle had followed from P. Dirac's equation of 1928. Anderson received the Nobel Prize in 1936.
The ring of the Large Hadron Collider is about 27 km long. In 2012 the Higgs boson was discovered there, and in 2013 F. Englert and P. Higgs received the Nobel Prize in Physics.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

De Broglie waves — Grade 11
Rutherford's experiment — Grade 11
The atomic nucleus and binding — Grade 11
Thermonuclear fusion — Grade 11
Detecting particles — Grade 11
Spin, the Zeeman effect and MRI — Year 1
Many-electron atoms — Year 1
Bands in solids — Year 1
Schrödinger and quantum tunnelling — Year 3
Quantum dots and the potential well — Year 3