Elementary Particles

Laboratorium

Zoom into a grain of salt by fifteen orders of magnitude — and build your own particles out of quarks.

A journey into a grain of salt

View width10⁻³ m

Build a hadron

Drag quarks into the bag (or click the buttons). Charges add up, and the colors must cancel out.

Your collection: still empty

How small is small?

5·10⁻⁴ mA grain of salt — about 0.5 mm, holding about 5·10¹⁸ atoms: nearly a billion times more than there are people on Earth.
2.8·10⁻¹⁰ mDistance between Na⁺ and Cl⁻ ions in a salt crystal.
~10⁻¹⁰ mAtom — a fuzzy cloud of electrons. Diameter around 0.1–0.3 nm.
~10⁻¹⁴ mNucleus — a few femtometers (1 fm = 10⁻¹⁵ m), yet it holds over 99.9% of the atom’s mass.
0.84·10⁻¹⁵ mProton — radius about 0.84 fm.
< 10⁻¹⁸ mQuark, electron — in measurements they behave like points; no structure can be seen inside them.

An atom the size of a stadium

An atom is 20,000 to 100,000 times larger than its nucleus (order of magnitude 10⁵).

If an atom were blown up to the size of a big stadium (about 300 m across), the nucleus would be a small pea (a few millimeters) in the middle of the field. The electrons are a fuzzy haze over the stands — and everything else is empty space. Even so, a table doesn’t let your hand through: the electron clouds repel each other, and the Pauli exclusion principle won’t let them “squeeze together.”

Stranger still inside a proton: the masses of its three quarks make up only about 1% of the proton’s mass. The rest is the energy of the quarks’ motion and of the gluon field — mass made of energy, just as E = mc² says.

Scale of the Universe — from 10⁻¹⁸ m Periodic table Quanta — the electron cloud

Laboratorium

Seventeen particles, four forces — and an honest list of what we still don’t know.

The Standard Model

click a tile · masses from the PDG (as of 2024)

Masses on a logarithmic scale

each tick is 10 times more

The photon and the gluon have no mass, so they don’t fit on this axis. The span from the neutrino to the top quark is at least 11 orders of magnitude — and nobody knows why.

Four forces

The relative strength is just an order of magnitude for two protons about 1 fm apart; it depends on energy and distance.

Quark confinement

Grab the antiquark and pull it away from the quark. The gluon string doesn’t weaken with distance.

distance0.40 fm

string energy0.39 GeV

force≈ 16 t

What the Standard Model doesn’t explain

It’s the best-tested theory in the history of physics — and certainly not the last.

Gravity

It isn’t in the Standard Model. The hypothetical graviton has never been observed, and combining gravity with quantum mechanics is still an open problem (see black holes).

Dark matter

Galaxies and clusters behave as if there were about 5 times more invisible mass than ordinary matter. No Standard Model particle explains it, and the search for new particles goes on.

Neutrino masses

Oscillations prove that neutrinos have mass, but the original Standard Model didn’t predict it. Where it comes from and exactly how big it is — nobody knows.

Matter outnumbering antimatter

The laws of physics treat them almost symmetrically, yet the Universe is made of matter. The known differences (CP violation) are far too small to explain it.

Dark energy

The expansion of the Universe is speeding up. This “something” accounts for about 70% of the energy of the Universe, and we don’t know what it is.

Why these numbers?

The model has about 19 (over 25 with neutrinos) parameters that are measured, not calculated: masses, charges, mixing angles. Why are there three generations? The theory doesn’t say.

Why don’t physicists like the name “God particle”? It comes from the title of a popular book by Leon Lederman (1993). As the story goes, the author wanted to call it “the goddamn particle” because it was so hard to find, but the publisher changed the title. The Higgs boson has nothing to do with religion, and it doesn’t “create” matter: it is the trace of a field that gives the W, the Z, quarks and the electron their mass. The mass of a proton — and of you — comes mostly from the energy of the strong interaction, though. Peter Higgs himself disliked the name.

Laboratorium

Smash protons, read the traces in the detector and hunt for the Higgs boson in the noise — just like physicists at CERN.

Event display

Magnetic field in the coil B3.8 T

The Large Hadron Collider

Energy of one beam6.8 TeV

collision energy13.6 TeV

dipole field8.09 T

γ factor7,248

slower than light by2.9 m/s

Find the Higgs boson

invariant mass of photon pairs · our own toy generator

show fitted background

significance of the excess 0.0σ

data collected0 batches

photon pairs0

in the 120–130 GeV window: data / background— / —

A toy model: the background is an exponentially falling spectrum, the signal a narrow Gaussian at 125.2 GeV (width 1.7 GeV — that’s the detector’s resolution). Each batch of data contains 1000 background pairs and on average 12 pairs from the Higgs; the numbers were chosen so that a discovery takes about 30 batches. We compute the significance from a background fit to the sides of the histogram and the excess in the 120–130 GeV window. In 2012, ATLAS and CMS needed several decay channels combined to pass 5σ.

Laboratorium

Every particle has its mirror image. When the two meet, pure energy is left.

Annihilation

drag the positron to the electron

Bubble chamber

Photon energy60 MeV Field B1.5 T

Antimatter for real

PET in the hospital

The patient receives glucose labeled with fluorine-18 (half-life about 110 min). Its nuclei undergo β⁺ decay and emit positrons. Each one travels a fraction of a millimeter, then annihilates with an electron, and two 511 keV photons fly off in opposite directions. A ring of detectors records them at the same moment, and from thousands of such lines builds an image of the places that use a lot of glucose — tumors, for example.

Radioactivity — β⁺ decay

Where did the antimatter go?

Right after the Big Bang there was almost as much antimatter as matter. For every billion particle–antiparticle pairs there was roughly one extra particle of matter. The rest annihilated, and that tiny surplus is what stars — and we — are made of. Where it came from, nobody knows; the known differences between how matter and antimatter behave are too small.

Antihydrogen at CERN

At CERN’s Antimatter Factory, antiprotons are slowed down and combined with positrons into atoms of antihydrogen. The ALPHA experiment trapped them in a magnetic trap (2010), later held them for over 15 minutes and measured their spectrum — the same as hydrogen’s. In 2023, ALPHA-g showed that antimatter falls down, just like ordinary matter.

An antimatter bomb? No

Annihilating 1 g of antimatter with 1 g of matter would release about 1.8·10¹⁴ J. But making antimatter costs billions of times more energy than it gives back, and all the antimatter ever produced at CERN adds up to fractions of a nanogram. At the current rate, 1 gram would take longer than the Universe has existed (an order-of-magnitude estimate).

Who predicted it?

In 1928, Paul Dirac combined quantum mechanics with special relativity. His equation had “too many” solutions — with negative energy. In 1931, Dirac interpreted them as an antielectron, and a year later Carl Anderson saw its track in a cloud chamber.

Bananas and antimatter

Bananas contain potassium, including radioactive potassium-40. Very rarely (about 0.001% of decays) K-40 decays by emitting a positron. So a banana gives off a tiny bit of antimatter now and then — completely harmless.

Laboratorium

Ghosts passing through the Earth and a rain of muons from space — particle physics without an accelerator.

Beta decay and the missing energy

n → p + e⁻ + ν̄ₑ · decay energy 0.782 MeV

show neutrino

Neutrinos from the Sun

0that’s how many neutrinos from the Sun have passed through your fingernail (about 1 cm²) since you opened this page — about 6.5·10¹⁰ per second, day and night (the Earth doesn’t get in their way)

Super-Kamiokande

Neutrino oscillations

Nobel Prize 2015: Kajita and McDonald

Arrival direction (angle from vertical)180° (from below) Neutrino energy1.0 GeV

Cosmic-ray shower

time dilation (relativity)

Muon calculator

A muon lives on average 2.2 µs (in its own frame). It is created about 15 km above the ground. Will it make it down?

Muon energy1.67 GeV

speed0.998 000 c

γ15.8

range without dilation657 m

range γβcτ10.4 km

survives 15 km (without)—

survives 15 km (with)—

Relativity — time dilation

Cloud chamber — a demonstration

Muons and other particles from space can be seen with your own eyes in a cloud chamber. In a sealed aquarium above a plate chilled with dry ice (−78 °C), a layer of supersaturated isopropyl alcohol vapor forms. A passing particle ionizes the air, and droplets condense on the ions — you see fleeting white streaks: thick and short (alpha particles), long and straight (muons), curly (electrons).

This experiment is for adults only or under a teacher’s supervision: dry ice burns with cold (wear gloves!) and must never be sealed in an airtight container; alcohol vapor is flammable and the room has to be ventilated. Many science centers show ready-made chambers — the easiest way to see one is there.

Polish footprints

Life of stars — fusion and neutrinos Radioactivity — beta decay

How does it work?

An elementary particle is one that — as far as we know — has no smaller parts inside. An atom isn’t one (it has a nucleus and electrons), and neither is a proton (it has quarks and gluons). According to the Standard Model, matter is built from quarks and leptons (including the electron, the muon and neutrinos), and forces are carried by bosons: the photon (electromagnetic), gluons (strong), W and Z (weak). The Higgs boson is the trace of a field that gives elementary particles their mass.

Quarks have fractional charges, and protons and neutrons are made of three of them:

p = uud: +⅔ +⅔ −⅓ = +1n = udd: +⅔ −⅓ −⅓ = 0π⁺ = ud: +⅔ +⅓ = +1Quarks also carry color charge (by convention: red, green, blue). Only “white” combinations can exist freely: three different colors (baryons) or a color plus its anticolor (mesons).

Mass is energy

Einstein showed that mass and energy are equivalent. That’s why in a collider new, heavier particles can be created from the energy of motion, and in annihilation mass turns into photons.

E = mc²E² = (pc)² + (mc²)²γ = 1√1 − v²/c²1 g of mass is 9·10¹³ J · electron 0.511 MeV · proton 938.3 MeV · each of the two photons from the annihilation of an e⁺e⁻ pair at rest carries 0.511 MeV

How to read tracks in a detector

In a magnetic field B, a charged particle feels the Lorentz force perpendicular to its motion, so its track bends into an arc. The greater the momentum, the straighter the track; the direction of the bend reveals the sign of the charge. From the energies and directions of the decay products, physicists reconstruct the invariant mass of the particle that decayed.

r = p|q|Br [m] ≈ p [GeV/c]0.3·B [T]m²c⁴ = (E₁ + E₂)² − |p₁ + p₂|²c²m_γγ = √2E₁E₂(1 − cos α)a 10 GeV/c track in a 2 T field has a radius of about 16.7 m, in a 4 T field about 8.3 m · α — angle between the photons

The statistics of discovery

A bump on a plot could be a fluke. Physicists measure how unlikely such a fluctuation would be if there were no new particle. The 5σ threshold means a chance of about 1 in 3.5 million.

Z = √2[n ln(n/b) − (n − b)]n — counts in the mass window · b — expected background · for large numbers Z ≈ (n − b)/√b

Muons and time dilation

L = γβcττ = 2.197 µscτ ≈ 659 mat v = 0.998c: γ ≈ 15.8 and an average range ≈ 10.4 km instead of 657 m

Simplifications: the collider events come from our own toy generator (seeded random sampling): the decay kinematics and track curvature are computed correctly, but jets, background and the detector response are heavily simplified, and the detector’s radial scale is nonlinear (the tracker is enlarged). The Higgs histogram is a toy model with hand-picked numbers. In the bubble chamber we assume a constant energy loss of 0.28 MeV/cm (liquid hydrogen) and ignore bremsstrahlung. Oscillations are computed for two flavors (ν_μ ↔ ν_τ) with Δm² = 2.5·10⁻³ eV² and maximal mixing. The cosmic-ray shower is schematic. In Rutherford’s experiment, backscattering is a dozen or so times more frequent than for Geiger and Marsden (about 1 in 8000), so you don’t have to wait for hours. Masses and discovery years from the PDG and CERN (as of 2024–2025).

A journey into a grain of salt

Build a hadron

How small is small?

An atom the size of a stadium

The Standard Model

Masses on a logarithmic scale

Four forces

Quark confinement

What the Standard Model doesn’t explain

Gravity

Dark matter

Neutrino masses

Matter outnumbering antimatter

Dark energy

Why these numbers?

Event display

The Large Hadron Collider

Find the Higgs boson

Annihilation

Bubble chamber

Antimatter for real

PET in the hospital

Where did the antimatter go?

Antihydrogen at CERN

An antimatter bomb? No

Who predicted it?

Bananas and antimatter

Beta decay and the missing energy

Neutrinos from the Sun

Super-Kamiokande

Neutrino oscillations

Cosmic-ray shower

Muon calculator

Cloud chamber — a demonstration

Polish footprints

Timeline of discoveries

Rutherford’s experiment

All discoveries

Units: eV, GeV and E = mc²

How does it work?

Mass is energy

How to read tracks in a detector

The statistics of discovery

Muons and time dilation

See also

Challenges

Did you know…?

Keys