Particle Detector Headquarters

Concept: Layered detectors identify particles by where they leave energy. Trackers bend charged particles in a magnetic field (curvature gives momentum), the EM calorimeter absorbs electrons and photons, the hadronic calorimeter absorbs protons, neutrons, pions and kaons, and only muons cross everything. Neutrinos leave nothing and are inferred from missing momentum. At a fixed momentum, time of flight over 10 m and the Cherenkov threshold β > 1/n (water: β > 0.75188) split species by mass, because E² − p² = m² is invariant.
Why two calorimeters: Electromagnetic showers (e⁻, γ) are compact — bremsstrahlung and pair production stop them in a thin, high-Z layer. Hadronic showers (p, n, π, K) are longer and more irregular because they proceed by the strong force, so they need a much thicker absorber behind that layer. One calorimeter cannot do both jobs: a thin EM calorimeter lets hadrons punch through; a coarse hadronic calorimeter cannot measure e/γ energy well. Hence EM calorimeter in front, HCAL behind.
Serves: Introductory particle / modern physics; anyone learning to read an ATLAS-style event display.
Inquiry: Fire each species at the same momentum and compare signatures; then lower or raise p and watch the TOF race and Cherenkov cones separate — or fail to separate — π, K and p.
Misconception: "Heavier particles punch deeper." Penetration depends on how a particle interacts, not on its mass: the heavy proton showers and stops in the hadronic calorimeter, while the far lighter muon — which neither feels the strong force nor radiates much — sails through every layer. Real muons below a few GeV can range out in thick calorimeters; this sim shows the idealized textbook signatures.

Principle	Where it appears
Predict, then test	The guided-inquiry prediction cards immediately fire the particle you chose, so the detector itself delivers the verdict.
Misconception targeted structurally	"Heaviest goes deepest" is one of the answer choices; choosing it fires a proton that visibly stops one layer short of the muon chambers.
Invariant vs. varying	All TOF racers share one momentum; only mass differs, so E, β and arrival time split while E² − p² = m² stays fixed.
Operational quantities	E, β, γ, TOF delay and the Cherenkov state are computed live from the same relativistic formulas exposed to the audit hook.
Formal layer on demand	Equations, figures and a live worked example live behind the ⚛︎ The Physics button; the scene teaches without them.

Teach me Hide Text

Speed

Guided Inquiry

1 · Reading the layers

Let’s start by reading the layers. Every collider discovery ends in a detector like this. An e⁻ enters from the left: the Tracker’s magnetic field bends it — negative charges one way, positive the other — and then it showers in the EM calorimeter. Where a particle dumps its energy is its fingerprint.

2 · Now fire a photon

Now let’s try something neutral. The e⁻ ionized its way through the Tracker, but a photon carries no charge. What do you think the detector will record?

3 · Who reaches the muon chambers?

Now for the deepest layer. Only one species crosses every layer to reach the outer Muon spectrometer. Which one do you think it is?

4 · The invisible particle

Every species so far has left some mark. Beta-minus decay’s other product is an electron antineutrino, one of the neutrino family — so what do you think the detector will record this time?

5 · Three identical fingerprints

Here’s a tricky one. π⁺, K⁺ and p all share one Signature: track → HCAL shower. At the same momentum the proton arrives last. So what do you think its energy E is?

6 · Turn up the momentum

One last race. At 1.0 GeV/c the π–p gap is 12 ns. Now raise every racer to 5.0 GeV/c — what do you think the arrival-time gaps will do?

That’s ATLAS and CMS in miniature. At high p, identifying particles needs other tricks — Cherenkov n=1.33 flips ON near 1.1 GeV/c for the proton. Still unfired: K⁺ and n. Why not give them a go?

Listen

Fire a particle

pion, m = 0.1396 GeV

Show previous tracks

Momentum p1.0 GeV/c

Show time-of-flight race

Measured

▾

Energy E—

β (γ)—

TOF, 10 m—

Cherenkov n=1.33—

Signature—

Mass shell (invariant)

Speed and boost

Time of flight

Cherenkov cone

Tracker bend, B = 2 T ⊗ into page (schematic)

The Physics

Particle detector headquarters · what this sim shows, the physics behind it, and every control

At a glance

A detector never sees a particle itself, only the layers it disturbs and how long it takes to arrive. This sim fires eight kinds of particle through the layers of a collider detector, so you can see how a few measurements tell them apart.

What you'll learn

How a particle's charge and momentum set the bend of its track.
How each layer responds to each kind of particle, and what that pattern reveals.
How mass enters a particle's energy, speed and arrival time at a given momentum.
How the Cherenkov threshold depends on speed and mass.

The layers the sim draws, from the beam outward. Particles enter from the left.

What's on screen

The layers, in the order a particle meets them: Tracker (grey), EM calorimeter (green), HCAL (orange) and three muon stations (blue).
The fired particle: a coloured track, with sparks where it showers. Earlier shots stay as dimmed tracks.
Energy meters on the two calorimeters, in GeV.
Measured panel: energy, speed, arrival time over 10 m, Cherenkov on or off, and the signature.
Time-of-flight race (optional strip below): light and three particles racing over 10 m.

See itFire a π⁺ at the opening 1 GeV/c. Watch for: a curved track through the Tracker, a shower further out, and the Signature line filling in.

The controls

Press ⌖ on a row to see where that control sits in the sim.

Control	What it changes	Range
Species	Which particle to fire: e⁻, γ, μ⁻, π⁺, K⁺, p, n or ν. Picking one arms the Fire button; it does not fire.	8 species opens on π⁺
⚡ Fire	Launches the chosen species at the chosen momentum. The previous track stays, dimmed.	button
Clear tracks	Removes the dimmed earlier tracks.	button
Show previous tracks	Shows or hides the dimmed earlier tracks (the last four are kept).	on / off opens on
Momentum p	The momentum of the fired particle, the same for every species. Moving it also arms Fire.	0.2–5.0 GeV/c opens at 1.0
Show time-of-flight race	Opens a strip below the detector: a light pulse, π⁺, K⁺ and p, each racing 10 m at the chosen momentum.	on / off opens off
Measured	Energy E, speed β (and γ), arrival time over 10 m with its delay behind light, Cherenkov on or off, and the signature.	panel
▶ Play / ⏸ Pause	Fires the armed particle, or freezes the flight so you can read it.	top bar
Speed	How fast the flight is animated. The physics and the numbers stay the same.	0.25×–4× opens at 0.5×
↻ Reset	Back to π⁺ at 1.0 GeV/c, with the earlier tracks cleared and the race strip hidden.	top bar

Fixed: B = 2 T (into the page), Cherenkov medium n = 1.33, flight path 10 m. The bend of each track is drawn schematically, not to scale.

Each layer asks one question

Identity is never measured directly. It is inferred from which layers respond, in order:

The Tracker shows whether the particle is charged, the calorimeters show where its energy stops, and the muon stations show whether it is still going.

Particle	Signature in the sim
e⁻	curved track → EM shower
γ	no track → EM shower
μ⁻	thin track through all layers
π⁺, K⁺, p	track → HCAL shower
n	no track → HCAL shower
ν	nothing: missing momentum

Electrons and photons shower in the EM calorimeter; hadrons feel the strong force and shower deeper, in the HCAL.
A muon only ionises, so it crosses every layer. A neutrino almost never interacts and leaves only a red arrow for the momentum that went missing.

Meters: e⁻ and γ book their full energy. Hadron meters book kinetic energy only. A muon books a small, capped amount.

See itFire a muon. Watch for: a thin track with a cross in each of the three muon stations, leaving the frame.

See itFire a neutrino. Watch for: no track and no shower, only a red dashed arrow marked as not detected.

A magnetic field bends charged tracks

The Tracker sits in a magnetic field. A singly charged particle moving across it follows a circle of radius r, with transverse momentum p_T in GeV/c, B in tesla and r in metres:

Here the tracks start perpendicular to B, so p_T = p, and L is the length of field crossed.

Charge sets the side. In the sim a positive track bends up and a negative one down. A neutral particle does not bend.
Momentum sets the size. The bend shrinks as 1/p. In a real 2 T field r = p/(0.3 B) is 1.67 m at 1 GeV/c and 8.3 m at 5 GeV/c.
Reading the curvature gives the momentum. It does not give the mass.

The arcs in the sim are schematic: they straighten steadily as p rises, but the angles are not to scale.

See itFire a π⁺, then an e⁻, both at 1 GeV/c. Watch for: the dimmed π⁺ track bending up and the new e⁻ track bending down.

See itFire a π⁺ at 1 GeV/c, then another at 5 GeV/c. Watch for: the 5 GeV/c track leaving the Tracker much straighter than the dimmed 1 GeV/c one.

Mass sets speed and energy at fixed momentum

π⁺, K⁺ and p share one signature, and the Tracker gives each the same p. What still differs is the mass, which sets E and β:

The mass shell. At fixed p, mass is the only thing left that can differ.

At p = 1 GeV/c	E (GeV)	β	10 m takes
π⁺	1.010	0.9904	33.68 ns
K⁺	1.115	0.8967	37.20 ns
p	1.371	0.7293	45.74 ns

A heavier particle has more energy and is slower, both at once. Light covers 10 m in 33.36 ns, so the time behind light is the signal:

Time of flight over d = 10 m, against a light pulse on the same track.

These are the sim's real controls: pick a chip or drag p and the detector follows.

See itRace a proton, with the π⁺ and K⁺, at 1 GeV/c. Watch for: the light marker finishing first and the proton last, each arrival time printed at the finish line.

Why time of flight fails at high momentum

As p grows, every β approaches 1. Expanding 1/β for pc ≫ mc² shows how fast the time differences collapse:

Every arrival-time gap falls as 1/p².

p (GeV/c)	p – π⁺ gap	K⁺ – π⁺ gap
1	12.06 ns	3.52 ns
2	3.41 ns	0.92 ns
5	0.57 ns	0.15 ns

The 1/p² form needs β ≈ 1. At 1 GeV/c it gives 14.4 ns against the exact 12.1 ns; at 5 GeV/c, 0.574 ns against 0.569 ns.
A timer good to 0.1 ns would see the K⁺–π⁺ gap drop below it near 6 GeV/c, beyond the sim's range. The sim does not model timing resolution.

See itRace a proton at 1 GeV/c, then at 5 GeV/c. Watch for: the three lanes landing far apart at 1 GeV/c and almost together at 5 GeV/c.

Cherenkov light switches on above a speed

A charged particle moving faster than light does in the medium, β > 1/n, radiates light in a cone. The sim uses n = 1.33, the value for water:

The threshold momentum and the cone angle.

The threshold depends on mass. It is 0.159 GeV/c for π⁺, 0.563 for K⁺ and 1.070 for p. At 1 GeV/c the π⁺ and K⁺ radiate and the proton does not.
The cone widens with β. Its half-angle starts at 0 at threshold and approaches arccos(1/n) = 41.2°. At 1 GeV/c, π⁺ is at 40.6° and K⁺ at 33.0°.
A neutral particle never radiates. The sim shows only whether the cone is on and its angle, not how much light.

See itRace a proton at 1.0 GeV/c, then at 1.2 GeV/c. Watch for: the Cherenkov readout flipping from off to ON, and a cone appearing behind the proton's marker in the race strip.

Where it matters

ATLAS and CMS. Both put a tracker in a solenoid field (2 T in ATLAS, 3.8 T in CMS), with calorimeters and muon chambers outside, and combine all four layers to name what came out of a collision.
Timing and Cherenkov counters. ALICE uses time of flight to separate pions, kaons and protons at low momentum. LHCb's RICH detectors use Cherenkov light at higher momentum.
Super-Kamiokande is a tank of water (n ≈ 1.33) that detects neutrinos by the Cherenkov rings of the charged particles they produce.

Go deeper: finding a neutrino by what is missing

The sim's layers wrapped around the beam, as in a real detector. The neutrino shows only as an imbalance.

Transverse momentum is conserved. Whatever the visible tracks do not balance must have left unseen.

Summary

In one line. A detector names a particle by combining the layers it crosses and the bend of its track with, where those leave a tie, its arrival time and its Cherenkov light, which both depend on its mass.

Key points

Charge sets which way a track bends; momentum sets how much (r = p/(0.3 B)).
Track, EM shower, HCAL shower and muon hits together form a signature.
At fixed p, a heavier particle has more energy, a smaller β and a later arrival, and the gaps shrink as 1/p².
Cherenkov light needs a charge and p above 1.140 m (for n = 1.33).

Common mix-ups

"A neutral particle can't be detected." It leaves no track, but a photon or neutron still deposits energy in a calorimeter.
"A slower particle has less energy." At the same momentum the heavier particle is slower and has more energy.
"More momentum makes particles easier to tell apart by time of flight." It makes them harder: every β tends to 1.

Things to try on your own

Turn on the race, fire a proton, and slide p from 0.2 to 5 GeV/c. Note the p where the finishing times look equal, then compare with the table in section 06.
Select K⁺ and step p up from 0.2 GeV/c. Find the step where Cherenkov turns on, and check it against 0.563 GeV/c.
Fire a photon and then a neutron, and compare which calorimeter each one fills.