---
title: "How to Read a Particle Collision Interactive Lab | Sandbox Physics"
description: "How do physicists reconstruct a collision they cannot see from what the detector records? Combine the detector layers."
canonical_url: "https://sandboxphysics.com/labs/particle-collider/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/particle-collider/"
last_modified: "2026-10-29"
---

High-energy physics · collision event display

# Particle Collider · Event Reconstruction Room

**How do physicists reconstruct a collision they cannot see from what the detector records?** Combine the detector layers. How much a track curves in the magnetic field gives its charge and transverse momentum. Calorimeters measure energy and jet direction, and muon chambers pick out particles that punch through everything inside them. If the total transverse momentum does not balance, something escaped unseen, such as a neutrino.

Inspect collision tracks in a three-dimensional detector, then build a mass spectrum from frozen muon-pair candidates. Change the selection, compare opposite-charge and same-charge pairs, and click the spectrum to inspect a recorded pair.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

This parametric toy generator teaches how to read event displays. It is neither real collision data nor a full particle-transport simulation. Track curvature follows $p_T\simeq0.3\,|q|BR$, and $\vec p_T^{\,\mathrm{miss}}=-\sum_i\vec p_{T,i}$ reconstructs the visible momentum imbalance. Jet examples treat track energies as massless; frozen muon-pair four-vectors retain the muon rest mass.

## Find a peak in the same set of events

Click the spectrum to show that frozen pair in the detector. Cuts select from the same simulated records.

Opposite charge Same-charge control

The simulated sample loads automatically.

· **$91.2\,\mathrm{GeV}/c^2$**

Selection and model

Minimum momentum across the beam $12\,\mathrm{GeV}/c$ Maximum absolute pseudorapidity $2.4$

The generator mixes a fixed-mass two-muon teaching resonance with a smooth continuum. The blurred preset changes the momentum response. It omits the natural width, radiation and a full detector simulation. Same-charge pairs are a control sample, with no background normalization implied.

$$
M^2c^4=(E_1+E_2)^2-c^2\lvert\boldsymbol p_1+\boldsymbol p_2\rvert^2
$$

[CERN Open Data: two-lepton analysis](https://opendata.cern.ch/record/101)

[From a collision to jets and inference: eight connected chapters](https://sandboxphysics.com/stories/collider-qcd/)

Start with four-momentum, work through clustering, response matrices and likelihoods, then check extrapolation against a public jet spectrum.

Physics tutorial

## Combine two tracks into a mass

**Background** A short-lived particle often decays before reaching the detector. Its daughter particles carry away energy and momentum that can reveal their common source.

**Why it matters** An individual pair may look ordinary. Place the masses of many pairs in a histogram and a peak can emerge where many candidates share the same parent mass.

Start with the essentials

- **Focus question**: How can two muon tracks reveal the mass of their common source?
- **One-sentence intuition**: Add the two energies and add the momenta with their directions. Their invariant mass groups candidates from a common parent around the same place in a spectrum.

### Core mathematical model

#### Combined energy and momentum

$$
M^2c^4=(E_1+E_2)^2-c^2\lvert\boldsymbol p_1+\boldsymbol p_2\rvert^2
$$

$M$ is the pair mass, $E_1,E_2$ are the particle energies, and $\boldsymbol p_1,\boldsymbol p_2$ are their momenta. Opposing momenta can cancel even though both energies are positive.

#### Bending across a magnetic field

$$
p_T[\mathrm{GeV}/c]\simeq0.3\left|q/e\right|B[\mathrm T]R[\mathrm m]
$$

At a fixed field, higher-momentum tracks bend less. Raising the field bends a selected pair more tightly while its recorded momenta and mass stay fixed.

### Common difficulties

#### Continuum events also enter the peak region

**Typical misconception** Every pair near the peak must have the same parent.

**Better mental model** A smooth continuum can contribute events at the same mass. Opposite-charge and same-charge histograms show the peak and a control sample separately. The control is not normalized into a background prediction.

#### Cuts change which events remain

**Typical misconception** A higher momentum threshold simply shrinks the whole histogram by one factor.

**Better mental model** Pairs with different masses and directions pass a cut at different rates. Watch both the number of accepted records and the shape as the selection changes.

### Run the experiment

1. 01

   #### Go from a mass bin to its tracks

   Click near the peak, then click far from it.

   **What to observe:** Each click selects a frozen candidate pair. Its record number, mass and tracks update together.

2. 02

   #### Blur the peak

   Compare Mass peak, Blurred peak and Continuum only.

   **What to observe:** A poorer momentum resolution broadens the mass peak. Removing the resonance leaves a smooth continuum. All three presets use labelled simulated records.

3. 03

   #### Select from the same records

   Open Selection and model. Raise the transverse-momentum cut and narrow the pseudorapidity range.

   **What to observe:** Fewer records pass, and each keeps its recorded momenta. Pseudorapidity describes direction relative to the beam; a smaller allowed absolute value keeps more transverse tracks.

4. 04

   #### Compare other event patterns

   Choose Dijet or Photon + jet and open Detector layers and event generation.

   **What to observe:** These presets generate separate teaching events for comparing tracks, calorimeters and penetrating signals. Return to Mass peak to resume the pair analysis.

Physical conclusion

One collision provides tracks; many collisions build a distribution. Energy and momentum connect the two, so a mass peak can be traced back to the candidate records that made it.

## Related experiments and articles

Particles and detectors · Reading path

### Detecting a passing particle

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Blackett and Occhialini let a particle take its own photograph**](https://sandboxphysics.com/stories/particle-evidence/blackett-counter-controlled-cloud-chamber/)
2. [Article **The pion leaves a second track in photographic emulsion**](https://sandboxphysics.com/stories/particle-evidence/powell-pion-emulsion/)
3. [Article **Alvarez’s group finds short-lived particles in combinations of tracks**](https://sandboxphysics.com/stories/particle-evidence/alvarez-resonance-events/)
4. [Article **Charpak turns a particle’s position into an electrical signal**](https://sandboxphysics.com/stories/particle-evidence/charpak-multiwire-chamber/)

Particles and detectors · Reading path

### Finding a new particle

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Two experiments met at the same narrow particle peak**](https://sandboxphysics.com/stories/particle-evidence/november-revolution-jpsi/)
2. [Article **The tau appeared through an electron, a muon and missing energy**](https://sandboxphysics.com/stories/particle-evidence/perl-tau-missing-energy/)

Particles and detectors · Reading path

### Testing the rules of matter

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **W and Z particles emerged from the collider debris**](https://sandboxphysics.com/stories/particle-evidence/ua1-ua2-w-z/)
2. [Article **Two mass peaks brought the Higgs field within reach**](https://sandboxphysics.com/stories/particle-evidence/higgs-discovery-mass/)

2 more groups

Collider physics · Reading path

### Collider physics from events to inference

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Reconstruct a collision and count its rate**](https://sandboxphysics.com/stories/collider-qcd/four-momentum-and-rates/)
2. [Article **Why a proton beam has many collision energies**](https://sandboxphysics.com/stories/collider-qcd/partons-and-factorization/)

Relativity as measurement · Reading path

### Relativity as measurement: clocks, light signals and four-momentum

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Four-momentum and the mass every frame agrees on**](https://sandboxphysics.com/stories/relativity-measurement/four-momentum-and-invariant-mass/)
2. [Lab **Collisions and Invariant Mass** Watch a collision from moving frames](https://sandboxphysics.com/labs/collision-four-momentum/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)