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.

Event topologyOpposite-sign dimuon

Reconstructed tracks0 / 0

Visible energy

E_{\mathrm{vis}}

$0\,\mathrm{GeV}$

Missing momentum

p_T^{\mathrm{miss}}

$0\,\mathrm{GeV}/c$

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.

Opposite chargeSame-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

A packet needs a place to wait

Front-end slotsCPU queue

Calorimeter signals across the recorded feed

Selected channels and decision clocks

Layer / sector	Fine ADC	Coarse ADC	Start / sample / stop ticks	Calibration and timing support

Independent probes reveal the selection

Fixed cohorts; unresolved cases remain in each denominator.

Probe counts and independent exposure

Exposure

Target probe decision

\text{Preparing}

Background probe decision

\text{Preparing}

\text{Preparing}

These empirical fractions describe the predetermined probes before resource competition. They are not probability confidence intervals; only complete output packets count as saved.

Immutable programmes and raw history

Import JSON / CSV

Save a new programme on the same feed. Reset retains eight-record history.

Recorded queue journal

Counter tick	Event	Actual stage / state

Physical and metrology scope

A known exact IP, central-plane trajectories and an ideal finite barrel define this slice. Receiver faces and readout paths use the same radii as the recorded hit model. Material showers, scattering, endcaps and real facility performance are excluded. Coarse and fine ADC channels have independent references; common calibration errors remain correlated.

Programme intervals are actual counter-edge commands. Output budget is rounded to an integer tick-per-byte divisor, so the applied rate can differ from the request. Timing qualification compares small relative spans before formatting UTC. A detector feed archived for teaching is distinct from the simulated saved-output stream. The modeled link encodes detector hits; independent field-condition monitors and calibration records are archived alongside it.

A fixed infinite-mass device receives momentum impulse. Particle deposited and escaping energies have a separate account. The source identity is absent from unknown raw and is never read by decisions.

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 misconceptionEvery pair near the peak must have the same parent.

Better mental modelA 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 misconceptionA higher momentum threshold simply shrinks the whole histogram by one factor.

Better mental modelPairs 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

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.
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.
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.
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.

Read the instrument principle, sources and limits

Focus question: Which losses come from the signature cut, and which come from finite resources?
One-sentence intuition: A threshold accepts an observable pattern. Keeping its complete packet also requires available buffers, processing time and space at the output.

Core mathematical model

Curvature gives a conditional momentum

p_T/(\mathrm{GeV}/c)=0.299792458\,|q/e|\,|B/\mathrm T|\,(R/\mathrm m)

Three calibrated tracking layers and the declared exact IP constrain a circle. The inner/outer layers fit it and the middle layer checks it. Insufficient curvature, ambiguous roads or failed field calibration withhold momentum.

Uncertainty enters the selection

s-3u_s\ge T

The teaching trigger accepts a supported signal above this guard band, rejects one certainly below the threshold, and marks the intervening region unresolved. Each OR branch keeps its independent support.

Wait for the complete packet

t_{\rm done}=t_{\rm start}+N_{\rm bytes}d_{\rm tick/byte}

Both timestamps are actual digital counter edges. An unfinished whole packet keeps its output-buffer space. Work that crosses the observation end stays pending.

Check the complete event account

N_{\rm arrived}=N_{\rm rejected}+N_{\rm veto}+N_{\rm dropped}+N_{\rm pending}+N_{\rm saved}

At a tied tick, existing completions free resources before new arrivals. A copied or still-transmitting packet is not yet saved.

State the reference population

\widehat\epsilon_{\rm probe}=N_{\rm decision}/N_{\rm tagged}

Predetermined tagged cohorts give finite passing fractions before resource competition, with unresolved cases retained in the denominator. They receive no probability confidence interval; queued saved fractions also concern a competing finite set.

Common difficulties

Passing is not complete storage

Typical misconceptionAn HLT accept means the event is already saved.

Better mental modelThe packet still needs output space and transmission time. The final byte must complete within the observation interval.

A tighter cut can release a resource

Typical misconceptionThe final saved set must shrink as a nested subset when a threshold rises.

Better mental modelThe per-event decision is monotone on fixed hits/calibration. Competing packets change the queue, so an event previously blocked can now finish.

Run the experiment

01
Follow the same hits
Inspect Detector, Readout and Trigger views. Change the first-level threshold while keeping a selected event and its ADC table.
What to observe: The raw source stays fixed. Coarse L1 and finer HLT decisions use different readable information.
02
Make a decision too late
Choose Decision arrives late. Compare the retention deadline and L1 decision ticks.
What to observe: A passing signature can be lost before software processing begins.
03
Separate CPU and output losses
Compare CPU queue fills and Output link slows. Inspect the final event states and unsent bytes.
What to observe: Queue drops and in-flight packets are different outcomes; only complete packets reach Saved.
04
Compare independent probes
Inspect the fit, heldout and blind probe groups, then export the selected JSON and CSV. Change live knobs, select an old record and import it again.
What to observe: Threshold selection changes the reference momentum distribution. Rebuilding leaves the archived hits and queue journal unchanged.

Physical conclusion

This mode replays96 immutable surrogate events and independent tagged reference exposures. Central-plane paths use a known IP and hard-edge field. Layer response, missing-hit probabilities and electronics are prescribed teaching models, not real showers or facility performance. Decisions use only ADC, sectors, clocks and independent calibration, with an explicit3-standard-uncertainty veto. Generator identity is excluded. CPU/output scheduling uses integer counter edges; only complete packets are saved and in-flight work remains pending at the observation end. Tagged probes support conditional efficiency; resource-competing saved fractions are finite-set observations. Magnets/absorbers are fixed infinite-mass external momentum reservoirs, not a finite isolated four-vector system. Markers and data pulses are enlarged/slowed. Unsupported curvature, ranges, calibration and ambiguous association withhold dependent inference.

A packet needs a place to wait

Calorimeter signals across the recorded feed

Independent probes reveal the selection

Immutable programmes and raw history

Core mathematical model

Combined energy and momentum

Bending across a magnetic field

Common difficulties

Continuum events also enter the peak region

Cuts change which events remain

Run the experiment

Go from a mass bin to its tracks

Blur the peak

Select from the same records

Compare other event patterns

Core mathematical model

Curvature gives a conditional momentum

Uncertainty enters the selection

Wait for the complete packet

Check the complete event account

State the reference population

Common difficulties

Passing is not complete storage

A tighter cut can release a resource

Run the experiment

Follow the same hits

Make a decision too late

Separate CPU and output losses

Compare independent probes

Related experiments and articles

Articles

Detecting a passing particle

Finding a new particle

Testing the rules of matter

Collider physics from events to inference

How physics instruments measure

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