Skip to main content
Sandbox Physics

Neutrinos · D04 · A planet-sized baseline

Atmospheric Neutrino Zenith Experiment

How can the direction atmospheric neutrinos come from reveal that some change flavor? Direction tells you how far the neutrino has traveled: a short way through the air from straight overhead, the whole Earth from straight below. Compare each direction with what you would expect there without oscillation. A shortfall that depends on both distance and energy points to flavor change; an error in the flux or the detector's acceptance would not produce that pattern.

Follow a neutrino through Earth, collect a sample of events from the whole sky, and compare the counts in each direction with two predictions. Switch energy bands to see which travel distances matter.

Interactive modelAtmospheric Neutrino Zenith Experiment
Travel distance—\text{—}
Muon survival probability—\text{—}
Selected simulated events—\text{—}
Up / down count ratio—\text{—}

A fixed sample of simulated sky events

Where do the events go missing?

Preparing the sky sample…

Upward through Earth

—\text{—}sampled events

No-oscillation prediction —\text{—}

A longer journey

Downward from the nearby atmosphere

—\text{—}sampled events

No-oscillation prediction —\text{—}

A shorter journey

Both directions use four bins, excluding the two nearest the horizon. The two cards share one bar scale.

Select a direction bin to inspect its ray. Use the arrow keys when the chart is focused. The sample stays frozen.

Sampled countsOscillation predictionNo-oscillation prediction

Error bars show the square root of the observed count. They give the size of counting fluctuations; they are not confidence intervals. The predictions use the same source and acceptance that generated the events. The up/down ratio leaves out the two central bins next to the horizon.

Read the ten direction bins

Energy bands use perfect true energy and direction. These simplified muon-flavor event counts omit backgrounds, lepton scattering angles and resolution; they cannot reproduce the experiment’s fitted significance.

Physics tutorial

The source is all around us. The baseline is not.

BackgroundCosmic-ray cascades in the atmosphere produce neutrinos. A detector at the surface receives some that travel a short way down from above and others that travel a long way up through Earth. In 1998, Super-Kamiokande used the shortfall of events in some directions as evidence for oscillation.

Why it mattersA flavor probability is not yet a prediction of how many events you will count. This Lab combines propagation with a stated teaching source spectrum, an exposure and a direction-dependent acceptance, then compares the generated counts with the integrated expectations.

Start with the essentials

Focus question
Does the upward deficit remain when source and acceptance are symmetric between the two hemispheres?
One-sentence intuition
Compare each direction with its own no-oscillation expectation: flux or acceptance alone can make the histogram uneven, but a flavor deficit over long baselines adds its own dependence on energy and direction.

Core mathematical model

Path length from the production shell to the detector

c=cos⁡θzL(c,h)=R2c2+2Rh+h2−Rc\begin{aligned}c&=\cos\theta_z\\L(c,h)&=\sqrt{R^2c^2+2Rh+h^2}-Rc\end{aligned}

The detector sits on the surface of a sphere of radius 6371 km. A positive cosine means the neutrino is going down; a negative one means it is coming up. All neutrinos are produced at one fixed height above the sphere, and the formula comes from intersecting a ray with that shell.

Muon-flavor survival

Pμμ=1−sin⁡2(2θ)sin⁡2ϕϕ=1.266933 Δm2eV2LkmGeVE\begin{aligned}P_{\mu\mu}&=1-\sin^2(2\theta)\sin^2\phi\\\phi&=1.266933\,\frac{\Delta m^2}{\mathrm{eV}^2}\frac{L}{\mathrm{km}}\frac{\mathrm{GeV}}{E}\end{aligned}

This is two-flavor, ultrarelativistic propagation in vacuum. A lower survival probability removes events from this simplified muon-flavor sample; it does not mean that Earth absorbed the neutrinos.

Assumed source and acceptance shapes

f(c)=1+a(1−c2)ϵ(c)=1−b(1−c2)\begin{aligned}f(c)&=1+a(1-c^2)\\\epsilon(c)&=1-b(1-c^2)\end{aligned}

The first factor raises the flux in horizontal directions; the second lowers the acceptance there. Both are the same for upward and downward directions. They are illustrative functions, not a fitted atmospheric flux or a detector calibration.

From spectrum to expected counts

λB=N02I∫Bq dE dcq=E−1.7f(c)ϵ(c)Pμμ\begin{aligned}\lambda_B&=\frac{N_0}{2I}\int_B q\,dE\,dc\\q&=E^{-1.7}f(c)\epsilon(c)P_{\mu\mu}\end{aligned}

Energy enters as its numerical value in GeV and is limited to 1–20 GeV; the normalizing integral in the denominator is the power-law weight integrated over that range. The event weight multiplies a teaching flux with power −2.7 by an interaction weight proportional to energy. The reference exposure is the expected total with no oscillation and both angular adjustments at zero.

Normalization check for the full no-oscillation sample

NnullN0=1+23(a−b)−815ab\frac{N_{\mathrm{null}}}{N_0}=1+\frac{2}{3}(a-b)-\frac{8}{15}ab

Integrating the even angular polynomial gives this independent check on the normalization. A larger acceptance loss lowers the expected total. With both angular adjustments off, the no-oscillation histogram is flat.

Common difficulties

Upward does not mean produced underground

Typical misconceptionThe upward sample comes from a source inside Earth.

Better mental modelThese neutrinos are produced in the atmosphere on the far side of Earth. The arrow points from where they are produced to the same surface detector. Earth only supplies a longer path, not a neutrino source.

A detector measures outgoing particles

Typical misconceptionThe plotted neutrino energy and direction are directly measured without uncertainty.

Better mental modelThis Lab assumes perfect reconstruction. In reality the muon direction differs from that of its parent neutrino, and a real analysis must include energy, efficiency, backgrounds and nuclear interactions. The simplified bins here are not the collaboration’s published bins.

Run the experiment

  1. 01

    Turn a direction into a distance

    Pick Through Earth, Horizon and Overhead in turn. Use Path detail to see the short downward ray.

    What to observe: From overhead, the distance equals the production height. Straight up from below, it adds Earth’s diameter. Even a horizontal path is longer than the height, because Earth is curved.
  2. 02

    Find the upward deficit

    Acquire Oscillating sky. Compare the sampled points with the green prediction and the dashed no-oscillation line.

    What to observe: Both predictions use the same flux, acceptance and exposure, so the gap between them comes from the survival probability. The points scatter because they are a finite sample of events.
  3. 03

    Use energy as a second check

    Select each recorded energy band, then change only the preview energy.

    What to observe: Each band button selects from the same recorded events and integrates both predictions over the same energy range. The preview energy changes only one hypothetical ray. At a given distance, a higher energy changes the oscillation phase.
  4. 04

    Run a control without oscillation

    Try No oscillation, then Uniform control. Change the horizontal flux and acceptance in the advanced controls and acquire again.

    What to observe: The counts can vary with direction even without oscillation. Because the source and acceptance functions are even, the expected up-to-down ratio stays at one when there is no oscillation, but a finite sample need not have equal counts.
  5. 05

    Collect more events and recount them

    Try Long exposure and vary the random seed. Export the record and sum the individual event rows into the ten bins.

    What to observe: Summing the CSV event rows gives back the displayed counts, and each bin also lists its two integrated predictions. A longer exposure shrinks the relative counting fluctuations. This teaching model does not report a discovery significance.

Related experiments and articles

Continue exploring

How flavor change is predicted and tested

Propagation through vacuum and matter predicts a flavor probability. How do solar, atmospheric, reactor and beam experiments test it?

  1. LabNeutrino Flavor PropagationStart with coherent vacuum propagation and ideal flavor trials.
  2. LabNeutrino Matter ResonanceFollow a rotating matter Hamiltonian and compare slow with sudden conversion.
  3. LabSolar Neutrino Flavor ObservatorySeparate electron flavor from total active solar flux with three reaction responses.
  4. You are hereAtmospheric Neutrino Zenith ExperimentTurn Earth-crossing baselines into direction-dependent event counts.
  5. LabReactor Near–Far SpectraFit the same near and far counts while testing calibration and normalization.
  6. LabLong-Baseline CP ObservatoryCompare both accelerator beam polarities on frozen spectra and separate CP phase, matter and response assumptions.

Neutrinos · Reading path

Understand flavor change and mass

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

  1. ArticleHow does the atmosphere make neutrinos all around us?
  2. LabCherenkov Light & Detector Rings
  3. ArticleSuper-Kamiokande: the neutrinos that took the long way
  4. Article2015: how did two very different experiments establish flavor change?
FeedbackSomething broken, confusing, or missing on this page?Tell us
What kind of feedback?

Sent with this page’s address, its Lab ID, the site language and your device type. Please leave out personal details. Feedback is kept for up to 12 months.Privacy policy