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Sandbox Physics

Neutrinos · D03 · SNO and the missing flavors

Solar Neutrino Flavor Observatory

Look inside a heavy-water detector. Replay three reaction channels, acquire a simulated exposure, then intersect their flux constraints. Can a weaker electron-only Sun explain the same record?

Interactive modelSolar Neutrino Flavor Observatory
Inferred electron flux—\text{—}
Inferred other active flux—\text{—}
Inferred total flux—\text{—}

THREE RESPONSES · ONE FROZEN EXPOSURE

The missing flavor leaves a fingerprint.

CC

Charged current

Electron flavor only

νe+d→p+p+e−\nu_e+d\to p+p+e^-
Recorded count—\text{—}
Inspected prediction, including background—\text{—}
NC

Neutral current

All active flavors

να+d→p+n+να\nu_\alpha+d\to p+n+\nu_\alpha
Recorded count—\text{—}
Inspected prediction, including background—\text{—}
ES

Elastic scattering

A weighted flavor mixture

να+e−→να+e−\nu_\alpha+e^-\to\nu_\alpha+e^-
Recorded count—\text{—}
Inspected prediction, including background—\text{—}

Solid bars are observed counts; thin bars are predictions at the inspected flux point. Every channel shares one count scale. Channel labels are ideal here; real SNO extracted overlapping populations with a joint statistical analysis.

Let the channel constraints intersect

Click a flux point, or use arrow keys on the chart. Shading shows one counting-fluctuation scale for each selected channel.

Both axes use 106 cm−2 s−110^6\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}

CCNCESBest fit
Inspected flux point—\text{—}
Response matrix, exact counts & optical hits

Counts per unit exposure and flux. The rows correspond to CC, NC and ES; backgrounds per exposure are shown separately. These are teaching coefficients, not measured SNO efficiencies.

A=(3000100100609.24),B=bT(20358)A=\begin{pmatrix}300&0\\100&100\\60&9.24\end{pmatrix},\qquad B=bT\begin{pmatrix}20\\35\\8\end{pmatrix}

Compare with the historical result

SNO’s 2002 paper reported electron and total active fluxes, under its stated boron-8 spectrum assumption. These published values are a separate reference; this simulator neither fits them nor reproduces the collaboration’s analysis.

Φe=1.76±0.05 (stat.)±0.09 (syst.)ΦNC=5.09−0.43+0.44 (stat.)−0.43+0.46 (syst.)\begin{aligned}\Phi_e&=1.76\pm0.05\,\mathrm{(stat.)}\pm0.09\,\mathrm{(syst.)}\\\Phi_{\mathrm{NC}}&=5.09^{+0.44}_{-0.43}\,\mathrm{(stat.)}^{+0.46}_{-0.43}\,\mathrm{(syst.)}\end{aligned}

106 cm−2 s−110^6\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}

SNO · 2002 original paper ↗

CONTINUE EXPLORING

From flavor to evidence

Propagation predicts a flavor probability. Which parts of the experiment turn an interaction into a usable record?

Physics tutorial

One source. Three different questions.

BackgroundRadiochemical experiments found too few solar electron neutrinos. SNO used heavy water to ask an additional question: how many active neutrinos arrived, regardless of flavor? Comparing charged-current, neutral-current and elastic-scattering responses separated a faint source from a change of flavor.

Why it mattersThis Lab makes the inference visible. Each channel defines a band in a two-dimensional flux plane. A single electron-sensitive rate cannot separate a weaker source from transformation; different sensitivities can.

Start with the essentials

Focus question
Can the same electron-channel count come from two Suns with different total active fluxes?
One-sentence intuition
The neutral-current rate counts active flavors together. A low electron-flavor rate need not imply a low total active flux.

Core mathematical model

Two flux components

Φx=Φμ+Φτ,Φ=Φe+Φx\Phi_x=\Phi_\mu+\Phi_\tau,\qquad\Phi=\Phi_e+\Phi_x

The second component contains the other two active flavors. This model cannot distinguish muon from tau flavor, and does not include sterile states.

Three ideal channel responses

λCC=300TΦe+20bTλNC=100T(Φe+Φx)+35bTλES=60T(Φe+0.154Φx)+8bT\begin{aligned}\lambda_{\mathrm{CC}}&=300T\Phi_e+20bT\\\lambda_{\mathrm{NC}}&=100T(\Phi_e+\Phi_x)+35bT\\\lambda_{\mathrm{ES}}&=60T(\Phi_e+0.154\Phi_x)+8bT\end{aligned}

Flux is numerical in millions per square centimeter per second; exposure is relative. The coefficients and known backgrounds are teaching choices. The fixed scattering weight illustrates a spectrum-dependent response, not a universal ratio.

A frozen counting record

Ni∼Poisson⁡(λi)N_i\sim\operatorname{Poisson}(\lambda_i)

Counts are independently sampled for three ideally distinguished channels. Real SNO fitted overlapping event populations and correlated uncertainties. No optical example is used to tag these aggregate counts.

Fit only the selected responses

Q=∑i∈S[Ni−Bi−T(AΦ)i]2max⁡(Ni,1)Q=\sum_{i\in\mathcal S}\frac{[N_i-B_i-T(A\boldsymbol\Phi)_i]^2}{\max(N_i,1)}

Unconstrained weighted least squares uses the observed count as a variance estimate, bounded below by one. Its local covariance and residual scores describe this approximation; neither is a calibrated confidence region or significance.

Photons reach the displayed sensor sphere

tj=n ∣rj−rv∣ct_j=\frac{n\,|\mathbf r_j-\mathbf r_v|}{c}

All scene rays end at their stored sensor coordinates, 9 meters from the center. Time starts at effective electron light emission, with water index 1.33. Refraction at acrylic, dispersion, scattering and neutron capture delay are omitted.

Common difficulties

A neutral-current flash is not a direct neutrino image

Typical misconceptionA neutron emits the light shown in the NC scene.

Better mental modelThe released neutron is captured; resulting gamma rays scatter electrons, which emit Cherenkov light. This direction-averaged illustration begins at that effective emission point and omits capture delay and diffusion.

A negative fit is an approximation warning

Typical misconceptionA negative other-flavor estimate is a physical negative flux.

Better mental modelThe fit is deliberately unconstrained. Near zero, counting fluctuations can move its estimate outside the physical region. A physical inference requires a boundary treatment, which this Lab does not supply.

Run the experiment

  1. 01

    Compare the reactions

    Select CC, NC and ES above the detector. Scrub the light-flight timeline and inspect the side and interaction views.

    What to observe: CC and ES show broadened electron cones. NC displays a direction-averaged capture flash: neutrons are neutral and are not the particles emitting Cherenkov light.
  2. 02

    Make two similar electron counts

    Acquire Faint Sun, then Changed flavors. Compare CC and NC using the common count scale.

    What to observe: The electron component is the same in those two presets. The larger active total raises NC counts; the simulation does not dim a source simply because electron flavor is depleted.
  3. 03

    Remove information

    Turn off NC, then ES. Keep only CC in the fit, then restore a second channel.

    What to observe: One rate constrains a line, not a unique point. CC plus ES can separate components but gives a larger other-flavor error than CC plus NC for this declared response.
  4. 04

    Inspect an electron-only explanation

    Inspect the best electron-only hypothesis and compare its predicted bars with the recorded counts.

    What to observe: That hypothesis is separately optimized on the selected channels. When the record requires another active component, fitting one channel alone cannot satisfy the others.
  5. 05

    Separate truth from inference

    Reveal the simulated source, vary the seed, and acquire a long exposure. Export the CSV.

    What to observe: The truth marker is independent of the fit. Counts fluctuate, so the best fit need not hit the source exactly. Every displayed count, response, illustrative hit and sensor coordinate is exported.