Explanation
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Prologue 1 · Scale: a galaxy

From a Black Hole to the Bottom of the Sea

The full life of one neutrino: born beside a supermassive black hole, eight billion years in flight, through the Earth, and into the ocean at P-ONE.

A neutrino is a tiny particle. Trillions pass through you every second, and you never feel them.

This is the story of one neutrino. It starts in a faraway galaxy. Let's zoom in to its middle.

Far beyond the Milky Way is a spiral galaxy like Messier 77 (also called NGC 1068), about 100,000 light-years across. Tightly wound arms of stars, edged with dark lanes of dust and dotted with pink clouds where new stars are forming, circle a compact, unusually bright centre.

To see what powers it, we zoom in tens of millions of times, from the whole galaxy to a region about half a light-day across.

In detail

The galaxy is modelled on NGC 1068, a well-studied nearby active galaxy.

  • Real distance: about 14 Mpc (≈ 47 million light-years). Here it is moved to redshift z ≈ 1, so the trip is cosmological (Prologue 7).
  • Type: Seyfert 2. We see its nucleus through a dusty torus.
  • That torus is Compton-thick: gas columns up to ~\(10^{25}\ \mathrm{cm^{-2}}\) block even X-rays. The corona is studied through reflected and hard X-rays.

Sources: Bauer et al. 2015; IceCube 2022.

Scroll to zoom in to its centre

Prologue 2 · Scale: light-hours

The engine at the centre

In the middle is a giant black hole. It pulls in gas, and the gas glows.

Above it floats very hot gas. Scientists think places like this make many neutrinos.

At the galaxy's heart, gas spirals into a black hole about ten million times heavier than the Sun. On the way in it forms a glowing accretion disc. Just above the inner disc sits a corona: thin gas at about a billion degrees, a few light-hours across, that shines brightly in X-rays.

A galaxy with a core like this is called an active galaxy, or active galactic nucleus (AGN). AGN are now the leading candidates for the sources of the high-energy neutrinos that IceCube sees. This one is modelled on the nearby active galaxy NGC 1068, which gives the strongest evidence so far for any single neutrino source.

In detail

The numbers behind the engine.

  • Black hole mass \(M \approx 10^7\,M_\odot\).

\(R_S = 2GM/c^2 \approx 3 \times 10^{10}\ \mathrm{m} \approx 100\) light-seconds

  • So a corona a few light-hours across is tens of \(R_S\) in size.
  • Its electrons are at \(kT_e \sim 100\) keV (~\(10^9\) K). They make X-rays by inverse-Compton scattering UV light from the disc.
  • IceCube saw about 79 neutrinos from NGC 1068, at 4.2σ, with a spectrum \(\propto E^{-3.2}\) between ~1.5 and 15 TeV.

Sources: IceCube 2022; Murase, Kimura & Mészáros 2020.

Prologue 3 · Scale: light-hours

A cosmic particle accelerator

Magnetic fields in the hot gas push protons around. Protons are tiny bits of atoms.

Over many pushes, a proton speeds up. Some end up incredibly fast.

The corona's magnetic field is turbulent, and its tangles move. A proton that meets one head-on bounces off with a little more energy; one that catches a tangle from behind loses a little. Head-on meetings are slightly more common, so on average the proton gains. This is stochastic (second-order Fermi) acceleration.

In models of coronae like NGC 1068's, protons reach around a PeV, and several PeV in the most favourable cases, before they escape or lose energy. Our neutrino needs one of these most energetic protons. Shocks and magnetic reconnection are other proposed accelerators.

In detail

Why protons gain energy on average (Fermi's idea).

  • Each bounce off a moving magnetic tangle (speed \(V\)) changes the energy by about \(\pm V/c\).
  • Head-on bounces are slightly more common, by a fraction ~\(V/c\).

\(\langle \Delta E/E \rangle \sim (V/c)^2\)

That is why it is called second-order. The gain stops when the fastest energy loss wins. In corona models that is usually Bethe–Heitler pair production, \(p\gamma \to p\,e^+e^-\).

Sources: Fermi 1949; Murase, Kimura & Mészáros 2020.

Sources: Murase, Kimura & Mészáros 2020; Kheirandish, Murase & Kimura 2021.

The panel follows one proton. Higher means faster.

The panel follows one proton. Its height is its energy, on a scale where each step up is a thousandfold. Filled dots are kicks that speed it up, hollow ones kicks that slow it down. Getting from 1 GeV to a few PeV, a millionfold rise, takes a great many of them; only a few are drawn.

Prologue 4 · Scale: light-hours

Making the neutrino

A fast proton hits a bit of light. The crash makes a new particle, called a pion.

The pion soon breaks apart. One of the pieces is our neutrino.

Neutrinos fly out in every direction. We follow just one.

The core is flooded with ultraviolet light from the disc and X-rays from the corona. A fast proton that hits one of these photons hard enough excites the \(\Delta^+\) resonance, which at once decays into a pion:

\(p + \gamma \to \Delta^+ \to n + \pi^+\) (≈ 1/3)  or  \(p + \pi^0\) (≈ 2/3)

"Hard enough" means a photon energy of at least about \(0.16\ \mathrm{GeV^2}/E_p\) in a head-on collision. For a 5 PeV proton that is about 30 eV, far ultraviolet; slower protons need X-rays.

In detail

When is a collision hard enough to make a pion?

\(E_p\,\varepsilon\,(1 - \cos\theta) \ge \tfrac12 m_\pi(2m_p + m_\pi)\)

  • \(E_p\): proton energy. \(\varepsilon\): photon energy. \(\theta\): angle between them.
  • Head-on, this threshold is \(E_p\varepsilon \approx 0.07\ \mathrm{GeV^2}\).
  • The \(\Delta(1232)\) peak needs \(E_p\varepsilon \approx 0.16\ \mathrm{GeV^2}\): a 0.34 GeV photon in the proton's frame.
  • The 1/3 : 2/3 split is the isospin Clebsch–Gordan ratio for \(\Delta^+\).
  • Each interaction takes about 20% of the proton's energy.

Sources: Kelner & Aharonian 2008; Particle Data Group 2022.

The \(\pi^+\) lives 26 ns in its own frame. At about 1 PeV, time dilation stretches that to about 0.2 s, some 50,000 km, still deep inside the corona. Then:

\(\pi^+ \to \mu^+ + \nu_\mu\)  ·  \(\mu^+ \to e^+ + \nu_e + \bar\nu_\mu\)

Our neutrino is the \(\nu_\mu\) from the pion's decay. The pion carries about a fifth of the proton's energy and the neutrino about a fifth of the pion's, so a 5 PeV proton gives a neutrino of about 200 TeV. The corona sends neutrinos like it out in every direction, and from here on we follow just one of them.

In detail

How the energy is shared, and what could change the flavour mix.

  • The \(\nu_\mu\) takes on average \((1 - m_\mu^2/m_\pi^2)/2 \approx 21\%\) of the pion's energy.
  • The three leptons from the muon share the rest roughly equally.
  • The muon lives ~100 times longer than the pion (\(c\tau\) = 659 m vs 7.8 m).
  • In strong magnetic fields it can lose energy before decaying. The source mix is then 0 : 1 : 0 instead of 1 : 2 : 0 (Prologue 5).

Sources: Kelner & Aharonian 2008; Particle Data Group 2022.

The \(\pi^0\) decays at once into two gamma rays. In the dense X-ray light around the core, most of them turn into electron–positron pairs (\(\gamma\gamma \to e^+e^-\)) before they can escape. That is why NGC 1068 is at least ten times brighter in TeV neutrinos than its TeV gamma rays could be.

Which sources make most of the neutrinos is still an open question. 200 TeV is at the upper end of what coronae are expected to reach: NGC 1068's neutrinos have a few TeV. Above about 1 PeV, AGN with jets may matter more. One such galaxy, the blazar TXS 0506+056, gave the first neutrino traced to a likely source, at about 290 TeV in 2017. Gamma-ray-bright blazars like it can make at most about 16% of the total.

Sources: photomeson production and its energy shares, Kelner & Aharonian 2008; particle lifetimes and the \(\Delta^+\), Particle Data Group 2022; NGC 1068, IceCube 2022.

Prologue 5 · Quantum mechanics

Changing flavour on the way

Neutrinos come in three kinds: electron, muon and tau.

As a neutrino travels, it keeps switching between kinds. By the time it reaches Earth, it could turn up as any of the three.

Each neutrino flavour (\(e\), \(\mu\), \(\tau\)) is a blend of three slightly different masses, so as it travels, the chance of finding each flavour swings back and forth. This is neutrino oscillation.

In detail

Over such long distances, the oscillations average out.

\(L_\mathrm{osc} = 4\pi E/\Delta m^2\)

  • At 200 TeV: 1.3 AU for \(|\Delta m^2_{31}| \approx 2.5 \times 10^{-3}\ \mathrm{eV^2}\).
  • And 45 AU for \(\Delta m^2_{21} \approx 7.4 \times 10^{-5}\ \mathrm{eV^2}\).

Gigaparsecs are far longer, so only the average survives:

\(P_{\alpha\beta} = \sum_i |U_{\alpha i}|^2\, |U_{\beta i}|^2\)

A muon-damped source (0 : 1 : 0, Prologue 4) gives the born-as-\(\nu_\mu\) row. So the flavour mix at Earth tells us about the source.

Sources: NuFIT 5.0, Esteban et al. 2020.

The swings soon blur into a steady mix. Switch the flavour at the top to change what the neutrino is born as: born as \(\nu_\mu\) (like ours, from pion decay), it ends up about 17% \(\nu_e\), 45% \(\nu_\mu\) and 38% \(\nu_\tau\).born as \(\nu_e\) (as from muon decay), it ends up about 55% \(\nu_e\), 17% \(\nu_\mu\) and 28% \(\nu_\tau\).born as \(\nu_\tau\) (which this kind of source hardly makes), it ends up about 28% \(\nu_e\), 38% \(\nu_\mu\) and 34% \(\nu_\tau\).

Each pion decay makes three neutrinos (as in Prologue 4): two of muon flavour and one of electron flavour. Add up their mixes and the neutrinos reaching Earth are roughly a third of each flavour:

Prologue 6 · Scale: a galaxy

Straight out of its galaxy

A neutrino has no charge, so magnetic fields cannot bend it, and almost nothing absorbs it.

Our neutrino was made beside the black hole, when a very fast proton crashed into light. Now it heads out of its galaxy.

Other particles from space get bent or blocked on the way. Neutrinos don't. So a neutrino points straight back home.

Charged cosmic rays from the same source spiral along magnetic fields and arrive from random directions. Gamma rays that escape the core travel straight too, but on the way they can be absorbed through interactions with intervening matter or with background radiation, such as the faint light that fills the space between galaxies. How likely that is depends on the photon's energy and on what it meets; at the highest energies, over distances like this one, most do not make it. Only the neutrino reliably keeps pointing straight back to where it was made.

In detail

Why only neutrinos point back.

  • Protons bend. At 10 PeV in a 1 μG field, \(r_L = E/ZeBc \approx 10\) pc, far smaller than a galaxy.
  • Gamma rays are absorbed. From z ~ 1, above ~100 GeV, by pair production (\(\gamma\gamma \to e^+e^-\)) on extragalactic background light. Above a few hundred TeV, on the CMB too.
  • Neutrinos pass. The intergalactic column is only ~\(10^{21}\) nucleons cm⁻², so the chance of interacting is ~\(10^{-13}\).

Sources: Franceschini, Rodighiero & Vaccari 2008.

Prologue 7 · Scale: the universe

Eight billion years in flight

Most high-energy neutrinos reaching Earth probably set off billions of years ago, when black holes were growing and stars forming fastest. This one travels for about 7.9 billion years.

Our neutrino has been travelling for about 7.9 billion years. When it set off, the Earth didn't exist yet.

Space has been stretching all that time. The stretch takes away half of the neutrino's energy.

The Sun and Earth form 4.6 billion years ago, when it is already more than 40% of the way here. Meanwhile the universe expands and stretches the neutrino like light, so it arrives with half its birth energy, about 100 TeV (redshift z ≈ 1.0). Its home galaxy is now about 11 billion light-years away.

Neutrinos have a tiny mass, under 0.45 eV, so it moves at almost exactly c. After the whole trip it trails light by at most about 1 picosecond. The stretching does not change the flavour averages.

In detail

The cosmology behind the numbers.

  • Planck 2018 ΛCDM: \(H_0 = 67.4\ \mathrm{km\,s^{-1}\,Mpc^{-1}}\), \(\Omega_m = 0.315\).
  • At z = 1: lookback time ≈ 7.9 Gyr, comoving distance ≈ 3.4 Gpc.
  • Energy redshifts as \(E_0 = E/(1+z)\): 200 TeV becomes 100 TeV.

A neutrino of mass \(m\) arrives late by:

\(\Delta t = \dfrac{m^2}{2E_0^2}\displaystyle\int_0^z \frac{dz'}{(1+z')^2\,H(z')}\)

KATRIN's limit, \(m < 0.45\) eV (90% CL), keeps that delay to about a picosecond.

Sources: Planck 2018; KATRIN 2025.

Prologue 8 · Scale: the Solar System

Arriving at the Solar System

It crosses the Milky Way, about 100,000 light-years across, in the last few thousandths of its trip. The Sun sits about 26,000 light-years from the centre.

It crosses our own galaxy, the Milky Way, near the very end of its trip.

It passes the Sun's neutrinos too. About 60 billion of them go through your fingernail every second.

From Neptune's orbit to the Earth takes about four hours. On the way it passes through a constant stream from the Sun: about 60 billion solar neutrinos cross every square centimetre at Earth each second.

In detail

Solar neutrinos are no problem. Atmospheric ones are.

  • Solar neutrinos are mostly below 0.42 MeV: eight orders of magnitude below this one.
  • Atmospheric neutrinos come from cosmic-ray air showers. Their spectrum falls roughly as \(E^{-3.7}\).
  • The astrophysical flux falls more slowly: about \(E^{-2.4}\) (IceCube: 2.37 ± 0.09).
  • So astrophysical neutrinos win above roughly 100 TeV.

Sources: IceCube 2022 (ApJ 928, 50); IceCube 2013.

Prologue 9 · Scale: the Earth

Straight through the Earth

Next it goes straight through the Earth. That takes about a fiftieth of a second.

Almost nothing else can do that. So anything coming up from below is almost surely a neutrino.

It arrives from 30° below the horizon. It enters the seafloor of the South Pacific near 12° S and crosses about 6,400 km of rock, dipping 850 km into the mantle, in 21 milliseconds.

At 100 TeV, about two in three neutrinos survive this path. Straight up through the core, fewer than one in five would.

In detail

How likely it is to make it through the Earth.

  • Path length: \(2R_\oplus \sin 30^\circ = R_\oplus \approx 6{,}400\) km.
  • Deepest point: \(R_\oplus(1 - \cos 30^\circ) \approx 850\) km down.

The chance of getting through is:

\(P = \exp(-N_A\, \sigma\, X)\)

  • \(X \approx 2.3 \times 10^9\ \mathrm{g\,cm^{-2}}\): the rock along the path (mean density ≈ 3.6 g cm⁻³).
  • \(\sigma \approx 3 \times 10^{-34}\ \mathrm{cm^2}\): the neutrino–nucleon cross-section at 100 TeV (CC + NC).
  • \(N_A = 6.02 \times 10^{23}\): nucleons per gram.

Result: \(e^{-0.42} \approx 0.66\), about two in three. Neutral-current hits only lower the energy. \(\nu_\tau\) regenerate (\(\nu_\tau \to \tau \to \nu_\tau\)) at lower energy.

Sources: Gandhi et al. 1998; Cooper-Sarkar, Mertsch & Sarkar 2011.

Coming up through the Earth is what makes it stand out: almost nothing else can cross the planet, so a particle arriving from below points to a neutrino.

Prologue 10 · Scale: 12,700 km → 3 km

Down to the seafloor

Now we zoom in from the whole Earth to the sea floor.

Next to the whole planet, the ocean is thinner than an apple's skin. At the bottom stands P-ONE, a planned neutrino detector.

The view zooms in about 4,000 times, from the whole planet to a slice of ocean a few kilometres across. The curve of the Earth flattens out as we go.

Seen to scale, the ocean is a thin film: 2.66 km of water on a planet 6,371 km in radius. Only at the end does it fill the view, with P-ONE's lines standing on the floor of the Cascadia Basin.

In detail

The site.

  • P-ONE plugs into Ocean Networks Canada's NEPTUNE observatory for power and data.
  • Its pathfinder, STRAW, measured how far light gets in the water: an attenuation length of about 28 m at 450 nm.
  • Unlike ice, seawater glows faintly on its own, from \(^{40}\)K decays and bioluminescence.

Sources: Agostini et al. 2020; Bailly et al. 2021.

Prologue 11 · Scale: the ocean floor

Into the ocean at P-ONE

It enters the water among P-ONE's sensors.

Almost every neutrino passes straight through. This one hits something.

Next, we zoom in on that crash.

It leaves the rock beneath the Cascadia Basin, off the west coast of Vancouver Island, and enters the water 2,660 m below the surface, among P-ONE's lines. Of all the neutrinos crossing P-ONE, only a tiny fraction interacts. This one does.

In detail

Why neutrino telescopes are so big.

\(\lambda_\mathrm{int} = 1/(N_A\, \rho\, \sigma) \approx 60{,}000\) km

  • That is in water, at 100 TeV.
  • So crossing 1 km of water, the chance of an interaction is ~\(2 \times 10^{-5}\).
  • The flux is small too: \(E^2\Phi \sim 10^{-8}\ \mathrm{GeV\,cm^{-2}\,s^{-1}\,sr^{-1}}\) per flavour near 100 TeV.
  • Together, that means a cubic kilometre or more.

Sources: Gandhi et al. 1998; IceCube 2013.

Next, the story zooms in on a single interaction. To keep one complete ring of light on screen, the close-up uses a lower-energy neutrino (about 1 GeV) and a conceptual wall of light sensors. The physics is the same. The full-scale version plays out in the P-ONE model at the end.

Keep scrolling to zoom into the water

01 · Scale: metres

Anatomy of a Muon Ring Anatomy of an Electron Ring Anatomy of a Tau Event

Now the interaction itself, step by step, from the invisible arrival to the light it leaves behind. Switch flavour at the top to compare.

A neutrino is passing through the deep water.

It's invisible. The dashed line shows its path.

A muon neutrino (\(\nu_\mu\)) carrying about 1 GeV is crossing the deep water near P-ONE.

An electron neutrino (\(\nu_e\)) carrying about 1 GeV is crossing the deep water near P-ONE.

A tau neutrino (\(\nu_\tau\)) carrying about 6.4 GeV is crossing the deep water near P-ONE. It needs at least 3.5 GeV to create a tau lepton, which is about 3,500 times heavier than an electron.

It has no electric charge and feels only the weak force, so it ionises nothing and gives off no light. The dashed line is a path inferred afterwards. No instrument sees the neutrino itself.

In detail

How rare an interaction is at these energies.

  • At a few GeV the cross-section is ~\(10^{-38}\ \mathrm{cm^2}\) per nucleon.
  • It is a mix of quasi-elastic scattering, resonant pion production and the start of deep inelastic scattering.
  • Mean free path in water: ~\(10^{14}\) cm, about ten astronomical units.
  • Tau threshold on a neutron at rest: \(E_\nu > [(m_\tau + m_p)^2 - m_n^2]/2m_n \approx 3.45\) GeV.

Sources: Particle Data Group 2022.

Keep scrolling: next comes a long zoom (about three screens) from the water down to a single molecule

02 · Zooming in · 1 of 3

How small can we go?

×1magnified so far, on the way to ×1010

×1010 means ten billion times: a 1 with ten zeros after it.

Every few scrolls the view shrinks tenfold. Within one screen of scrolling you go from the length of your arm to the width of a single molecule.

The water isn't empty. Each power of ten reveals a crowd you could never see: fish, plankton, bacteria, viruses, all drawn at their true size (just far more crowded than real seawater). Hover over any of them to find out what it is.

Watch the neutrino's arrow: it never moves. Everything else is shrinking past it.

02 · Scale: picometres · 2 of 3

One water molecule

Here is one water molecule: one oxygen atom and two hydrogen atoms.

Here it is: H₂O. One oxygen atom holding two hydrogen atoms, 95.8 pm apart at an angle of 104.5°.

The clouds are its electrons. Almost all of an atom is empty space: if this molecule were the size of a stadium, each nucleus would be a pea at its centre.

A litre of water holds about 3 × 1025 of these molecules. The neutrino is heading for just one of them.

A litre of water holds about 30 million billion billion of these molecules. The neutrino is heading for just one of them.

In detail

What a passing particle actually tugs on.

  • O–H bond: 95.8 pm. H–O–H angle: 104.5°, nearly tetrahedral because of oxygen's two lone pairs.
  • Dipole moment: 1.85 D. This is what a passing charge polarises in section 06.

02 · Scale: femtometres · 3 of 3

Into the nucleus

Now we zoom into the middle of the oxygen atom. It holds 8 protons and 8 neutrons.

The neutrino needs a neutron. Hydrogen has none, so it's oxygen.

Another hundred-thousandfold zoom, to the oxygen-16 nucleus: 8 protons and 8 neutrons packed into about 5 fm.

Why oxygen and not hydrogen? Each hydrogen nucleus is a lone proton. The simplest charged-current reaction for a neutrino needs a neutron to turn into a proton, and only the oxygen has them.

Almost every neutrino crosses the whole tank, and the Earth, without touching anything. This one comes within range of a neutron.

In detail

The target is a neutron inside a nucleus, and that matters.

  • Fermi motion: \(k_F \approx 225\) MeV/c in \(^{16}\)O.
  • Binding energy: about 25 MeV.
  • Also: Pauli blocking, multi-nucleon (2p2h) channels, final-state interactions.
  • These nuclear effects are among the largest uncertainties in GeV neutrino experiments.
  • Hydrogen still plays a part: \(\nu_\mu p \to \mu^- p\,\pi^+\), and for antineutrinos \(\bar\nu_\mu p \to \mu^+ n\).

Sources: Particle Data Group 2022.

03 · Weak interaction

A W boson changes the neutron

The crash

The neutrino swaps a tiny particle, a W boson, with a neutron.

The neutrino becomes a muonelectrontau. The neutron becomes a proton.

The neutrino exchanges a \(W^+\) boson with a down quark. The neutrino becomes a negatively charged muonelectrontau lepton, and the down quark becomes an up quark: the neutron (udd) is now a proton (uud).

\(\nu_\mu + n \to \mu^- + p\)\(\nu_e + n \to e^- + p\)\(\nu_\tau + n \to \tau^- + p\)

Charge balances: 0 + 0 = (−1) + (+1). The charged lepton always matches the neutrino's flavour, which is how a detector can tell which flavour arrived.

The W is drawn hugely enlarged. It exists so briefly that its range is about 0.002 fm, roughly 1/400 of a proton's width.

In detail

Why the weak force is weak at these energies.

  • The W's range is \(\hbar/M_W c \approx 2.5 \times 10^{-3}\) fm.

At \(Q^2 \ll M_W^2\) the exchange shrinks to a contact interaction:

\(G_F/\sqrt2 = g^2/8M_W^2, \quad G_F = 1.166 \times 10^{-5}\ \mathrm{GeV^{-2}}\)

  • The amplitude carries a factor \(V_{ud} \approx 0.974\).
  • Quasi-elastic scattering uses vector form factors from electron scattering (CVC) and an axial form factor, usually a dipole with \(M_A \approx 1\) GeV.

Sources: Llewellyn Smith 1972; Particle Data Group 2022.

04 · Final state

The lepton and the hadronic debris

What comes out

Out shoots a muonelectrontau, almost as fast as light.

A proton gets knocked to the side.

The muon takes most of the energy, 800 MeV of motion, and carries on in the neutrino's direction. The new proton recoils at a wide angle, balanced by the neutron's own motion inside the nucleus, with only about 20 MeV, and may jostle other nucleons on its way out.

The electron takes most of the energy, about 800 MeV, and carries on in the neutrino's direction. The new proton recoils at a wide angle, balanced by the neutron's own motion inside the nucleus, with only about 20 MeV, and may jostle other nucleons on its way out.

The tau takes about 6 GeV and carries on in the neutrino's direction. The proton recoils harder than in the other flavours, with about 300 MeV. At this energy the debris is often a spray of pions instead (deep inelastic scattering); the simplest channel is shown.

The nucleus left behind is oxygen-15 in an excited state. It can relax by emitting a gamma ray of about 6 MeV.

Speeds are to scale here: the muon moves at 0.993 c, about five times faster than the proton.

Speeds are to scale here: the electron moves at 0.9999998 c, about five times faster than the proton.

Speeds are to scale here: the tau moves at 0.955 c and the proton at 0.65 c.

In detail

Working out the neutrino's energy from the lepton alone.

Treat the target as a neutron at rest with binding energy \(E_b\), and write \(M = m_n - E_b\):

\(E_\nu = \dfrac{2ME_\ell - (M^2 + m_\ell^2 - m_p^2)}{2(M - E_\ell + p_\ell\cos\theta_\ell)}\)

  • \(E_\ell, p_\ell, \theta_\ell\): the lepton's energy, momentum and angle to the beam.
  • Water Cherenkov experiments use this for quasi-elastic events.
  • The leftover \(^{15}\)O has a hole in its \(p_{3/2}\) shell, and de-excites with a 6.18 MeV gamma ray.

Sources: Particle Data Group 2022.

Keep scrolling: the view now zooms back out, about \(10^{15}\) times, following the lepton from the nucleus to metres of water

Keep scrolling: now we zoom back out

05 · Scale: metres

Faster than light, in water

Light is slower in water than in space. The muon is faster than that.

So the muon outruns light in water. That's allowed!

Back at detector scale. Water's refractive index is n ≈ 1.33, so light in water travels at c/n, about 0.75 c. The muon moves at 0.993 c.

That breaks no law. The muon is slower than light in a vacuum, but faster than light in this medium.

The proton stops within about a centimetre and stays dark. To radiate it would need a momentum above 1.07 GeV/c.

In detail

Who is fast enough to glow.

\(\beta > 1/n \iff \gamma > n/\sqrt{n^2 - 1} \approx 1.52\)

  • Muon: kinetic energy above 54 MeV.
  • Electron: above 0.26 MeV.
  • Proton: momentum above \(m_p/\sqrt{n^2 - 1} \approx 1.07\) GeV/c, so this one stays dark.
  • The 800 MeV muon loses about 2 MeV cm⁻¹ (Bethe–Bloch).

Sources: Particle Data Group 2022.

An electron starts a shower

Light is slower in water than in space. The electron is faster than that, so it glows.

The electron soon splits its energy into more particles. They split again. This makes a shower.

Back at detector scale. Light in water travels at about 0.75 c, and the electron moves at 0.9999998 c, so it radiates at once.

But an electron is 200 times lighter than a muon, and nuclei deflect it easily. Within about 36 cm (one radiation length) it typically loses much of its energy to bremsstrahlung photons. Those photons turn into electron–positron pairs, which radiate again: an electromagnetic shower.

In detail

How big the shower is in water.

  • Radiation length \(X_0 = 36.1\) cm.
  • A photon converts after \(9X_0/7 \approx 46\) cm on average.
  • Critical energy \(E_c \approx 80\) MeV.
  • Peak: \(t_\mathrm{max} \approx \ln(E/E_c) - 0.5 \approx 1.8\,X_0\), about 65 cm in.
  • Width: Molière radius \(R_M \approx (21\ \mathrm{MeV}/E_c)\,X_0 \approx 10\) cm.

Sources: Particle Data Group 2022.

The tau decays almost at once

The tau breaks apart almost at once, too fast to see.

It breaks into a pion, some gamma rays, and a new neutrino.

Back at detector scale. The tau lives only 290 femtoseconds. Even at 0.955 c and with time dilation (\(\gamma \approx 3.4\)), it travels about 0.28 mm before decaying, far too short to see here.

About two thirds of tau decays produce hadrons. This one is the most common single mode (about 25%): \(\tau^- \to \pi^- \pi^0 \nu_\tau\). The \(\pi^0\) decays at once into two gamma rays.

The proton travels about 50 cm and stays dark, below its 1.07 GeV/c threshold.

In detail

Why the tau is gone within a millimetre.

\(\gamma\beta c\tau = 3.38 \times 0.955 \times 87.0\ \mu\mathrm{m} \approx 0.28\ \mathrm{mm}\)

  • \(\tau^- \to \pi^-\pi^0\nu_\tau\) goes mostly through the \(\rho^-(770)\).
  • The tau is the only lepton heavy enough to decay into hadrons.
  • The \(\pi^0\) decays to \(\gamma\gamma\) 98.8% of the time, after \(c\tau = 25\) nm.

Sources: Particle Data Group 2022.

To fit a whole ring on screen, a conceptual sensor wall now stands 5.5 m away: an imaginary surface of light sensors used to illustrate where and when Cherenkov light arrives. P-ONE uses sensors distributed along strings, not a solid wall.

To fit it on screen, we add an imaginary wall of light sensors.

06 · Emission

Cherenkov radiation

Particles faster than light in water make a flash of blue light.

It's like a sonic boom, but with light. It's called Cherenkov light.

As a fast charged particle passes, its electric field briefly polarises the water molecules along its path, and they radiate as they relax. Normally those wavelets cancel out.

A particle faster than light in water outruns them, so they add up into one coherent shock front, the optical version of a sonic boom.

In detail

How much light, and how fast it travels.

Photons per unit path and wavelength (Frank–Tamm):

\(\dfrac{d^2N}{dx\,d\lambda} = \dfrac{2\pi\alpha z^2}{\lambda^2}\left(1 - \dfrac{1}{\beta^2 n^2}\right)\)

  • \(z\): the particle's charge. \(\alpha \approx 1/137\). \(n\): refractive index.
  • Over 300–600 nm, with \(\sin^2\theta_C \approx 0.43\), that is about 330 photons per cm.
  • More light at short wavelengths (\(\propto 1/\lambda^2\)), so it looks blue.
  • Timing uses the group index \(n_g \approx 1.38\), not the phase index \(n \approx 1.34\).

Sources: Particle Data Group 2022.

Yield: about 330 photons per centimetre between 300 and 600 nm, rising toward blue and ultraviolet (\(\propto 1/\lambda^2\)). That is why the glow looks blue.

In a shower, every electron and positron faster than 0.75 c radiates. The total light follows the total charged track length, about 4 m here, so an 800 MeV electron gives about as much light as the muon.

The charged pion radiates like a muon whenever its momentum exceeds 160 MeV/c. The gamma rays are neutral and stay dark until they convert into electron–positron pairs, on average about 47 cm later.

07 · Geometry

The cone of light

Many cones, smeared

Several cones

The light spreads out in a cone.

Like the wake behind a boat.

The shower makes many cones. Together they look blurry.

There are a few cones: one sharp, some blurry.

Every photon leaves at the same angle to its particle's path, and that angle depends only on the particle's speed:

\(\cos\theta_C = 1/(n\beta) \;\Rightarrow\; \theta_C \approx\) 41°

The wavefronts join into a cone with its tip on the muon, opening at 90° − \(\theta_{C}\) ≈ 49° from the track. In three dimensions it sweeps forward like a bow wave. This side view slices through its middle.

Each shower particle makes its own cone around its own direction. The particles scatter and spread, so the cones overlap at slightly different angles and the light smears into a thick, blurred band (drawn as a soft dashed front) instead of one crisp cone.

Each light source makes its own front around its own direction. The pion is one straight particle, so its front is a crisp cone (sharp lines) starting at the vertex. Each gamma stays dark until it converts, then its shower's front grows from that point as a blurred band, because its many particles point in slightly different directions. The fronts' axes differ, so they land as separate rings.

In detail

What sets the cone, and what blurs it.

\(\cos\theta_C = 1/(n\beta) \;\Rightarrow\; \theta_C \approx 41^\circ\) for \(\beta \to 1\)

  • Dispersion shifts \(\theta_C\) by under a degree across the visible.
  • Muon multiple scattering, \(\theta_0 \approx (13.6\ \mathrm{MeV}/\beta cp)\sqrt{x/X_0}\), adds about 1.5° rms over the first metre.
  • Shower particles point many ways, so a cascade's light peaks near \(\theta_C\) with long tails.

Sources: Particle Data Group 2022.

08 · Aftermath

The cone closes

The muon slows down. When it gets too slow, the light stops.

Then the muon stops and breaks apart. That makes one last small flash.

The muon loses about 2 MeV per centimetre to ionisation, so \(\beta\) drops and the angle narrows. When \(\beta\) falls below \(1/n\), at a kinetic energy of about 54 MeV, emission stops, 3.4 m from the vertex.

The muon drifts a few more centimetres and comes to rest. About 2.2 µs later it decays into an electron and two neutrinos, or, about one time in five, is captured by an oxygen nucleus. The decay electron makes a faint ring of its own that tags the event.

In detail

The end of the track.

  • Range of an 800 MeV muon in water: about 3.7 m.
  • A stopped \(\mu^-\) can be captured by oxygen (\(\mu^- p \to \nu_\mu n\)). Its lifetime drops from 2.20 to 1.80 μs, so ~18% are captured.
  • Decay electrons follow the Michel spectrum, up to 52.8 MeV. Their delayed hits tag the event.

Sources: Suzuki, Measday & Roalsvig 1987; Particle Data Group 2022.

The shower fades out

The shower particles slow down and stop.

The light slowly fades out.

Below the critical energy, about 80 MeV in water, the electrons stop making new photons and only ionise. Scattered back and forth, they slow down and drop out one by one.

The light fades over a couple of metres instead of closing to a point, and no single particle ends the event the way the muon does.

In detail

Why the light measures energy well.

  • Below \(E_c\), ionisation beats radiation, so no new particles are made.
  • Longitudinal profile: \(dE/dt \propto t^{a-1}e^{-bt}\), with \(b \approx 0.5\).
  • Total charged track length \(\propto E\) (about 4 m here). So the amount of light measures the energy.

Sources: Particle Data Group 2022.

Breakup, conversion, escape

The pieces fade

The pion hits a nucleus and breaks up. The gamma-ray showers fade.

The new neutrino escapes unseen. It takes some energy with it.

About 1.3 m out, the pion hits a nucleus and breaks up (the hadronic interaction length in water is about 83 cm), spraying a few slower particles. The gamma showers fade out like an electron's.

The tau neutrino from the decay leaves the detector unseen and carries energy away, one reason tau events are hard to reconstruct.

In detail

What makes tau events hard.

  • Hadronic interaction length in water: ~83 cm.
  • Pion breakup products are mostly slow or below Cherenkov threshold, so the light ends.
  • The escaping \(\nu_\tau\) biases the energy estimate low.
  • The decay smears the tau's direction.

Sources: Particle Data Group 2022.

09 · Detection

A ring on the wall

Sensors on the wall catch the light. It makes a sharp ring.

The middle lights up first, the edge last.

Photomultiplier tubes on the conceptual sensor wall record where light lands and when. The cone projects as a disc with a sharp outer edge. Light from the start of the track makes the edge, and light emitted as the muon slowed fills it in.

The centre lights first, 20 ns after the interaction, and the rim last, at 32 ns, because the muon outran its own light.

In detail

From hits to a muon.

  • A likelihood fit to hit charges and times gives the vertex, direction and momentum.
  • Ring sharpness separates μ-like from e-like rings, with roughly 1% mis-identification for single rings.

Sources: Super-Kamiokande 2003.

A fuzzy ring

The light makes a blurry ring.

Sharp ring: muon. Blurry ring: electron. That's how detectors tell them apart.

The shower's light lands as a ring with a thick, blurred edge. It is all emitted within a few metres of the vertex, so it forms a band rather than a filled disc. First light reaches the wall at 20 ns.

Fuzzy versus sharp is the main way water Cherenkov detectors such as Super-Kamiokande tell \(\nu_e\) events from \(\nu_\mu\) events.

In detail

What can fake an electron.

  • A neutral-current \(\pi^0\) makes two gamma rings.
  • If they merge, or one is faint, it looks like one electron.
  • This is the main background in \(\nu_e\) appearance searches.

Several overlapping rings

The light makes a few overlapping rings.

Other events look similar. So scientists count them up instead of naming each one.

Light arrives as overlapping rings: a sharp one from the pion and fuzzy ones from the two gamma showers. First light reaches the wall at 20 ns.

Multi-ring patterns like this are typical of tau events, but ordinary deep inelastic events look similar. Water Cherenkov detectors can only pick out tau neutrinos statistically, as Super-Kamiokande did for taus appearing from oscillating atmospheric muon neutrinos.

In detail

How Super-Kamiokande saw tau neutrinos.

  • Atmospheric \(\nu_\mu\) oscillate into \(\nu_\tau\) over an Earth diameter.
  • Only \(E_\nu > 3.5\) GeV can make a tau, so the signal is upward-going and multi-ring.
  • A neural network picks tau-like events; a fit finds the excess.
  • Result: no tau appearance is excluded at 4.6σ.

Sources: Super-Kamiokande 2018.

Keep scrolling to see this flavour in the full P-ONE array

10 · Scale: kilometres

The same physics across the P-ONE array

Colour = when the light arrived: white first, indigo lastSize = how much light a module caughtDashed line = the neutrino, entering through the same patch of seafloor for every flavour

The crash above was tiny, just a few metres. P-ONE is built for neutrinos with far more energy. Their light spreads over many lines of sensors.

An electron neutrino makes a round burst of light.

A tau neutrino can make two bursts: one where the tau is made, one where it breaks up.

A muon neutrino makes a long streak of light, heading up from inside the Earth.

The event above spans only a few metres of water, less than the 50 m gap between two modules. The Pacific Ocean Neutrino Experiment (P-ONE) is designed for neutrinos with TeV energies and more, whose light spreads across many lines. Its layout is still being optimised. This model uses one design under study: 69 vertical lines in three triangular clusters of 23, with neighbouring lines 80 m apart, anchored to the floor of the Cascadia Basin, 2,660 m below the surface off Vancouver Island.

This simulation shows an electron-neutrino cascade inside the array. At TeV to PeV energies the electron's shower and the hadronic debris are each only about 10 m long. Seen from modules 50–80 m apart they form a single point-like burst: the light spreads out as a sphere and the hits make a round blob in space and time. Cascades point back poorly but measure energy well. Like every event here, this neutrino arrives from below, through the Earth.

This simulation shows a tau-neutrino double bang. At PeV energies time dilation stretches the tau's flight to about 50 m per PeV, so the interaction cascade and the tau's decay can sit far enough apart to see as two bursts joined by a faint track. The neutrino arrives from below; tau neutrinos survive the trip through the Earth because a tau that forms on the way decays back into a lower-energy tau neutrino. For display, events are chosen with 250–450 m between the bangs. Hit times use the same colours as every other event, so the double bang shows up as two separate bursts: early (white) modules around the interaction and later (blue to indigo) modules around the decay. About a sixth of tau decays give a muon instead of a second cascade.

This simulation shows an upgoing muon from a neutrino that interacted inside the array. Only neutrinos can cross the Earth, so an upgoing track points to a neutrino. The hadronic debris flashes at the vertex, the muon's Cherenkov cone sweeps across the lines, and each module that catches light lights up.

In detail

Why tracks point so well.

  • Above ~1 TeV, muon losses are radiative (bremsstrahlung, pair production, photonuclear), so \(dE/dx \propto E\).
  • Its range reaches kilometres of water.
  • That long lever arm gives sub-degree pointing.

Sources: Particle Data Group 2022.

In detail

Cascades: good energy, rough direction.

  • The light still peaks near 42° to the shower axis.
  • Scattering in the water washes this out over tens of metres.
  • So energy is measured well, but direction only to several degrees at best.

In detail

When a double bang becomes visible.

\(\gamma c\tau \approx 49\ \mathrm{m} \times E_\tau/\mathrm{PeV}\)

  • At PeV energies the tau takes about ¾ of the neutrino's energy.
  • Two bangs need to be tens of metres apart or more, so they appear around a PeV.
  • Below that, a \(\nu_\tau\) CC event looks like one cascade.

Sources: Particle Data Group 2022.

Drag to orbit · scroll or pinch to zoom · right-drag to pan · drag the purple ring to move where the neutrino enters

0.00 µs

Computed, not drawn

  • The muon's slowdown is integrated centimetre by centimetre from an approximate Bethe energy-loss rate, starting at 800 MeV kinetic energy.
  • Each photon leaves the track at the local angle \(\cos\theta = 1/(n\beta)\) and travels at c/n. The cone, its narrowing and its closing all emerge from that rule.
  • Brightness along the track follows the Frank–Tamm yield, proportional to \(\sin^2\theta\), so light fades as the muon nears threshold.
  • Wall hits and arrival times come from the same photons, including the centre-first timing.
  • The muon leaves along the neutrino's direction. The proton's wide recoil angle is balanced by the struck neutron's own motion inside the nucleus (Fermi momentum, up to about 225 MeV/c).

Simplified

  • The side view is a 2D slice through a 3D cone. Brightness is relative, not a photon count.
  • Electron and gamma showers come from a small seeded simulation: bremsstrahlung roughly every radiation length (36 cm), pair production, 2 MeV/cm ionisation, a critical energy of 78 MeV and multiple scattering. It reproduces the shape and fuzziness, not detailed shower statistics.
  • The tau event uses one fixed decay, \(\tau^- \to \pi^- \pi^0 \nu_\tau\), with energies and angles chosen to conserve momentum and give the ρ meson's mass. The pion's breakup is reduced to two outgoing secondaries.
  • The muon track is straight. Real muons wiggle slightly from multiple scattering and knock out electrons that add a little extra light.
  • The refractive index is fixed at 1.333. For the ring, a small spread stands in for colour dispersion. Absorption and scattering in the water are ignored.
  • The nucleus is a flat cluster of spheres and the W boson is enlarged. Time is slowed unevenly between stages.
  • The conceptual sensor wall sits 5.5 m from the vertex. Super-Kamiokande's tank is about 40 m across.

The journey

  • The source: a non-jetted (Seyfert-type) active galactic nucleus modelled on NGC 1068, placed far away (redshift ≈ 1) because most of the diffuse neutrino flux is expected to come from distant sources. Neutrinos are made in the hot corona above the inner accretion disc, within roughly 30–100 Schwarzschild radii of the black hole (a few light-hours for ten million solar masses). Protons are accelerated stochastically by turbulence and make pions mainly on the disc's UV and the corona's X-ray photons (\(p\gamma\)); proton–proton collisions also contribute in some models. Each neutrino takes about 1/20 of the parent proton's energy, so a 200 TeV neutrino needs a proton of about 5 PeV. The core is drawn schematically: the black hole, disc, corona and dusty torus are not to one scale. The disc's colours (hotter inward), its faster inner orbits, the brighter side turning towards us (Doppler beaming) and the light bent over the black hole (gravitational lensing) are shown qualitatively, not computed.
  • How sure this is: AGN are the leading candidates, not a settled answer. NGC 1068 is 4.2σ evidence, below the 5σ usually needed for a discovery; NGC 4151 and other X-ray-bright Seyferts show weaker excesses of about 3σ. Gamma-ray-bright blazars (jetted AGN) can supply at most about 16% of the diffuse flux, while X-ray-bright AGN could supply anywhere from about 11% to all of it. The Galactic plane also emits neutrinos (4.5σ) but cannot explain the whole sky. Other proposed sources, such as tidal disruption events and supernovae running into dense gas, are not ruled out.
  • Cosmology: flat ΛCDM with \(H_0\) = 67.7 km/s/Mpc and \(\Omega_m\) = 0.31. A 7.9-billion-year trip corresponds to redshift ≈ 1, halving the energy. The lag behind light assumes the KATRIN upper limit, \(m_\nu\) < 0.45 eV.
  • Flavour colours (\(\nu_e\) pink, \(\nu_\mu\) orange, \(\nu_\tau\) indigo) are chosen to stay distinct with common colour-vision deficiencies and in greyscale, and are the same throughout the page. In the oscillation chart each flavour is a solid line in its own colour, labelled directly where it ends.
  • Oscillations are calculated, not measured: the three-flavour vacuum formula with the NuFIT 5.0 best fit (Esteban et al., JHEP 09 (2020) 178, normal ordering with SK atmospheric data). Prologue 5 shows neutrinos born as \(\nu_\mu\) at 100–400 TeV (\(E^{-2}\), illustrative) on a log distance axis out of the host galaxy: the swings (1.3 AU and 45 AU at 200 TeV) are resolved near the source, and the average settles on the flavour averages within a few hundred AU. Wave-packet decoherence for a single neutrino may happen inside or beyond its galaxy, depending on the poorly known packet size; it does not change the averages. The source mix 1 : 2 : 0 assumes pion decay with muons decaying before they lose energy; averaged, it reaches Earth as 1.00 : 1.20 : 1.15 with these parameters (exactly 1 : 1 : 1 if \(\theta_{23}\) were 45°), shown on the page as "about a third each".
  • Expanding space: the cosmic web and the distance between the two galaxies scale with the ΛCDM scale factor a(t), so that distance doubles during the trip (from about 5.5 to 11 billion light-years at z ≈ 1). Gravitationally bound galaxies don't expand, so they keep a fixed size. The neutrino advances by comoving distance (∫ c dt / a), so it covers ground faster early on. Simplifications: the galaxies are drawn thousands of times larger than to scale, and the web is illustrative.
  • Galaxies: both are drawn as about 20,000 individual stars, so the spiral arms show what they really are, regions where stars (and gas) are more crowded, not solid structures. Young blue-white stars sit mostly in the arms, older warm stars spread through the disc and crowd into the bulge; faint glows stand in for stars too faint to see one by one, with dust lanes along the arms and a few pink star-forming regions. Arms are logarithmic spirals. The host galaxy is modelled on Messier 77 (NGC 1068): seen nearly face-on, with a large bright bulge and two tightly wound main arms (pitch about 13°). The Milky Way is a barred spiral: a central bar, two major arms (Scutum–Centaurus and Perseus) starting at its ends, two minor arms, and the short Orion Spur, on which the Sun sits 26,000 light-years from the centre (pitch about 12°). Both patterns are illustrative, not maps. In reality the arms are density waves that stars pass through, turning more slowly than the stars orbit; here each pattern simply turns as a whole at its pattern speed (Milky Way 25 km/s/kpc, host 28 km/s/kpc), slowed for display: about 120 million years of rotation is shown over the flight, while a real galaxy turns about 36 times during the 7.9-billion-year trip.
  • Earth crossing: arrival 30° below the horizon gives a 6,371 km chord with its deepest point 854 km down. Survival uses a total neutrino–nucleon cross-section of about \(2.6 \times 10^{-34}\,\mathrm{cm^2}\) at 100 TeV. The cosmic distances, the galaxy drawings and the Solar System (square-root orbits) are not to scale.
  • The globe is cut open along P-ONE's meridian (127.7° W), so the neutrino's whole path, from 12° S to 47.8° N, lies on one cut face. Layer radii are to scale. Coastlines come from the Apache ECharts world map.

Sources: where the neutrino comes from

  • IceCube Collaboration, “Evidence for neutrino emission from the nearby active galaxy NGC 1068”, Science 378, 538–543 (2022), doi:10.1126/science.abg3395. The 4.2σ excess, TeV energies, and a neutrino flux at least ten times any TeV gamma-ray flux.
  • F. D'Ammando, “Active Galactic Nuclei as high-energy neutrino sources”, Astron. Astrophys. Rev. (2026), doi:10.1007/s00159-026-00168-9, arXiv:2606.30764. Review: coronae as gamma-ray-obscured neutrino sources up to about 1 PeV, the 30–100 Schwarzschild-radius production zone, jets at higher energies, and the Seyfert results.
  • S. Jain, D. Hooper and F. Halzen, “Evaluating the contribution of active galactic nuclei to the diffuse high-energy neutrino flux”, JCAP 05 (2026) 045, doi:10.1088/1475-7516/2026/05/045. Blazars at most 16%; X-ray-bright AGN between about 11% and all of the flux.
  • K. Murase, S. S. Kimura and P. Mészáros, “Hidden cores of active galactic nuclei as the origin of medium-energy neutrinos: critical tests with the MeV gamma-ray connection”, Phys. Rev. Lett. 125, 011101 (2020), doi:10.1103/PhysRevLett.125.011101. Stochastic acceleration of protons to PeV energies by turbulence in AGN coronae.
  • IceCube Collaboration, “IceCube search for neutrino emission from X-ray bright Seyfert galaxies”, ApJ (2025), doi:10.3847/1538-4357/addd05, arXiv:2406.07601. NGC 4151 at about 3σ (local).
  • IceCube Collaboration et al., “Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A”, Science 361, eaat1378 (2018), doi:10.1126/science.aat1378; and IceCube Collaboration, “Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert”, Science 361, 147–151 (2018), doi:10.1126/science.aat2890. The 290 TeV neutrino and the earlier flare.
  • A. Kheirandish, K. Murase and S. S. Kimura, “High-energy neutrinos from magnetized coronae of active galactic nuclei and prospects for identification of Seyfert galaxies and quasars in neutrino telescopes”, ApJ (2021), arXiv:2102.04475. Proton acceleration and neutrino production in coronae.
  • S. R. Kelner and F. A. Aharonian, “Energy spectra of gamma rays, electrons and neutrinos produced at interactions of relativistic protons with low energy radiation”, Phys. Rev. D 78, 034013 (2008), arXiv:0803.0688. Photomeson (\(p\gamma\)) production: the threshold, and the shares of energy passed to pions and neutrinos.
  • Particle Data Group, R. L. Workman et al., “Review of Particle Physics”, Prog. Theor. Exp. Phys. 2022, 083C01, doi:10.1093/ptep/ptac097. Pion and muon lifetimes and decays, and the \(\Delta(1232)\) resonance.
  • IceCube Collaboration, “Observation of high-energy neutrinos from the Galactic plane”, Science 380, 1338–1343 (2023), doi:10.1126/science.adc9818.

The P-ONE model

  • Published figures: lines about 1 km tall with 20 modules spaced 50 m, seafloor at 2,660 m. Each optical module holds 16 PMTs.
  • Layout: the "large cluster" geometry from P-ONE's layout studies, 69 lines in three triangular clusters of 23 on a triangular grid with neighbouring lines 80 m apart. The collaboration's earlier baseline was 7 clusters of 10 lines; the geometry is still being optimised, so this is one candidate, not the final design. Assumed: the lowest module 50 m above the seafloor, and the cabling drawn on the seafloor.
  • Modules are drawn about 20 times their real 43 cm size so they show up at kilometre scale.
  • Light model: phase index 1.343 (Cherenkov angle 41.9°), group index 1.38, attenuation length 28 m, about 0.0125 m² of effective photon-collecting area per module. Muon light grows with energy through stochastic losses (ionisation 0.24 GeV/m plus \(3.3 \times 10^{-4}\) per metre times the energy). Scattering is a simple random delay. Background light from potassium-40 decays and bioluminescence is left out.
  • Electron and tau events in 3D treat each cascade as a point source that radiates evenly in all directions, which is a fair approximation at 50–80 m once light has scattered. Tau flight is 49 m per PeV of tau energy. Decays split 65% hadrons, 18% electron, 17% muon.
  • All 3D events arrive from below along one shared path, 30° below the horizon as in the prologue, entering the water through the same patch of seafloor so the flavours can be compared. At PeV energies the Earth absorbs most electron and muon neutrinos crossing its full diameter, so shallow paths like this one are where such events come from. Tau flights are clamped to 250–450 m so the two bangs land on different lines. Hits use the same time colours and size-by-light as the far-wall view in section 09.
  • Sources: P-ONE demonstrator, ICRC 2023 expected performance, P-ONE overview (arXiv 2111.13133), optical calibration systems (arXiv 2603.09495), in-situ calibration systems (ICRC 2025).

Sources: life in the deep water

For the facts given when you hover over the animals in the zoom from the ocean to a water molecule. Sizes are typical adult sizes; the animals are drawn to scale but far more crowded than in real seawater.

  • E. A. Widder, “Bioluminescence in the ocean: origins of biological, chemical, and ecological diversity”, Science 328, 704–708 (2010), doi:10.1126/science.1174269. Counterillumination by belly light organs; luciferases.
  • S. H. D. Haddock, M. A. Moline and J. F. Case, “Bioluminescence in the sea”, Annu. Rev. Mar. Sci. 2, 443–493 (2010), doi:10.1146/annurev-marine-120308-081028. Which animals glow, including copepods and radiolarians, and why.
  • X. Irigoien et al., “Large mesopelagic fishes biomass and trophic efficiency in the open ocean”, Nature Communications 5, 3271 (2014), doi:10.1038/ncomms4271. Mesopelagic fish, mostly lanternfish, measured acoustically and at least ten times more abundant than earlier estimates.
  • R. Proud, M. J. Cox and A. S. Brierley, “Biogeography of the global ocean's mesopelagic zone”, Current Biology 27, 113–119 (2017), doi:10.1016/j.cub.2016.11.003. The deep scattering layer seen by sonar worldwide.
  • A. L. Alldredge and M. W. Silver, “Characteristics, dynamics and significance of marine snow”, Prog. Oceanogr. 20, 41–82 (1988), doi:10.1016/0079-6611(88)90053-5. What marine snow is made of, and how fast it sinks.
  • M. Zarubin, S. Belkin, M. Ionescu and A. Genin, “Bacterial bioluminescence as a lure for marine zooplankton and fish”, PNAS 109, 853–857 (2012), record. Glowing bacteria are eaten, and spread, more often.
  • E. V. Armbrust, “The life of diatoms in the world's oceans”, Nature 459, 185–192 (2009), doi:10.1038/nature08057. Diatoms make most of the organic matter that feeds life in the sea.
  • W. B. Whitman, D. C. Coleman and W. J. Wiebe, “Prokaryotes: the unseen majority”, PNAS 95, 6578–6583 (1998), doi:10.1073/pnas.95.12.6578. Bacteria per millilitre near the surface and in deep water.
  • C. A. Suttle, “Viruses in the sea”, Nature 437, 356–361 (2005), doi:10.1038/nature04160. Viruses' abundance and their role in recycling carbon and nutrients.
  • Y. Y. Watanabe, C. Lydersen, A. T. Fisk and K. M. Kovacs, “The slowest fish: swim speed and tail-beat frequency of Greenland sharks”, J. Exp. Mar. Biol. Ecol. 426–427, 5–11 (2012), doi:10.1016/j.jembe.2012.04.021. The sleeper shark's close relative cruises at 0.34 m/s.
  • A. A. Myrberg, “The acoustical biology of elasmobranchs”, Environ. Biol. Fishes 60, 31–45 (2001), doi:10.1023/A:1007647021634. Sharks hear best at low frequencies and are drawn to sounds like struggling prey.
  • D. A. Mann and S. M. Jarvis, “Potential sound production by a deep-sea fish”, J. Acoust. Soc. Am. 115, 2331–2333 (2004). Swim-bladder sound muscles in deep-sea fishes, and a probable deep-sea fish call recorded by hydrophones.
  • A. Širović, J. A. Hildebrand and S. M. Wiggins, “Blue and fin whale call source levels and propagation range in the Southern Ocean”, J. Acoust. Soc. Am. 122, 1208–1215 (2007), eScholarship. Blue whale calls of about 189 dB at 25–29 Hz, located up to 200 km away.
  • R. Burnham, “Learning about whales by listening for their calls”, Frontiers for Young Minds 8 (2020), doi:10.3389/frym.2020.00055. Seafloor and glider hydrophones listening for whales off Vancouver Island.
  • P-ONE Collaboration, “Two-year optical site characterization for the Pacific Ocean Neutrino Experiment P-ONE in the Cascadia Basin”, Eur. Phys. J. C 81 (2021), doi:10.1140/epjc/s10052-021-09872-5, arXiv:2108.04961. Bioluminescence (10 kHz to several MHz per sensor) and potassium-40 as the site's background light.

Refractive index of watern ≈ 1.333
Cherenkov angle, \(\beta \to 1\)41.4°
Muon threshold54 MeV · 120 MeV/c
Proton threshold1.07 GeV/c
Photon yield, 300–600 nm≈ 330 / cm
Muon energy loss in water≈ 2 MeV / cm
Muon lifetime2.197 µs
\(^{16}\mathrm{O}\) charge radius2.70 fm
W boson range≈ 0.0025 fm
Tau production threshold\(E_\nu \approx 3.5\) GeV
Tau lifetime · cτ290 fs · 87 µm
Radiation length of water36 cm
This event: neutrino energy≈ 0.95 GeV
Muon kinetic energy800 MeV
Muon track length3.7 m
Light emitted over3.4 m · 12 ns
This event: neutrino energy≈ 0.95 GeV
Electron energy800 MeV
Total charged track in shower4 m
This event: neutrino energy≈ 6.4 GeV
Tau energy · flight6 GeV · 0.28 mm
Decay\(\tau^- \to \pi^- \pi^0 \nu_\tau\)
\(\pi^- \cdot \gamma \cdot \gamma\) energies2.4 · 1.4 · 0.8 GeV