How is power conserved when neutrinos oscillate?

One of the vital shocking discoveries within the twentieth century was the conclusion that neutrinos don’t essentially stay the identical species of particle as they journey via the Universe, however quite can change from one kind of neutrino (electron, muon, or tau) into one other. This taught us that the unique formulation of the Commonplace Mannequin, which asserted that neutrinos can be fully massless, was essentially incomplete, and that neutrinos would as an alternative be required to have mass. As of 2023, it’s nonetheless the one recognized means that particle physics has given us any indication that one thing else is on the market past the Commonplace Mannequin.

However it raises an attention-grabbing puzzle. In any case, if there are three species of huge neutrino (and antineutrino) on the market within the Universe, the observations educate us that the neutrinos themselves all have completely different relaxation plenty from each other. Does this imply that once they oscillate from one species to a different, since E =mc², that power is not conserved? That’s what Alan Finkel desires to know, asking:

“On condition that neutrinos are recognized to oscillate between flavors, and every taste is a distinct mass-energy, how is the power conserved?”

I’ll spoil you first: power actually is conserved. However in an effort to perceive how, you first want to know fairly a number of counterintuitive issues about neutrinos themselves. Let’s begin originally.

The neutrino is an intriguing and attention-grabbing particle. This infographic lays out a few of the neutrino’s fundamental stats alongside enjoyable information.

Credit score: Diana Brandonisio/DOE/Fermilab

Neutrinos started as a purely theoretical concoction to unravel an issue: the issue of power conservation in radioactive decays. Within the early days of nuclear and particle physics, we knew that some atomic nuclei — that’s, certain combos of protons and neutrons — had been unstable, and would emit a number of particles. The three important varieties that we knew of had been:

  1. alpha (α) decay: the place a nucleus emits “an α-particle” (or a helium-4 nucleus) with 2 protons and a pair of neutrons, the place the daughter nucleus and the α-particle, mixed, preserve each the power and momentum of the unique nucleus.
  2. beta (β) decay: the place a nucleus emits “a β-particle” (or an electron), reworking one of many authentic nucleus’s neutrons right into a proton, the place the electron and the daughter nucleus’s power and momentum had been virtually, however not fairly, conserved.
  3. gamma (γ) decay: the place a nucleus in an excited state (i.e., with a heavier relaxation mass than a typical, ground-state nucleus) emits a high-energy photon (often known as a γ-particle), and rearranges itself right into a lower-energy state whereas maintaining the identical variety of protons and neutrons. The brand new nucleus plus the emitted photon, when in comparison with the unique nucleus, additionally preserve each power and momentum.

The issue was with β-decay, and that’s what led Wolfgang Pauli, in 1930, to hypothesize the existence of a brand new particle: the neutrino.

radioactive beta decay

Schematic illustration of nuclear beta decay in a large atomic nucleus. Beta decay is a decay that proceeds via the weak interactions, changing a neutron right into a proton, electron, and an anti-electron neutrino. Earlier than the neutrino was recognized or detected, it appeared that each power and momentum weren’t conserved in beta decays; it was Wolfgang Pauli’s proposal {that a} new, tiny, impartial particle existed.

Credit score: Inductiveload/Wikimedia Commons

In Pauli’s formulation, there can be an additional particle that was emitted throughout β-decay — a particle that was practically invisible and that had by no means been detected — that carried away that “lacking” power and momentum, and which allowed for the whole lot to be conserved, in spite of everything. As a result of that particle wanted to haven’t any electrical cost and needed to be extraordinarily low in mass, because the “lacking power” from many noticed β-decay occasions was barely perceptible, Pauli named it a neutrino: Italian for “little impartial one.”

After all, Pauli was extraordinarily disillusioned together with his personal proposed resolution to the β-decay drawback, stating, “I’ve executed a horrible factor, I’ve postulated a particle that can’t be detected.”

Though it took an additional 26 years for the primary neutrino (technically, an antineutrino produced by a nuclear reactor) to be detected, it was shortly realized that not solely had been neutrinos actual, however they performed a tremendously necessary function in nuclear physics, and specifically within the fusion reactions that happen inside stars. Within the Sixties, scientists started constructing bigger and extra delicate neutrino detectors, and eventually started detecting neutrinos generated within the nuclear reactions inside our personal Solar. And instantly, a horrible, new drawback arrived on our doorstep.

solar neutrino

It isn’t simply photons and charged particles that carry power away from the Solar, but additionally photo voltaic neutrinos, that are produced within the Solar’s core and hardly work together in any respect with different particles. A complete of roughly ~1% of the Solar’s power is emitted within the type of these photo voltaic neutrinos.

Credit score: APS/Alan Stonebraker

You see, we all know how stars work. By the Sixties, we knew extra than simply the fundamentals of how fusion in stars labored: we knew the way to calculate what number of neutrinos must be produced and the way a lot power they ought to hold away. And since we had begun to detect neutrinos instantly, we additionally believed we knew what their cross-section (which determines their interplay fee) must be inside a detector, and therefore we had a theoretical prediction for the speed and power distribution of neutrinos that we anticipated to see.

When the info started coming in, issues began to look actually good. Straight away, neutrino indicators began showing within the detector, with the suitable energies, momenta, and course to be in line with being generated by the Solar: photo voltaic neutrinos. The experiment was working! Because the scientists collected increasingly information, they started to see the form of the power spectrum, and as soon as once more, it matched up with the theoretical predictions very properly.

It led an incredible many scientists to consider that we truly knew what we had been speaking about when it got here to neutrinos, regardless of their elusive nature. However others strongly disagreed, as a result of there was one large puzzle that arose from the info: regardless of the whole lot we anticipated, solely about ⅓ of the anticipated variety of neutrinos that we anticipated seeing had been truly showing within the detector.

solar neutrino detector kamiokande

Experiments comparable to Tremendous-Kamiokande, which include monumental tanks of (proton-rich) water surrounded by arrays of detectors, are essentially the most delicate instruments humanity has to detect neutrinos from the Solar. In comparison with the variety of electron neutrinos we naively anticipated to seem within the detector, the measured sign is just about one-third of the expected worth.

Credit score: Kamioka Observatory, ICRR, College of Tokyo

This puzzle quickly grew to become often known as the photo voltaic neutrino drawback. Many physicists in the neighborhood had been fast to dismiss the significance of the issue, as they believed that both:

  • the experimental physicists engaged on the detection aspect didn’t know what they had been doing, and had constructed a less-efficient detector than that they had anticipated,
  • or that the theorists engaged on calculating their fashions of the Solar and the neutrino flux it emitted over time didn’t know what they had been doing, and their calculations had been merely predicting absurdities that didn’t line up with what we noticed.

Physics is tough, in spite of everything, and it wouldn’t have been too shocking if one in every of these avenues had turned out to be right. However the photo voltaic neutrino drawback was a cussed one; as increasingly neutrino detectors had been constructed and we started detecting them in a number of methods, we started ruling out the chance that experimentalists had been in error. As our understanding of stars, neutrinos, and nuclear & particle physics improved, we started to exclude a wide range of attainable sources of error that theorists might’ve been making. By the Eighties and Nineties, it grew to become abundantly clear that the unique claims of each experimentalists and theorists engaged on the photo voltaic neutrino drawback had been right all alongside, and one thing actually was amiss.

atmospheric neutrino

Whereas cosmic ray showers are frequent from high-energy particles, it’s principally photons, muons, neutrinos, and electrons that make it right down to Earth’s floor. Nearly the entire neutrinos produced through cosmic ray showers are muon neutrinos, however that doesn’t essentially imply the entire detected neutrinos can be muon neutrinos.

Credit score: Alberto
Izquierdo; Francisco
Barradas Solas

An enormous clue got here alongside once we grew to become delicate to detecting a second supply of naturally-produced neutrinos: neutrinos generated in Earth’s environment. You see, the Universe is stuffed with cosmic rays: high-energy particles, principally protons, of astrophysical origin that come from all all through the Universe. When these particles strike the highest of the environment, they produce particle showers: largely pions, which are available in three varieties: π+, π, and π0. The impartial pions (π0) which can be produced decay into photons, however the charged pions (π+ and π) decay, principally into muons (and antimuons) and a distinct species of neutrino: muon neutrinos (and antineutrinos).

As soon as once more, theorists went via the difficulty of calculating the anticipated flux of neutrinos, and sought to measure their sign power within the neutrino detector. For the photo voltaic neutrinos, they had been seeing an occasion fee that was about ⅓ of what was predicted, however this time, for the atmospheric neutrinos, they had been seeing an occasion fee that was nonetheless low, however much less low: about ⅔ of what was predicted.

Nonetheless, this didn’t create a brand new, atmospheric neutrino drawback, however quite pointed the way in which in the direction of the reply: neutrinos weren’t massless like we had initially anticipated, however quite behaved just like the quarks did. They’d mass, and due to this fact they had been able to mixing collectively, and oscillating from one species into one other.


Neutrino detectors, just like the one used within the BOREXINO collaboration right here, usually have an infinite tank that serves because the goal for the experiment, the place a neutrino interplay will produce fast-moving charged particles that may then be detected by the encircling photomultiplier tubes on the ends. Detectors which can be delicate to atmospheric neutrinos, versus photo voltaic neutrinos, are optimized in very alternative ways.

Credit score: INFN/Borexino Collaboration

We had recognized about quark mixing for a while already, and the essential idea is that this: there are two methods to have a look at quarks, by way of mass and by way of taste. When there’s an interplay between two particles and a quark is a part of that interplay, some properties of that quark are decided explicitly and don’t change once they propagate via area, comparable to mass. Nonetheless, in case your detectors are delicate to a distinct property of these quarks, comparable to taste, you’re not going to see a 1-to-1 match between what we name “mass eigenstates” and “taste eigenstates,” however quite — like so many issues in quantum physics — there’s solely a chance distribution of what kind of taste you’re going to watch.

If we apply this identical reasoning to each photo voltaic and atmospheric neutrinos, we are able to provide you with an image in our heads the place, at any time when a neutrino is generated, it comes together with a definitive set of properties: it’s a particular taste of neutrino with a particular relaxation mass that’s 100% decided. Nonetheless, when it propagates, it propagates with a set mass, however its “taste” will not be. As such, when it interacts with one other particle in a while (for instance, inside your detector), you possibly can solely compute a chance distribution for what kind of taste — electron, muon or tau neutrino — you’re truly going to watch.

neutrino oscillation

Vacuum oscillation chances for electron (black), muon (blue) and tau (crimson) neutrinos for a selected set of blending parameters, starting from an initially produced electron neutrino. An correct measurement of the blending chances over completely different size baselines will help us perceive the physics behind neutrino oscillations and will reveal the existence of some other forms of particles that couple to the three recognized species of neutrino. For neutrinos to oscillate, they will need to have non-zero mass. If further particles (comparable to darkish matter particles) carry power away, the general neutrino flux will present a deficit.

Credit score: Strait/Wikimedia Commons

Within the case of photo voltaic neutrinos, the interactions contained in the Solar initially produce predominantly electron neutrinos and antineutrinos, which then propagate with a set, unchanging mass. Within the case of atmospheric neutrinos, the interactions between particles (arising from charged pion decays) initially produce predominantly muon neutrinos and antineutrinos, which once more propagate with a particular and unchanging mass alongside their journey subsequent to their technology.

As they propagate via the Universe, nonetheless, whether or not they’re propagating via the vacuum of area or via matter, time is passing for these huge particles. Identical to something quantum mechanical with a number of attainable outcomes, the chance of measuring any explicit taste is time-dependent, which signifies that through the time in-between measurements and/or interactions, the flavour of those neutrinos will not be decided: it may be described as a superposition of all three (electron, muon, tau) prospects.

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However the one factor that by no means modifications through the time in between the 2 interactions — the place it’s generated and the place it’s detected — is the mass of the neutrino, which stays fixed throughout propagation. Solely when it seems in your detector does it tackle one of many “taste” values, and these are much less restricted than you may suppose.

neutrino energy

Neutrinos are available in all kinds of energies and have been noticed (and calculated) to have all kinds of cross-sections. Neutrinos have been detected from an infinite variety of sources, however by no means left over from the Massive Bang, as their cross-section is way too low to be accessible to experiment. Even so, neutrino-particle interactions ought to have sufficient power, even at the moment, to allow all attainable taste oscillations.

Credit score: J. A. Formaggio and G. P. Zeller, Rev. Mod. Phys., 2012

For instance, for photo voltaic and atmospheric neutrinos, the power of the neutrinos that seem in our detectors are all the time within the ~mega-electron-volt (MeV) vary or above. By comparability, the remainder plenty of the neutrinos species themselves are properly under a single electron-volt (eV) apiece. Any interplay that happens between neutrinos (or antineutrinos) and matter (or antimatter) — not less than, the interactions that we all know the way to detect — doesn’t have any mass restriction on what forms of oscillations are and will not be admissible. With the energies that virtually happen, all prospects can be found.

The three flavors of neutrino that we are able to observe, electron, muon, and tau, do all have completely different plenty, even when we aren’t certain of precisely what these plenty are or which taste is heaviest and which is lightest. However we are able to think about a situation the place the lightest, lowest-mass neutrino is slow-moving, nonetheless, such because the neutrinos left over from the new Massive Bang. What occurs when that neutrino — propagating with its fastened mass — has a really low chance of interacting with some kind of matter. Nonetheless, all the opposite forms of matter that exist are a lot extra huge than neutrinos that until they’re virtually at relaxation with respect to 1 one other (which, by the way in which, would make their chance of interacting negligibly small), there can be sufficient power out there from the collision to allow oscillation into both of the opposite two species.

quantum particles

Neutrinos and antineutrinos are copious inside this Universe, however we are able to solely detect which taste (electron, muon, or tau) the neutrino is when it interacts with one other particle. Throughout the in between instances, when it’s touring, it’s in an indeterminate state.

Credit score: Jefferson Lab/DOE

What’s essential to acknowledge is that power conservation should all the time be obeyed, and that should you did hypothetically have a low-mass neutrino work together at low-energies with a large particle, you’ll have a set of constraints so far as “which sort of neutrino” will be revealed from that interplay. If we assume that the tau neutrino is the heaviest and the electron neutrino is lightest, there could also be as a lot as a ~0.03 eV distinction (or so) between them by way of relaxation mass power. Until not less than that a lot kinetic power is accessible from the interplay to allow the neutrino to alter taste from an electron neutrino to a tau neutrino, that chance can be forbidden.

Nonetheless, there’s a lot we don’t but learn about neutrinos, together with what the plenty of the electron, muon, and tau neutrinos truly are. Measuring photo voltaic and atmospheric neutrinos have taught us what the variations between the propagating mass values (technically, the sq. of these values) are, however we haven’t but discovered what absolutely the plenty of every of the three forms of neutrino truly are, nor do we all know which of them are heaviest and that are lightest. Till we study extra, that is the restrict of what we learn about neutrinos. Relaxation assured, regardless of how difficult they might seem, each interplay they ever bear nonetheless obeys the conservation of power!

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