B What do we know about neutrino-neutrino scattering?

[pines-demon]

I was reading about Gargamelle experiment from the 1970s. It is supposed to be the experiment that proved weak neutral currents (leading to the discovery of the Z boson). However as I understand it, it was from the interaction of neutrinos with electrons or neutrinos with nucleons. I was wondering if it possible to detect neutrino-neutrino scattering. The three most cited papers in Google Scholar about n-n scattering are on astrophysics, supernovae and cosmological events (e.g. https://doi.org/10.1103/PhysRevD.51.1479). However, I was wondering if it was possible to measure evidence of neutrino-neutrino scattering with a neutrino experiment on Earth.

 

[Orodruin]

A terrestrial neutrino-neutrino scattering experiment would not be feasible. The cases where neutrino-neutrino scatterings would be relevant, such as in supernovae and the early Universe, involve extreme neutrino densities not attainable in a terrestrial experiment.

 

[pines-demon]

A terrestrial neutrino-neutrino scattering experiment would not be feasible. The cases where neutrino-neutrino scatterings would be relevant, such as in supernovae and the early Universe, involve extreme neutrino densities not attainable in a terrestrial experiment.

So even if we had high-energy cosmic neutrinos coming into the experiment it would not be enough?

 

[snorkack]

Are you referring to elastic scattering (neutrinos scatter off each other as still neutrinos) or inelastic scattering (two neutrinos collide and for something else)?

 

[pines-demon]

Are you referring to elastic scattering (neutrinos scatter off each other as still neutrinos) or inelastic scattering (two neutrinos collide and for something else)?

Elastic scattering.

 

[snorkack]

Elastic scattering.

Incoming two invisible neutrinos, outgoing ditto. What is there to detect?

 

[phinds]

So even if we had high-energy cosmic neutrinos coming into the experiment it would not be enough?

No, it would not. You need incredibly extreme neutrino density for there to be collisions.

 

[snorkack]

No, it would not. You need incredibly extreme neutrino density for there to be collisions.

And even if you did have that extreme density, an elastic collision would still be something that stays undetected (only invisible neutrinos leaving).

 

[pines-demon]

Incoming two invisible neutrinos, outgoing ditto. What is there to detect?

Maybe deflections from the neutrino paths? Or maybe differences in interaction when neutrinos are of different flavor?

 

[snorkack]

Maybe deflections from the neutrino paths? Or maybe differences in interaction when neutrinos are of different flavor?

Since they are invisible, we don´t see their paths, deflected or not.

 

[pines-demon]

No, it would not. You need incredibly extreme neutrino density for there to be collisions.

Maybe a secondary question. If we had like a huge cloud of neutrinos (probably is the size of the milky way). What differences one expects from non-interacting neutrino gas from the interacting one?

 

[pines-demon]

Since they are invisible, we don´t see their paths, deflected or not.

I mean I was asking about experiments, so one could have two beams of neutrinos that intersect and detect their scattering directions.

 

[mfb]

In principle, yes - shoot two beams at each other and look for neutrinos scattered at an angle - but the cross sections are many orders of magnitude too small to make this work. We can't even observe the inelastic process neutrinos -> leptons/hadrons and there we would have a useful detection efficiency for the products.

 

[snorkack]

In principle, yes - shoot two beams at each other and look for neutrinos scattered at an angle - but the cross sections are many orders of magnitude too small to make this work. We can't even observe the inelastic process neutrinos -> leptons/hadrons and there we would have a useful detection efficiency for the products.

How good are the existing neutrino detectors at spotting invisible -> visible processes?
A high energy neutrino arrives with tiny rest mass. Which means that the total momentum of products is tightly tied to the their energy. When these don´t match, does that stick out?
Neutrino-neutrino inelastic collision would release energy into the visible particles but not enough momentum (because that is partly cancelled). How about other improbable processes - proton decay, wimp decay, wimp annihilation etc.? Do neutrino detectors incidentally look for all such rare and improbable events?

 

[Orodruin]

Which means that the total momentum of products is tightly tied to the their energy.

I don't understand why you think this. The total momentum of the neutrino would be essentially the same as the neutrino energy. That does not impose any direct constraints on the products. In particular not if, as the OP suggests, you collide a neutrino with another neutrino. You will have some CoM frame that has some total energy available for the products and some speed relative to the lab frame.

How about other improbable processes - proton decay, wimp decay, wimp annihilation etc.? Do neutrino detectors incidentally look for all such rare and improbable events?

It is the other way around originally. Detectors looking for proton decays found neutrinos from varying sourcese. KamiokaNDE was short for Kamioka Nucleon Decay Experiment. Of course, neutrino detectors today could look (and do look) for other rare processes.

WIMP decay or WIMP annihilation would require WIMPs to actually be present at the detector. It would be significantly easier to look for indirect evidence of such processes in astrophysical settings in general, which is what people do.

 

[snorkack]

I don't understand why you think this. The total momentum of the neutrino would be essentially the same as the neutrino energy. That does not impose any direct constraints on the products. In particular not if, as the OP suggests, you collide a neutrino with another neutrino. You will have some CoM frame that has some total energy available for the products and some speed relative to the lab frame.

That´s why I suggested that the neutrino-neutrino collision might be somewhat distinct.
You start with a test mass of stable, cold and transparent (in certain range) matter. All common processes to create energetic particles there have been ruled out. For example, few high energy charged particles (such as muons) enter - and when they do, they are tracked coming in and identified.
This leaves only uncommon processes.
But some of these I thought would have constraints on energy, momentum, spin and flavour.

• Absorption of neutrino - since the neutrino has little rest mass, it is bound to have momentum p≅E/c in some direction of space. Which means that the energy and momentum deposited in the products must match strictly, and the products must also receive the spin (1/2) and flavour (one lepton or antilepton)
• Elastic scattering of neutrino - since the initial neutrino continues to fly on, its flavour cannot be deposited. The momentum of products seem to me should be bigger than E/c - consider the example of a neutrino Rutherford reflected straight back, then the momentum of products would be almost 2E/c, but the energy of the products would be the recoil energy of the massive target. Even if the neutrino proceeds direct forward and is just decelerated, the moment Δp delivered on the products must be ΔE/c
• Collision of two neutrinos - since their momenta partly cancel, the released momentum would be smaller than E/c, because the energies add as scalars but momenta as vectors.

So, do the detectors show this kind of details, which would identify discrepancies with more likely alternative reactions?

 

[ohwilleke]

Sticking to the headline question:

"What do we know about neutrino-neutrino scattering?",

and not the OP body text, we can calculate what we expect to happen in the Standard Model as extended to include neutrinos to high precision. While it isn't a trivial calculation, it isn't that hard to calculate for either an elastic or inelastic collision (and no one is expecting the extreme parts per billion precision of the muon g-2 calculation, parts per thousand precision would be welcome and sufficient for a first attempt and unlike muon g-2 at a first attempt level of precision, hadronic QCD contributions which are the main source of uncertainty in the muon g-2 prediction, would be small enough to ignore in the calculations of predicted neutrino scatterings). At the calculation level, we can leverage the knowledge of physical constants and efficient calculation methods and the structure of the Standard Model from non-neutrino contexts to make our "educated guess" a very well informed one. Having such a narrow and precisely defined target signal to look for could also facilitate great efficiencies in designing the experimental setup.

And, there are enough experiments measuring neutrino properties that we can say with considerable comfort that neutrinos behave consistently with the neutrino extended Standard Model. In particular, there are lots of experiments that have searched for non-standard neutrino interactions, and while individually, no one experiment can rule out all possible non-standard neutrino interactions definitively, collectively, none of them have found statistically significant evidence of non-standard neutrino interactions that have been replicated and confirmed, although there have been occasional minor tensions interpreted as statistical flukes.

I would also quibble with the characterization of neutrinos as "invisible", although they are far harder to detect (especially at low energies) than charged particles, and than more massive neutral particles. We have detectors specifically designed to detect neutrinos and they do routinely detect neutrinos. They aren't very efficient (i.e. they detect only a modest percentage of neutrinos that pass near them) but they are not 0% efficient either.

As a practical matter it would be a very expensive experiment (because you have to increase the scale sufficiently to get a statistically significant number of detection events after all of the events you miss due to detector inefficiency). It would also require a very good characterization of the neutrino background from neutrinos other than the ones you are trying to collide that would swamp the signal you are looking for. But progress is being made at developing labs in places like deep mineshafts to reduce the background noise (e.g. from cosmic ray muons that produce neutrinos when they decay), and progress is also being made at characterizing the background accurately, for the purpose of direct dark matter detection experiments. This characterization of the neutrino background could be borrowed from these experiments.

Is this viable to do in a direct, brute force manner right now? Probably not.

But it isn't beyond the range of what might be possible to do in a laboratory setting at some point in the future. Also, someone might come up with a more subtle and efficient and tractable way to measure this in the future than just crudely shooting beams of neutrinos at each other and surrounding them with massive arrays of neutrino detectors.

Neutrino physics is the youngest part of the Standard Model. The discovery that they are massive and oscillate was only made in 1998, and we are still working out the approximate values of the last few physical constants that describe neutrino oscillation and mass now. Important parts of neutrino physics are a quarter century behind other parts of Standard Model physics. But that doesn't mean that we couldn't get there some day.

 

[Orodruin]

And, there are enough experiments measuring neutrino properties that we can say with considerable comfort that neutrinos behave consistently with the neutrino extended Standard Model. In particular, there are lots of experiments that have searched for non-standard neutrino interactions, and while individually, no one experiment can rule out all possible non-standard neutrino interactions definitively, collectively, none of them have found statistically significant evidence of non-standard neutrino interactions that have been replicated and confirmed, although there have been occasional minor tensions interpreted as statistical flukes.

This depends on what you imply with "considerable" comfort. People are very good at coming up with new models that would imply non-standard neutrino interactions in different places. Most people I know that work on neutrino NSIs have entered believing that they should be able to kill them off completely or at least severely constrain them, but they always seem to pop back out by people making up new models that evade bounds. Given a particular model, it is usually relatively easy to provide strong bounds, but it is more difficult to do so completely model-independently.

In particular, neutrino-neutrino interactions mediated by a scalar interaction would have a very particular asymmetric flavour structure, but induce no NSIs in neutrino interactions with charged leptons at tree level.

I would also quibble with the characterization of neutrinos as "invisible", although they are far harder to detect (especially at low energies) than charged particles, and than more massive neutral particles. We have detectors specifically designed to detect neutrinos and they do routinely detect neutrinos. They aren't very efficient (i.e. they detect only a modest percentage of neutrinos that pass near them) but they are not 0% efficient either.

"Modest percentage" is pushing it. The percentage is almost zero. The SuperK event rate for boron-8 neutrinos is around 300 per day (without oscillations, less with). Compare this to how many solar neutrinos pass through the SuperK detector per second - the solar neutrino flux is around $7 \cdot 10^{10}$ per cm ² per second.

But it isn't beyond the range of what might be possible to do in a laboratory setting at some point in the future. Also, someone might come up with a more subtle and efficient and tractable way to measure this in the future than just crudely shooting beams of neutrinos at each other and surrounding them with massive arrays of neutrino detectors.

People already have. Neutrino-neutrino interaction would play a significant role in the flavour evolution for supernova neutrinos. There is a lot of literature on this subject. The problem is waiting for a nearby supernova and making sure you have some good detectors running.

Neutrino physics is the youngest part of the Standard Model. The discovery that they are massive and oscillate was only made in 1998, and we are still working out the approximate values of the last few physical constants that describe neutrino oscillation and mass now. Important parts of neutrino physics are a quarter century behind other parts of Standard Model physics. But that doesn't mean that we couldn't get there some day.

While you can extend the SM by neutrino mixing and masses in a quite model independent way, it is still unclear what the mass generating mechanism is (and we may never know for sure).

 

[ohwilleke]

This depends on what you imply with "considerable" comfort. People are very good at coming up with new models that would imply non-standard neutrino interactions in different places. Most people I know that work on neutrino NSIs have entered believing that they should be able to kill them off completely or at least severely constrain them, but they always seem to pop back out by people making up new models that evade bounds. Given a particular model, it is usually relatively easy to provide strong bounds, but it is more difficult to do so completely model-independently.

But there is also no positive evidence for NSIs.

"Modest percentage" is pushing it. The percentage is almost zero. The SuperK event rate for boron-8 neutrinos is around 300 per day (without oscillations, less with). Compare this to how many solar neutrinos pass through the SuperK detector per second - the solar neutrino flux is around $7 \cdot 10^{10}$ per cm ² per second.

If you could get 300 events a year over ten years, that would be enough.

People already have. Neutrino-neutrino interaction would play a significant role in the flavour evolution for supernova neutrinos. There is a lot of literature on this subject. The problem is waiting for a nearby supernova and making sure you have some good detectors running.

Not as clean as would be ideal, but yes.

While you can extend the SM by neutrino mixing and masses in a quite model independent way, it is still unclear what the mass generating mechanism is (and we may never know for sure).

It isn't clear to me that the mass generating mechanism would be relevant to neutrino-neutrino scattering.

 

[Orodruin]

But there is also no positive evidence for NSIs.

Indeed not, but still models allowing relatively large NSIs keep popping up like weed. Absence of evidence is not evidence of absence. Just constraints. And constraints are often model dependent. This is why model independent bounds on NSI remain fairly weak whereas model dependent bounds generally do better. Often the model dependent bounds can be put by involving other effective operators the model would also give rise to.

Even loop level bounds (ie, connecting neutrino legs with a W and thus turning a diagram with external neutrinos into a diagram with charged leptons) suffer from generally being model dependent.

If you could get 300 events a year over ten years, that would be enough.

Its 300 events per day. But that was not the point, the point was that this is a miniscule fraction of all solar neutrinos passing through the detector, which is order $10^{23}$ per day. That’s a detection efficiency of order 0.0000000000000000001%, which I would not call ”a modest percentage”.

I think it was Borexino that at some point produced a popular scientific cartoon featuring ”Nino the neutrino”, a solar neutrino heading towards Borexino and looking forward to being detected. Of course the end was tragic. Both Nino and most of its friends just passed through both the Earth and the detector …

It isn't clear to me that the mass generating mechanism would be relevant to neutrino-neutrino scattering.

That wasn’t a comment on scattering. It was a comment regarding the general state of neutrino physics and highlighting the fact that learning the standard oscillation parameters will not be sufficient to obtain a satisfactory model (in the sense of understanding where the masses come from) - although perhaps a model that is sufficient to describe observations.

 

[snorkack]

Its 300 events per day. But that was not the point, the point was that this is a miniscule fraction of all solar neutrinos passing through the detector, which is order $10^{23}$ per day. That’s a detection efficiency of order 0.0000000000000000001%, which I would not call ”a modest percentage”.

Which was the context in which I meant "invisibility". It is massively unlikely to detect two neutrinos that interact in the same event, let alone detect all four neutrinos that do.

 

[ohwilleke]

Which was the context in which I meant "invisibility". It is massively unlikely to detect two neutrinos that interact in the same event, let alone detect all four neutrinos that do.

A recently observed rare kaon decay took observations of the decays of 400 billion kaons produced in many trillions of collisions over six years to observe. Highly improbable things are observed on a regular basis in particle physics. (And, the statement about 300 a day was implying that a much lower number of events than what SuperK sees would be all that would be necessary.) It would certainly be difficult, but scientists are remarkably good at doing very difficult things.

 

[Orodruin]

A recently observed rare kaon decay took observations of the decays of 400 billion kaons produced in many trillions of collisions over six years to observe. Highly improbable things are observed on a regular basis in particle physics. (And, the statement about 300 a day was implying that a much lower number of events than what SuperK sees would be all that would be necessary.) It would certainly be difficult, but scientists are remarkably good at doing very difficult things.

I think you are missing the point about just how rare it would be to see elastic neutrino-neutrino scattering, which is what @snorkack is discussing. Apart from controlling the incoming neutrino energies, which is nigh impossible by itself by the very nature of how neutrino beams can be produced, you would need to measure both of the scattered neutrinos to confirm an increase in double-neutrino events at the appropriate invariant mass. With a detection rate of one in $10^{23}$ for each scattered neutrino, this would imply both scatters are detected with a probability of order $10^{-46}$. This would require about a factor $10^{35}$ more neutrino-neutrino scatters than the number of Kaon decays in your example (probably closer to $10^{36}$ if you also want statistics, but who’s counting?) And then it is also significantly easier to get to observe produced particles decaying than to get neutrinos to scatter off eachother.

TLDR; Don’t hold your breath.