# Neutrino Masses and Speed

It was hard to miss the 2011 OPERA neutrino speed measurement that indicated superluminal neutrino speeds (and turned out to be a measurement error), but measurements of neutrino masses and speeds have a long tradition.

Neutrinos are very light particles that interact via the weak interaction and gravity only. There are three types of neutrinos: electron neutrinos, muon neutrinos and tau neutrinos (and their corresponding antiparticles). Neutrinos are mainly produced in beta decays and some fusion reactions.
Their weak interaction makes it hard to detect them – they can travel through the whole Earth easily with a tiny probability of an interaction. Neutrino experiments need huge detectors (up to some cubic kilometers) to find them at a reasonable rate.

Neutrino discovery
The electron neutrino was predicted in 1930 based on beta decays. Without the neutrino, it would be a two-particle decay, the electron would always be emitted with the same energy, and the remaining atom would always get a fixed (smaller) energy as well. Experiments clearly showed a continuous spectrum of the electron energy, so a third particle has to take the missing energy (and momentum) away.

Quantum mechanics allows to predict the electron energy spectrum depending on the (known) electron mass and the unknown neutrino mass. Observations quickly revealed that this new particle has to be very light compared to the electron – the experiments were just able to set upper limits. It had to be so extremely light that physicists expected it to be completely massless.

The electron neutrino was detected directly in 1956 (based on neutrinos from a nuclear reactor), without a better way to measure its mass. The muon and tau neutrino were discovered later, but the corresponding muon and tau decays are so high-energetic that it is hard to estimate the neutrino mass – only very high upper limits (~0.2 MeV, 18 MeV) are known from those decays. But why should we bother, if the particles are massless anyway?

Neutrino mixing
The Homestake experiment in the 1960s was designed to measure neutrinos from the sun. Neutrinos there could react with chlorine and produce radioactive argon plus an electron. The produced argon (about two atoms per day) was collected and the decays were measured. The observed rate was only 1/3 of the predicted rate. It was sufficient to confirm that nuclear fusion is the source of solar power, but as more experiments saw the same discrepancy something had to be wrong. This became known as the “solar neutrino problem”.

The chlorine to argon reaction is possible with electron neutrinos only. It was proposed that the different types can transform into each other. This “neutrino mixing” requires non-zero neutrino masses. The Sudbury Neutrino Observatory was the first experiment that could clearly detect muon and tau neutrinos coming from the sun.[1] It used heavy water, all neutrino types can split this into neutron plus proton, the neutron then gets captured and emits a high-energetic photon. The electron neutrino has the additional option to convert a neutron into a proton and an electron. That way, both the total neutrino flux and the flux of electron neutrinos could be measured. The experiment could confirm neutrino mixing. Later, mixing was also discovered in neutrinos from atmospheric muon decays and from neutrino beams from particle accelerators.

The mixing experiments show that neutrinos do have mass, but how large are they? Unfortunately, neutrino mixing does not allow to measure the masses directly. It mainly allows to find the absolute differences of the squared masses. One difference is about (75±2) meV2 and the other two are about (2450±50) meV2. The absolute differences mean the ordering of the masses is not known. There are two options – two lighter types and one heavier type (“normal ordering”) or one lighter type and two heavier types (“inverted ordering”). While the absolute masses could be anything, heavy neutrinos (a few hundred meV or more) would mean all three would have extremely similar masses in both cases. At least one type needs a mass of at least 50 meV.
Side remark: Mixing implies that the flavour eigenstates (“electron neutrino”, …) are not mass eigenstates (“m=123 eV”), so strictly speaking something like “the mass of an electron neutrino” does not exist. What experiments really measure is a superposition of mass eigenstates – I’ll ignore this detail here.

Tritium decay electron energy spectrum. Plotted by user Zykure at Wikipedia.

Current status
The current best direct upper limit on the electron neutrino mass comes from tritium beta decay: the mass has to below 2 eV.[2] Combined with mixing experiments, all three masses have to below 2 eV.

Another interesting way to measure neutrino masses comes from cosmology. In the early universe neutrinos were an important contribution to the energy density in the universe. The way they “cool” (and reduce their energy density) with expansion depends on the mass, it is different for relativistic particles and non-relativistic particles. This leaves traces in the cosmic microwave background. Planck and other experiments constrain the sum of the three neutrino masses, it has to be below 230 meV.[3] The precise value depends a bit on the model used.

At first glance, a measurement of the neutrino speed looks like a nice way to estimate neutrino masses: measure energy and speed, and relativity tells you the mass. Well… a 1 MeV neutrino from a nuclear reaction with a mass of 1 eV travels at roughly (1-10-12) times the speed of light. For a 1 GeV neutrino from an accelerator this gets even worse with (1-10-18). While light travels 1000 kilometers, the neutrino just gets behind by 1 nanometer or 1 femtometer respectively.
There is no way to see such a tiny difference, so measurements are expected to be consistent with the speed of light. Those measurement are still interesting: apart from light, the neutrinos should be the fastest things where we can measure the speed. It is a test of special relativity. In 2011 the OPERA collaboration announced that their measurements seem to indicate neutrinos that are faster than the speed of light by one part in 40,000.[4] They later discovered that a loose cable spoiled clock synchronisation at one point, and published updated results that are in agreement with the speed of light.[5] Due to the increased interest, multiple other experiments performed speed measurements, the most recent one (MINOS) this week[6]. All results agree with the speed of light, and a deviation has to be smaller than 1 part in 500,000.
This precision is remarkable – it requires to synchronize clocks with a precision of nanoseconds, and distance measurements as precise as a millimeter per kilometer. All the detectors are deep underground, where GPS does not work. In addition, how do you keep clocks synchronized if relativistic time dilation tells you the clocks at the accelerator site run faster than the clocks at your detector?

Again, astronomy gives a different approach. Experiments on Earth are limited by the size of Earth, sources in space give much longer baselines. Those sources are rare – supernova SN1987A is the only one where detected neutrinos could clearly be related to the supernova event. The neutrinos (24 detected in total) were detected about three hours before the visible light of the supernova reached Earth. No superluminal neutrinos here either, however – the supernova is not designed for our precision experiments. The neutrinos get emitted at the time the core collapses, it takes some time until the explosion reaches the surface. Supernova models allow to estimate this, and neutrino detectors can compare the arrival time of lower-energetic and higher-energetic neutrinos. This allows to constrain the neutrino speed to be close to the speed of light within 2 parts in a billion. It also translates to an upper limit of about 6 eV for neutrino masses.[7] The measurement is 28 years old, current detectors should be able to get much better results with a new supernova in a suitable distance.

Future experiments

The KATRIN experiment currently tries to push those limits down to 0.2 eV.[2] KATRIN does not study the whole spectrum. The electrons can have up to 18.6 keV kinetic energy, it is sufficient to study electrons above 18.5 keV only. A non-zero neutrino mass changes the shape at the very end of the spectrum slightly. There is no detector that can measure an electron energy of 18.6 keV as precise as 1 eV, so an electrostatic filter has to be installed that blocks all electrons below a specific energy. The measured rate of electrons passing the filter then gives the total fraction of electrons above the filter energy. Roughly one electron in five trillion is within the last eV of the spectrum, one in six hundred trillion within the last 0.2 eV (if the neutrino is lighter than that). To find those rare events, the decay rate has to very high and the background has to be understood very well. In addition, multiple effects limit the energy resolution – the tritium molecules can get some (variable) part of the energy for molecular excitations, electrons can scatter on their way to the detector, a completely homogeneous electric field for the filter is not possible and other issues.

While the 50 meV discussed above is only a lower limit, it is often expected that the heaviest neutrino is not much heavier than that. Several experiments try to reach this sensitivity. Cosmological constraints could get better and distinguish between normal and inverted ordering. More sensitive mixing experiments are another option: the main effect is independent of it, but smaller deviations depend on the ordering. When neutrinos travel through matter, they rarely make a hard interaction, but they are still surrounded by an electron field which alters their effective mass (in the same way electrons in metals behave different from free electrons). Therefore, mixing in matter is different from mixing in space, and the difference depends on the ordering.

Multiple experiments aim to determine the correct ordering within the next 5 to 10 years. Absolute mass measurements might follow.

Cosmology and beta decay lab experiments could come together in the future: PTOLEMY aims to directly detect the relic neutrino background from the big bang, and measure the energy of beta decays much more precisely than before.

An incomplete list of future neutrino experiments (planned or under construction):
DUNE
INO
JUNO
KATRIN
PROJECT8

Tags:
28 replies
1. PWiz says:

The neutrino said "nice post!". The neutrino read the physics insight post.#causalityjokes

2. Orodruin says:

Latest news in the neutrino sector: The first T2K anti-neutrino data was presented at the EPS-HEP conference this morning (see slides [URL=’https://indico.cern.ch/event/356420/session/10/contribution/322′]here[/URL]).

Summary: T2K observes 3 ##barnu_e## candidates. The expectation (including background) for ##delta_{CP} = -pi/2## and normal mass ordering is 3.7, with the expectation for any other combination of the neutrino parameters being larger. On its own, this is not yet enough to rule out the no-oscillation hypothesis in the anti-neutrino run, but the result is suggestively close to the expectation of the previous hint on ##delta_{CP}## from the combination of T2K neutrino results with reactor neutrino data. Exciting times!

3. Orodruin says:

Another update: OPERA now has 5 ##nu_tau## events, finally reaching the ##5sigma## level for the appearance of ##nu_tau##s in a ##nu_mu## beam. It does not do much in terms of determining the oscillation parameters, but it is an important consistency check.

4. ChrisVer says:

@Orodruin With 3 anti-nu events, how can this be an exciting time?
Or is it going near the expectation for δcp=-π/2 and normal hierarchy?

5. Orodruin says:

@Orodruin With 3 anti-nu events, how can this be an exciting time?
Or is it going near the expectation for δcp=-π/2 and normal hierarchy?

Well, first of all, T2K is getting antineutrino data. Getting both neutrino and antineutrino data is important in looking for CP violation (naturally). Second, the hint for maximal CP violation from T2K neutrino data is (assuming standard oscillations) an up-fluctuation regardless of where you are in parameter space. This is further accentuated by the fact that there is some tension with reactor data. Until the antineutrino run, essentially all there was was an up-fluctuation which was most likely in the case of maximal CP violation. Now there is a number of antineutrino events which are not statistically significant on their own, but suggestively twinkling their eyebrows at the previous best fit. We will know more over the coming years as T2K accumulates more data in the antineutrino run.

Also, more events would have been less exciting. It is the fact that there are hardly any events which is the signature trademark of ##delta_{CP} = -pi/2##.

6. strangerep says:

Current status
The current best direct upper limit on the electron mass comes from tritium beta decay: the mass has to below 2 eV.[URL=’https://www.physicsforums.com/insights/neutrino-masses-speed/#ref1′][2][/URL] Combined with mixing experiments, all three masses have to below 2 eV.

Typo? Should that be “electron neutrino mass” ?

7. mfb says:

Typo? Should that be “electron neutrino mass” ?

Oh sure. Fixed, thanks.

8. Ygggdrasil says:

Kajita and McDonald just won the Nobel prize in physics for their discovery of neutrino oscillations, which showed that neutrinos have mass. [URL]http://www.nobelprize.org/nobel_prizes/physics/laureates/2015/press.html[/URL]

9. ChrisVer says:

Kajita and McDonald just won the Nobel prize in physics for their discovery of neutrino oscillations, which showed that neutrinos have mass. [URL]http://www.nobelprize.org/nobel_prizes/physics/laureates/2015/press.html[/URL]

I think they didn’t know to whom to award the prize… afterall the solar neutrino problem was the most important indication for neutrino oscillations and the nobel prize was awarded because of that.

10. vanhees71 says:

[URL]http://www.nobelprize.org/nobel_prizes/physics/laureates/2002/[/URL]

I think this year’s prize is very well deserved. It’s among the most interesting discoveries in fundamental particle physics of the recent years (including the discovery of the Higgs in 2012 with Nobel prizes in 2013).

11. ChrisVer says:

That’s why personally I didn’t find the prize of this year any more interesting than the one (worthfully) awarded in 2002.

12. Oceans_Unmoving says:

I’m having trouble understanding why oscillations prove that neutrinos have mass. Why couldn’t a massless particle oscillate?

13. ChrisVer says:

Neutrino flavors (electron, muon and tau) are not mass eigenstates, but rather a mixture of mass eigenstates ν_1 , ν_2 & ν_3. As a result when you want to let the flavor neutrinos to propagate in time via the Hamiltonian (recall from QM that the state evolution with time is equal to the Hamiltonian operator acting on the state) you get for example:
$$nu_e(t)= e^{iHt} nu_e (0)$$
now since the Hamiltonian is giving the energy when acting on mass eigenstates you’re better to write the RHS of the equation in mass eigenstates and then you will obtain an exponential having the mass squared of the i-th eigenstate.
Finally as known from QM the probability of a transition from electron neutrino for example to muon is the square of the amplitude of those 2- that square brings in an additional mass squared of the j-th eigenstate and together with the first you get an o)cillation pattern for the probability governed by also the difference of the squared masses.
If they were zero (massless neutrinos), or I think degenerate (I’m not sure about this but I just put it to be checked) the oscillations would not occur and an electron neutrino would propagate as an electron neutrino forever. If there is any difference to the masses squared, oscillations occure and you have transitions.
So the fact that we saw missing electron neutrinos from the sun was telling us neutrinos are massive :razz:

14. Orodruin says:

I think they didn’t know to whom to award the prize… afterall the solar neutrino problem was the most important indication for neutrino oscillations and the nobel prize was awarded because of that.

The 2002 prize was awarded for the detection techniques used in neutrino astronomy, not for any oscillation measurement. The Super-Kamiokande atmospheric neutrino result is widely considered the first evidence for actual neutrino oscillations, the solar neutrino problem could have had other explanations. By measuring the total flux of neutrinos of any flavour and comparing with the electron neutrino flux, SNO was able to confirm that neutrinos do change flavour on the way from the Sun.

One curious thing to mention is that the solar neutrino flavour conversion mechanism is not really oscillations per se, at least not for the high energy boron-8 neutrinos, but rather resonant matter enhanced flavour conversion. Essentially all boron-8 neutrinos arriving at Earth do so in the second mass eigenstate.

15. Shyan says:

I know that Bruno Pontecorvo is dead now and people can’t give him any prize, but why no mention of his name?

16. Orodruin says:

I know that Bruno Pontecorvo is dead now and people can’t give him any prize, but why no mention of his name?

He was mentioned in the detailed presentation by the Royal Academy, but this is not something that media picks up on. It is not usually the case to mention other people in the short motivation which in this case was “for the discovery of neutrino oscillations, which shows that neutrinos have mass”.

17. Shyan says:

He was mentioned in the detailed presentation by the Royal Academy, but this is not something that media picks up on. It is not usually the case to mention other people in the short motivation which in this case was “for the discovery of neutrino oscillations, which shows that neutrinos have mass”.

Would he share the prize if he was alive?

18. Orodruin says:

Would he share the prize if he was alive?

I think that is a hypothetical question that only the Nobel committee could answer if anyone – and even if they knew the answer they would not tell anyone. The first step would have been to have someone nominating him, but I think that would be a minor hurdle.