## Saturday, 14 May 2016

### Plot for Weekend: new limits on neutrino masses

This weekend's plot shows the new limits on neutrino masses from the KamLAND-Zen experiment:

KamLAND-Zen is a group of buddhist monks studying a balloon filled with the xenon isotope Xe136. That isotope has a very long lifetime, of order 10^21 years, and undergoes the lepton-number-conserving double beta decay Xe136 → Ba136 2e- 2νbar. What the monks hope to observe is the lepton violating neutrinoless double beta decay Xe136 → Ba136+2e, which would show as a peak in the invariant mass distribution of the electron pairs near 2.5 MeV. No such signal has been observed, which sets the limit on the half-life for this decay at T>1.1*10^26 years.

The neutrinoless decay is predicted to occur if neutrino masses are of Majorana type, and the rate can be characterized by the effective mass Majorana mββ (y-axis in the plot). That parameter is a function of the masses and mixing angles of the neutrinos. In particular it depends on the mass of the lightest neutrino (x-axis in the plot) which is currently unknown. Neutrino oscillations experiments have precisely measured the mass^2 differences between neutrinos, which  are roughly (0.05 eV)^2 and (0.01 eV)^2. But oscillations are not sensitive to the absolute mass scale; in particular, the lightest neutrino may well be massless for all we know.  If the heaviest neutrino has a small electron flavor component, then we expect that the mββ parameter is below 0.01 eV.  This so-called normal hierarchy case is shown as the red region in the plot, and is clearly out of experimental reach at the moment. On the other hand, in the inverted hierarchy scenario (green region in the plot), it is the two heaviest neutrinos that have a significant electron component. In this case,  the effective Majorana mass mββ is around 0.05 eV.  Finally, there is also the degenerate scenario (funnel region in the plot) where all 3 neutrinos have very similar masses with small splittings, however this scenario is now strongly disfavored by cosmological limits on the sum of the neutrino masses (e.g. the Planck limit Σmν < 0.16 eV).

As can be seen in the plot, the results from KamLAND-Zen, when translated into limits on the effective Majorana mass, almost touch the inverted hierarchy region. The strength of this limit depends on some poorly known nuclear matrix elements (hence the width of the blue band). But even in the least favorable scenario future, more sensitive experiments should be able to probe that region. Thus, there is a hope  that within the next few years we may prove the Majorana nature of neutrinos, or at least disfavor the inverted hierarchy scenario.

mfb said...

> Neutrino oscillations experiments have precisely measured the mass differences between neutrinos, which are roughly 0.05 eV and 0.01 eV.

They do not measure mass differences. They can only measure the (absolute) differences of squared masses. If the lightest neutrino is very light (~1 meV), then you get those numbers as approximate differences in the masses. If the lightest neutrino has a mass of e.g. 50 meV, then the heaviest one is just ~20 meV heavier and the last one is extremely close to one of those.

KamLAND observed a better limit than expected due to statistical fluctuations, improving that significantly will take some time.

Jester said...

That's right, I should not have omitted the squares. Fixed.

Abraham said...

If neutrinos are massive and if they travel at light speed,what might be the implications for the validity of special relativity?

Thanks

Abraham

Alex said...

It's crazy that these bounds have fallen by roughly two orders of magnitude in less than a decade. Hope we can actually nail them down soon.

mfb said...

@Abraham: Neutrinos are expected to be a tiny bit slower than the speed of light - something like one part in 10^15 (but depending on their energy), which means experimentally we don't see a significant difference to the speed of light.

Anonymous said...

I have a hard time grasping the meaning of "a tiny bit slower than the speed of light". I'm just a layman, but I thought something either travels at the speed of light, or else it is in an inertial frame of reference and it's speed can only be measured relative to other objects in inertial frames of references. If a neutrino were emitted from a decaying neutron that was moving away from us at extremely high velocity, we ought to measure it's velocity (assuming there was a way to do so) as being very much slower than the speed of light, not just "a tiny bit slower", not so?

Unknown said...

Anonymous: yes, that's right, but as you say, that object would have to be moving away *extremely* fast. And because the mass is so small, any appreciable amount of energy is going to correspond to a really huge velocity. So a slow neutrino, if you could get one, would be hard to detect at all due to having a very, very small energy.

All the neutrinos we normally talk about detecting, and all the ones generated by things like nuclear reactors in our reference frame, are moving relative to us at very close to the speed of light.

Anonymous said...

However these limits suppose neutrino is Majorana particle. But how can be neutrino Majorana particle (i.e. its own antiparticle), if neutrino and antineutrino have different characterictics, e.g. opposite chirality? How can two particles experimentally proven to be different be supposed to the same? It's like claiming that one is equal to two.

Alex Small said...

Searching for Majorana particles with KamLAND-Zen sounds like what sine chemistry grad students did when I was in school, but they got in trouble with the DEA.

Unknown said...

Anonymous: neutrinos and antineutrinos have NOT been proven to be different. That's the reason experiments like this are done: to find out whether they have different characteristics or not. No one knows whether they do.

mfb said...

@Anonymous 01:29: There are a few slow neutrinos around (no need to have high-speed neutrons: in every beta decay energy is shared between neutrino and electron, without a minimal energy for them), but their number is completely negligible. More than 99.9999% of the neutrinos should be faster than 99.99999% the speed of light - and I guess I could add more "9" with an actual calculation. This statement is independent of the reference frame.

mfb said...

For clarification: the numbers in my previous comment are for neutrinos we use for speed measurements (accelerator-based or from supernovae). There are many neutrinos left from the big bang, they form the cosmic neutrino background. They could be quite slow, but they are really hard to see, and as we don't know where exactly they come from we cannot measure their speed even if we can find them in the future (PTOLEMY is a proposed experiment for finding those neutrinos: https://arxiv.org/abs/1307.4738 ).

Anonymous said...

Xezlec:

Sorry, but the very first detection of neutrinos used reaction Cl + nu -> Ar + e- and it measured neutrino deficit of 1/3, what was correct (neutrino oscillation were not known at that time). If neutrino and antineutrino were the same, the reaction Cl + nu -> S + e+ also would take place and the measured deficit would be 1/6. From that times, all neutrino detectors were constructed to measure either neutrinos or antineutrinos and no evidence against the assumption that neutrino and antineutrino are different was found.

Alex Small said...

What if neutrinos are Majorana particles but the mass hierarchy is normal and the rate of 0vBB decays is way too low to detect for a few decades? Are there other ways of deciding the Dirac vs Majorana question? Are there processes where you would get a factor of two difference in a rate because Dirac neutrino fields are 4-component objects while Majorana neutrino fields are 2-component objects?

Alternately, what are the prospects for getting the absolute neutrino mass scale from cosmological observations in the next ten years?

Jester said...

Alex, I think the answer is negative: the 2 additional Dirac components are decoupled and cannot be observed. The only way to see the Majorana nature is to observe lepton violating processes, which are forbidden in the Dirac case.

As for the cosmology, in the standard scenario it can only tell us the sum of the neutrino masses, so if the lightest one is much lighter than the others it will contribute little to the sum and thus we will not be able to pin down its contribution.

Jester said...

Concerning the discussion of neutrino vs anti-neutrino above, I think there's some confusion here. Whether in the Majorana or Dirac case, what we traditionally call the neutrino is distinct from the anti-neutrino, because it has a different helicity (-1/2 vs 1/2). So one cannot say that the Majorana neutrino and anti-neutrino are the same objects: they interact differently with matter. What distinguishes the Majorana neutrino is that it doesn't carry any conserved quantum number, in particular lepton number is violated.

mfb said...

Cosmology together with mixing can work to fix the masses. If cosmology determines the sum of neutrino masses to be <80 meV, then we know they have normal ordering and we know that two are quite light. The uncertainty for the lighter two (with increasing precision and assuming the lightest one is below 10 meV: the lightest one) would be determined by the uncertainty on the sum, as the mass of the heavier one can be determined much more accurately then.

Alex Small said...

So, in practice, Majorana neutrinos are something that can be ruled in but not ruled out?

Unknown said...

Jester: if that's the case, someone ought to update the Wikipedia article for "Majorana fermion", which states that a Majorana fermion is its own antiparticle. You're saying it isn't, right? Also, isn't helicity a reference-frame-dependent quantity? I am now really confused.

Alex Small said...

Anon@21:25-

An electron anti-neutrino is right-handed, and it can be absorbed by a proton to produce a neutron and a positron. An electron neutrino is left-handed, and it can be absorbed by a neutron to produce a proton and electon. The big question, which nobody knows the answer to, is what would happen if you switched to a reference frame where the helicity flips? If neutrinos are Majorana particles then when you switch reference frames an electron neutrino turns into an electron anti-neutrino that can be absorbed by a proton to produce a neutron and a positron, and an electron anti-neutrino turns into an electron neutrino that can be absorbed by a neutron to produce a proton and electron.

If neutrinos are Dirac particles then when you switch reference frames the left-handed electron neutrino turns into a right-handed particle that can't do anything, and the right-handed electron anti-neutrino turns into a left-handed particle that can't do anything.

Jester said...

Xezlec "...Wikipedia article for "Majorana fermion", which states that a Majorana fermion is its own antiparticle." This is a simplification. The point is that a Majorana fermion describes *two* states, not one. For a relativistic Majorana fermion these two states have opposite helicities. If the mass is small, there is a fermion number +/-F associated with the two helicities which is approximately conserved. Then we can call one state fermion and the other state anti-fermion. This is the case for Majorana neutrinos: the mass is small and the lepton number is always conserved (so far). Therefore we can label one of the states neutrino and the other antineutrino, and the two are unambiguously distinguished by the value of the lepton number. What is meant in the Wikipedia article is that, since lepton number is ultimately violated for Majorana neutrinos, this distinction fails for some rare processes. But it does not change the fact that the two neutrino states are distinct, and have distinct interactions.

Alex, yes, I think that unless someone has a new brilliant idea, in practice we can only confirm the Majorana nature but never exclude it.

Brian Dolan said...

It seems to me that there is a confusion in the discussion between helicity and chirality . The physical properties of a neutrino (or any fermion for that matter) are determined by its chirality, which comes in two forms: positive and negative. Helicity also comes in two forms, right and left handed. Chirality is Lorentz invariant and cannot be changed by a boost, but helicity can be flipped by a boost.

Helicity and chirality are the same thing for a massless particle but not for a massive particle (no matter how small the mass). For this reason chirality is often referred to as right or left handed, to add to the confusion.

An electron neutrino cannot turn into an anti-neutrino by switching reference frames.

JPH said...

Jester: "Alex, yes, I think that unless someone has a new brilliant idea, in practice we can only confirm the Majorana nature but never exclude it."

Wait, you're saying that there's no observable that can definitively conclude a particle is a Dirac fermion? Don't they have a different mass term, a different number of degrees of freedom, and different amplitudes due to exchanges? For example, in Dirac vs Majorana dark matter there is p-wave suppression vs. not in the annihilation cross section. Wouldn't there be some cross section that would differ between the two models?

Brian Dolan said...

I realize that I should qualify my earlier statement "An electron neutrino cannot turn into an anti-neutrino by switching reference frames." To be more precise, if the electron neutrino is Dirac if cannot turn into an anti-neutrino by switching reference frames. If it is Majorana it is already its own anti-particle, and this is true in any intertial reference frame, so again there is no question of changing from one to the other by switching reference frames.

For the Majorana case a massive electron neutrino can be absorbed by a proton to produce a neutron and a positron and it can be absorbed by a neutron to produce a proton and an electron --- either can happen. The neutrino is a mixture of positive and negative chirality states and which outcome is most likely depends on how much of each the wave function contains.

mfb said...

> Alex, yes, I think that unless someone has a new brilliant idea, in practice we can only confirm the Majorana nature but never exclude it.

Why not? Let's say we get accurate direct mass measurements from (single) beta decay, cosmology, neutrino mixing and so on, and we have inverted ordering OR the lightest mass is not in the range of 1 to 10 meV. As far as I understand the neutrinoless beta decay searches, they can exclude the then found masses >under the assumption< of Majorana masses - which means the assumption of Majorana masses is wrong.

Anonymous said...

slide is taken from this paper: https://arxiv.org/pdf/1605.02889v1.pdf

RBS said...

So at this time there's no lower bounds on any of the neutrino masses, whatsoever? We only know for certain that they aren't zero?

Jester said...

To be pedantic, we only know for certain that at least two of them are non-zero.

RBS said...

No, I'm wrong:

> Neutrino oscillations experiments have precisely measured the (squared) mass differences between neutrinos, which are roughly 0.05 eV and 0.01 eV.

The bigger of the two positive numbers cannot be smaller than their absolute difference. So m^2 must be > 0.05 and m > 0.2.. for the heavier one. And there's another one that has to be > 0.1 eV, right?

andrew said...

In a normal hierarchy the minimum combined sum of the three neutrino masses must be at least ca,. 0.058 eV. In an inverted hierarchy it can be higher, but bounds from Planck data tightly constrain any inverted hierarchy to close to the higher minimum inverted hierarchy sum of neutrino masses. The lightest neutrino mass in a normal hierarchy could range from zero to about 0.05 eV. I think most observers, forced to guess, however, would put it somewhere in the vicinity of 0.002 eV to 0.0001 eV or so.

RBS said...

From the statement above it follows that the combined sum of masses must be greater than 0.3... eV. Please tell me I didn't miss something obvious in the grade 3 arithmetics :(

ma^2 - mb^2 > 0.05 -> ma^2 > 0.05 -> ma > 0.2...
mx^2 - my^2 > 0.01 -> mx^2 > 0.01 -> mx > 0.1
ma + mx + my > ma + mx > 0.3...

RBS said...

Also, if we had an idea about neutrino density in the Universe (do we? apologies for hogging your blog Jester, there's no edit feature for the comments) and under assumption that there's no "preferred" neutrino flavour we could estimate the average neutrino background mass as > 0.1 * D eV/mcm^3. To compare it with the DM density ~ 0.3 * 10^ -3 eV/mcm^3 i.e. if there's at least 3 neutrinos per each 10 mcm cubic, DM will have to be the neutrinos, right?

mfb said...

@RBS: See the update in the blog post. The 0.05 and 0.01 eV are the "non-squared values", i. e. sqrt(m1^2 - m2^2). The differences of squared masses are (0.05 eV)^2 and (0.01 eV)^2.
If neutrinos show a mass structure remotely similar to charged leptons and quarks, then they have a normal (...) ordering, with the lightest one below 5 meV, the next one somewhere at 7-10 eV, and the heaviest one at about 50 meV, for a total mass sum of about 60 meV. Everything else would be a big surprise I think.

The neutrino contribution to the cosmic energy density is known, and small (~0.001). At least for the three discovered neutrino types. The Cosmic Energy Inventory: https://arxiv.org/abs/astro-ph/0406095

RBS said...
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RBS said...
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Jester said...

not sure which ones i should suppress... in case, you can do it yourself.