Negative Neutrino Mass Squared: Accepted Paper Analysis

[PeterDonis]

I just came across this paper arguing that the electron neutrino may have negative mass squared:

http://arxiv.org/abs/1408.2804

It says it has been accepted for publication. I'm wondering if anyone has seen it and can comment on the paper's arguments.

 

[ShayanJ]

Weren't tachyons only instabilities in fields and not actual particles?

 

[Vanadium 50]

I don't see where it has been accepted. If a referee, I would probably not accept it. There's very little new here - Ehrlich has been going on about this for more than a decade.

It is absolutely true that the neutrino mass experiments that measure m-squared allow it to go negative in their fits. To do otherwise biases the result high. It is also true that these measurements come out negative - the PDG average is -0.6 +/- 1.9 and the statement "Given troubling systematics which result in improbably negative estimators of m2 in many experiments we use only Kraus 05 and Lobashev 99 (I think they mean Aseev 11) for our average." They then go on to comment on exactly how these two measurements are better than the ones they supersede and how the systematics are better controlled.

As for the cosmological measurements, I am not at all surprised that if one replaces constants in the calculation that the results shift, nor that with the right set, the mass squared can go negative. However, what I don't see is a good argument that these are the right constants to use, apart from the fact that they give interesting conclusions.

For me to believe neutrinos are tachyons, I would prefer to see one strong piece of evidence rather than a lot of weak ones.

 

[goyalvishal4]

Weren't tachyons only instabilities in fields and not actual particles?

Existence of Tachyons is not yet established. But If it establish it would be actual particles with imaginary mass energy and negative time. Further they will loss energy with increase in time.

 

[goyalvishal4]

I don't see where it has been accepted. If a referee, I would probably not accept it. There's very little new here - Ehrlich has been going on about this for more than a decade.

It is absolutely true that the neutrino mass experiments that measure m-squared allow it to go negative in their fits. To do otherwise biases the result high. It is also true that these measurements come out negative - the PDG average is -0.6 +/- 1.9 and the statement "Given troubling systematics which result in improbably negative estimators of m2 in many experiments we use only Kraus 05 and Lobashev 99 (I think they mean Aseev 11) for our average." They then go on to comment on exactly how these two measurements are better than the ones they supersede and how the systematics are better controlled.

As for the cosmological measurements, I am not at all surprised that if one replaces constants in the calculation that the results shift, nor that with the right set, the mass squared can go negative. However, what I don't see is a good argument that these are the right constants to use, apart from the fact that they give interesting conclusions.

For me to believe neutrinos are tachyons, I would prefer to see one strong piece of evidence rather than a lot of weak ones.

http://phys.org/news/2014-12-faster-than-light-particles.html

This article is mentioning it to be accepted in journal Astroparticle Physics http://www.journals.elsevier.com/astroparticle-physics/

However On Journal Webpage It is not there

 

[ChrisVer]

For me negative neutrino masses squared would be a disaster, because then what kind of cosmological contribution would one have?...So indeed systematic errors can play important role in determining the value.

 

[ShayanJ]

Existence of Tachyons is not yet established. But If it establish it would be actual particles with imaginary mass energy and negative time. Further they will loss energy with increase in time.

I read it here:

In the 1967 paper that coined the term,[1] Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,[5] and instead represent an instability known as tachyon condensation.[3] Nevertheless, negative squared mass fields are commonly referred to as "tachyons",[6] and in fact have come to play an important role in modern physics.

(From this page.)

 

[goyalvishal4]

I read it here:

(From this page.)

check this part of your link containing details http://en.wikipedia.org/wiki/Tachyon#Fields_with_imaginary_mass
It is for field whose uncondensed states are tachyons but after tachyonic condensation they become positive squared mass.
But its only one case which is partially tachyonic as final excitations are not tachyons, only intermediate are. Even Higgs Boson has imaginary mass in uncondensed phase
Tachyons is rather general term whether possible or not, but include excitation which would actually travel faster than light

 

[mfb]

The paper talks about a decay chain p->n->p->n->... for high-energetic particles. Do they want to violate special relativity? Otherwise I don't think that makes sense.
I don't see enough evidence to introduce negative squared masses and violations of special relativity just to get better fits to current experimental data. It does not help to have 6 measurements consistent with the proposed negative value - they also have to be completely inconsistent with positive values to make the model interesting.

 

[Vanadium 50]

Do they want to violate special relativity?

Yes.

 

[PeterDonis]

Weren't tachyons only instabilities in fields and not actual particles?

This Usenet Physics FAQ article has a good discussion of tachyons:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

 

[PeterDonis]

I would prefer to see one strong piece of evidence rather than a lot of weak ones.

This was my sense after skimming the paper, that it was giving multiple very weak pieces of evidence but no strong evidence (AFAIK no strong evidence exists of neutrinos, or any other particles, being tachyons). Thanks for the confirmation. :)

 

[mfb]

Yes.

Then they need really strong evidence. Especially in a field where 2-3 sigma effects come and go all the time and even 5 sigma effects can disappear.

 

[ShayanJ]

This Usenet Physics FAQ article has a good discussion of tachyons:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Thanks for that. But this only treats scalar tachyons which isn't useful when we talk about neutrinos. I checked some QFT texts but non of them treat tachyons(which isn't surprising). Not much was on internet too. Can you suggest a text that treats tachyons?(Specially fermionic ones)

 

[PeterDonis]

this only treats scalar tachyons

The original paper by Bilaniuk and Sudarshan (referenced in the article) turns out to be available online:

https://www.uam.es/personal_pdi/ciencias/jcuevas/Teaching/Taquiones.pdf

It doesn't explicitly discuss solutions of equations of motion the way the Usenet article does; however, the considerations raised in the paper appear to me to apply to any tachyonic particle, regardless of spin.

Can you suggest a text that treats tachyons?(Specially fermionic ones)

Google shows a number of articles that appear to discuss tachyonic solutions of the Dirac equation. AFAIK the general solution properties of the Klein-Gordon equation that are discussed in the Usenet article should also hold for the Dirac and Maxwell equations, since both of those are known to be consistent with relativistic causality.

 

[ShayanJ]

The original paper by Bilaniuk and Sudarshan (referenced in the article) turns out to be available online:

https://www.uam.es/personal_pdi/ciencias/jcuevas/Teaching/Taquiones.pdf

It doesn't explicitly discuss solutions of equations of motion the way the Usenet article does; however, the considerations raised in the paper appear to me to apply to any tachyonic particle, regardless of spin.
Google shows a number of articles that appear to discuss tachyonic solutions of the Dirac equation. AFAIK the general solution properties of the Klein-Gordon equation that are discussed in the Usenet article should also hold for the Dirac and Maxwell equations, since both of those are known to be consistent with relativistic causality.

But I think whether or not the following sentence is true, depends to a high extent on the equation that the particle obeys. This is the main reason I ask for further references. Or its a general thing not depending much on spin?

localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal.

 

[PeterDonis]

I think whether or not the following sentence is true, depends to a high extent on the equation that the particle obeys.

I don't have a reference, as I said, but I'm curious why you think this would depend to a high extent on the equation of motion. The Dirac and Maxwell equations share a lot of properties with the Klein-Gordon equation, including, as I mentioned, consistency with relativistic causality. Indeed, multiplying the Dirac equation by its complex conjugate gives you the Klein-Gordon equation (this is one way of expressing the fact that two fermions with opposite spins can form a zero-spin bound state). So I'm not sure why you would expect a drastic difference in the behavior of tachyonic solutions to these equations.

 

[Matterwave]

If neutrinos are Tachyons, wouldn't the neutrinos from SN1987A have arrived here much earlier? Is this addressed in the paper? My internet connection is very poor, and loading it is taking some time lol.

 

[PeterDonis]

If neutrinos are Tachyons, wouldn't the neutrinos from SN1987A have arrived here much earlier?

Not if their energy was large enough for their velocity to be sufficiently close to the speed of light. (Of course, that "sufficiently close" might be a problem--I haven't run the numbers to see if the required energy would be compatible with what was detected.)

Is this addressed in the paper?

Not as far as I can see.

 

[Matterwave]

From what I know of neutrinos from SN1987A, the fact that they arrived ~3 hours ahead of the light means their speed is bound very close to the speed of light. It originated from the LMC I believe, so it has been traveling to us for ~150,000 years... that they arrived only 3 hours early limits their speed to c to one part in a billion.

 

[Vanadium 50]

If neutrinos are Tachyons, wouldn't the neutrinos from SN1987A have arrived here much earlier?

No. The limit is determined by the dispersion in arrival times - we don't have an absolute measurement of when SN1987A happened. That limit can be expressed as the |m²| < few eV².

 

[TachyonBob]

Regarding my tachyon paper which HAS BEEN accepted by Astroparticle Physics, there are too many misconceptions, false statements and ad hominem arguments made about it here to reply to them. I certainly have not claimed that I have definitively proven the electron neutrino is a tachyon, only that each observation is consistent with that possibility. While each of the 6 observations may be "weak" i.e., have more mundane explanations, the interesting thing is that they all reinforce each other, not by each being consistent with nu_e being a tachyon, but by each yielding the very same tachyonic mass value within their uncertainty. The paper should be seen as a stimulus to others (especially cosmic ray researchers) to check their archived data for the 4.5 PeV signal proposed. However, unless we have another galactic supernova soon, the definitive answer as to whether I am right may need to wait until the KATRIN experiment (starting data taking this year) has 3-5 years of data. .

 

[Vanadium 50]

Not if their energy was large enough for their velocity to be sufficiently close to the speed of light.

Isn't it if their energy were small enough for their velocity to be sufficiently close to the speed of light? As a tachyon gains energy, it slows down.

However, as I mentioned earlier, we don't have a stopwatch that tells us when SN1987A went off, so we can't use absolute time measures (except the very crudest - we know the neutrinos arrived the same day as the light, and probably only about 3 hours before). One needs to look at the difference in arrival times, and that suggests that (assuming non-tachyonic neutrinos) that the mass is less than about 15-20 eV, and probably less than 10.

 

[TachyonBob]

With respect to the next supernova you do not need to know when it "went off." As I discuss in my paper there is research done by supernova modellers which indicates strongly that there should be millisecond time scale oscillations in the neutrino output. (Imagine a rapid in/out oscillation in density.) If the neutrino mass is large enough, these ms-scale oscillations will be "smeared out" due to different travel times to reach Earth. Given the observed neutrino arrival times one can then "unsmear" the data by finding the neutrino mass that best unsmears it. Check the reference on this given in my paper if you are really interested.

 

[PeterDonis]

Isn't it if their energy were small enough for their velocity to be sufficiently close to the speed of light? As a tachyon gains energy, it slows down.

As a tachyon gains energy, it slows down closer and closer to the speed of light. So the more energy it has, the closer its speed is to the speed of light. A tachyon with small energy would have a speed much, much larger than the speed of light.

 

[TachyonBob]

What you say is true, but the problem is that for the smallest energy neutrino that can be detected (around 0.3 MeV) the speed is so close to c that no Earthly experiment could hope to detect the difference. That is why I say measuring their mass is a much more sensitive test

 

[vanhees71]

From a more theoretical perspective: Are all the fundamental problems with interacting tachyons solved yet? Is the S-matrix of a model containing tachyons unitary and Poincare invariant etc.?

 

[TachyonBob]

I am not a theorist, so I cannot say with any authority that they have or have not been. As I noted in the paper Lorentz invariance is a long-standing problem, and various theorists have found ways to modify it so as to describe effective Lagrangians for tachyons. You should look at a recent paper by Jentschura & Wundt that I cited which considers the kinds of "hard choices" that need to be made in order to have a successful theory of tachyonic neutrinos. Chodos and Kostelecky have also written about this, as has Ngee-Pong Chang.

 

[vanhees71]

Ok, I'll have a look, but I'm pretty doubtful, whether you have all these constraints fulfilled one expects from a physically sensible S-matrix (unitarity, causality, Poincare covariance, linke-cluster principle).

 

[Matterwave]

No. The limit is determined by the dispersion in arrival times - we don't have an absolute measurement of when SN1987A happened. That limit can be expressed as the |m²| < few eV².

I admit I am not very knowledgeable about theoretical tachyons, and I can't even access this paper since my internet connection is so poor. So I can't really comment much further lol.

 

[Orodruin]

My question is the following: Are these observations actually computing the same thing? Neutrinos are mixed and a priori there is no such thing as an electron neutrino mass. If you look at 0nubb experiments, they are measuring an effective electron neutrino mass involving all of the mass eigenstates, mixings with the electrons and the Majorana phases of the PMNS matrix. The combination that should appear in tritium beta decay is different and does not provide the possibility of phase cancellation.
I do not know enough CR physics to know what combination would appear as the effective electron neutrino mass in those. However, with the quoted mass square it seems to me that all neutrino mass eigenstates would be degenerate and thus tachyons.

If part of this is explained in the paper I had a difficulty finding it as I am currently half absent and only access the internet on my iPhone, which makes reading a paper difficult.

 

[OmCheeto]

Would it be possible to avoid the negative mass, by applying a small mass to photons?
Someone once told me that it was theoretically possible.

of Ask Dr. Neutrino Date: 97/03/13
If photons have a small rest mass, they can no longer move at the speed we call "c". I know its confusing that in this situation "c" can no longer be described as the "velocity of light", but the situation is completely consistent and satisfactory, and is open to various experimental tests, which yield the limit of about 10^-20 eV for the photon mass.

The value doesn't seem to have changed much over the last 17 years:

Is there any experimental evidence that the photon has zero rest mass?
...It is almost certainly impossible to do any experiment that would establish the photon rest mass to be exactly zero. The best we can hope to do is place limits on it. ...
The new limit is 7 × 10−17 eV ...

{edit} ps. Where are my manners? Welcome to PF TachyonBob! :)

 

[ChrisVer]

Neutrinos are mixed and a priori there is no such thing as an electron neutrino mass

Are you sure about this? Because in certain interaction channels they give the boundaries of flavor neutrino masses (such as Tritium for the electron neutrino).
In general the flavor neutrinos are a mixture of fixed mass-eigenstates, so they can have a mass...
eg. for 3 flavors there exists &lt;\nu_e | m | \nu_e &gt; = a_1 m_1 + a_2 m_2 + a_3 m_3 \ne 0
where a_i are given by the PMNS matrix.

 

[Orodruin]

Are you sure about this? Because in certain interaction channels they give the boundaries of flavor neutrino masses (such as Tritium for the electron neutrino).

Yes. This type of experiments essentially assume that the mass eigenstates are degenerate. There are also studies of the beta decay spectrum for the case when the experiment is accurate enough to resolve the mass differences between the mass eigenstates, in which case the spectrum looks quite different.

eg. there exists <νe|m|νe>=a1m1+a2m2+a3m3≠0 = a_1 m_1 + a_2 m_2 + a_3 m_3 \ne 0

This is essentially the combination that appears in 0nubb experiments (or rather the square of this). For tritium decay, you usually see $m_{\nu_e, \rm eff} = \sum_i |U_{ei}|^2 m_i$.

 

[mfb]

Yes. This type of experiments essentially assume that the mass eigenstates are degenerate.

For previous tritium experiments this was probably a very good approximation, given the large upper limits compared to the small m^2 differences. I saw a KATRIN talk discussing those differences, but it is questionable if they can see it if I remember correctly.

 

[Vanadium 50]

From oscillations we know that the largest mass difference squared is about (1/20 eV)². Tritium endpoint experiments are sensitive at the eV level. So the degeneracy assumption is not unreasonable.

 

[TachyonBob]

Tritium experiments measure the "effective mass" squared of nu_e, defined as the weighted average defined by a formula given above by Orodruin, so it makes no difference as to whether or not they are degenerate. It's not like some tritium events record m_1, others m_2, etc. Based on KATRIN simulations they may be able to see my postulated mass.

 

[bcrowell]

The paper talks about a decay chain p->n->p->n->... for high-energetic particles. Do they want to violate special relativity? Otherwise I don't think that makes sense..

There is a good discussion of this in Chodos et al., Null Experiments for Neutrino Masses, Mod. Phys. Lett. A 7, 467 (1992), http://www.physics.indiana.edu/%7Ekostelec/lay/91chodoskosteleckypottinggates.pdf . Their discussion of whether this means there's Lorentz violation is ... nuanced.

 

[Orodruin]

Tritium experiments measure the "effective mass" squared of nu_e, defined as the weighted average defined by a formula given above by Orodruin, so it makes no difference as to whether or not they are degenerate. It's not like some tritium events record m_1, others m_2, etc. Based on KATRIN simulations they may be able to see my postulated mass.

If tritium experiments had infinite resolution, what they would see would be three cutoffs in the spectrum, with the one corresponding to $\nu_3$ being more difficult to see due to the small mixing. If they are degenerate (within the experimental resolution) it does not matter much to use one or the other.

My question is more related to what combination of the masses that is measured in each of your observations. In particular, the 0nubb observation can be off from the actual mass of the mass eigenstates by a factor of two even if they are degenerate due to Majorana phase interference.

 

[PAllen]

There is a good discussion of this in Chodos et al., Null Experiments for Neutrino Masses, Mod. Phys. Lett. A 7, 467 (1992), http://www.physics.indiana.edu/%7Ekostelec/lay/91chodoskosteleckypottinggates.pdf . Their discussion of whether this means there's Lorentz violation is ... nuanced.

They propose, in discussion of null experiments, that whether a given type of decay occurs is observer dependent. That is, a muon seen to decay by a certain channel by one observer, is seen not to decay this way by a different observer. My reactions is nonsense. Am I missing something? Does a consistent tachyonic neutrino model really incorporate such a thing? I would label it inconsistent if it did.

[edit: Ok, they cover this question a bit later in the paper. It's not totally ridiculous.]

 

[bcrowell]

They propose, in discussion of null experiments, that whether a given type of decay occurs is observer dependent. That is, a muon seen to decay by a certain channel by one observer, is seen not to decay this way by a different observer. My reactions is nonsense. Am I missing something? Does a consistent tachyonic neutrino model really incorporate such a thing? I would label it inconsistent if it did.

[edit: Ok, they cover this question a bit later in the paper. It's not totally ridiculous.]

They don't say that a decay in one frame is a non-event in another. They say that a decay in one frame is an absorption in another. The particle being absorbed is from a background that is present in one frame and not the other. This can supposedly happen because the vacuum is not Lorentz-invariant.

 

[vanhees71]

Again my question: Is there a theory of interacting tachyons with a proper S-matrix and causality intact?

 

[bcrowell]

From a more theoretical perspective: Are all the fundamental problems with interacting tachyons solved yet? Is the S-matrix of a model containing tachyons unitary and Poincare invariant etc.? [...] Again my question: Is there a theory of interacting tachyons with a proper S-matrix and causality intact?

Doesn't the Jentschura paper basically answer this? Jentschura and Wundt, "Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay," Eur.Phys.J.C 72 (2012) 1894,http://arxiv.org/abs/1201.0359

The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. [...] [W]e conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix [...]

This reads to me as a "no" answer to your question.

 

[Orodruin]

This reads to me as a "no" answer to your question.

Conclusion: If neutrinos are tachyons, then we have more problems to worry about than whether or not the measured mass squared values from different experiments agree. Similar to worrying about oscillation experiments having a $\sin^2(2\theta)$ best fit larger than one a few years back.

 

[bcrowell]

Conclusion: If neutrinos are tachyons, then we have more problems to worry about than whether or not the measured mass squared values from different experiments agree. Similar to worrying about oscillation experiments having a $\sin^2(2\theta)$ best fit larger than one a few years back.

I think we saw this in the OPERA superluminal neutrino debacle. Tachyons as real particles are so hard to accommodate theoretically that for six months we had a cottage industry of theorists trying and failing to do so.

 

[Orodruin]

Sadly, it also shows how willingly (some parts of) the community jumps at an experimental anomaly without proper verification of the results ... Had it been true it would of course have been sensational and worthy of the effort, but extaordinary claims should have extraordinarily strong verification.

 

[Vanadium 50]

They say that a decay in one frame is an absorption in another.

Neither "decay" or "absorption" is really the right word here. A tachyonic neutrino is spacelike, not timelike, so terms that describe when it appears and when it disappears are ill-suited to the situation. Using language suitable for timelike intervals to describe spacelike ones will be, at best, confusing.

 

[vanhees71]

I think we saw this in the OPERA superluminal neutrino debacle. Tachyons as real particles are so hard to accommodate theoretically that for six months we had a cottage industry of theorists trying and failing to do so.

Well, but as a theorist I must admit that this is the most shameful issue about this. The only mistake of the OPERA collaboration was the somewhat careless treatment of the issue in the popular-science press. I think it was NY times that took their arXiv paper, which was a cry for help rather than the claim to have found superluminal neutrinos. Then a plethora of "theory papers" appeared at the arXiv, most of which were either trivial, and nobody should have thought that the OPERA collaboration wouldn't have checked such trivial possibilities and many obviously wrong to begin with. There were of course also serious papers showing that the OPERA result provoked huge trouble for theory. At the end it turned out to be a loose connection in a fiber and some bug in an time-measuring oscillator, partially compensating each other. That can happen at such a delicate experiment, but that (pseudo-)theorist put so many non-sense papers on the arXiv is really a waste of time for all the referees who had to review the papers at the journals :-(. Last but not least it made a very bad impression on the public opinion concerning science. In Germany, it's anyway a bit difficult to argue with some people about the necessity and usefulness of expensive big-science experiments and then you have a hard time to explain that such issues take time to be clarified. I had some reactions by lay people in the direction that this is proof that Einstein was wrong with the relativity and all the maths-loaden theoretical physics anyway (math is hated by most laymen in Germany, which has some sad tradition; even Goethe was against math and mathematicians). I usually tell them they shouldn't use their cell phones, androids, computers, and GPS anymore if they think math and physics is so bad :-(. Sorry for this OT rambling.

In any case, one has to check carefully these experimental results on the neutrino mass squares being negative. It may be even a problem with the correct analysis of the meaning of the what was measured and evaluated, given the fact that neutrinos are oscillating. I've no clue about this issue. Even neutrino oscillations are a big mess in the theoretical literature with claims as far reaching as saying that QFT is not applicable (even Lipkin wrote papers with this idea). In my opinion it's the opposite:

It can only be clearly understood using QFT, evaluating processes with proper asymptotic free states (which are necessarily always mass eigenstates and thus cannot be the neutrinos), which means one has to describe the production process and the detection process with wave functions peaking at the space-time points of detection, clearly defining the locations of the "near- and far-side detectors". I think, it's pretty easy, and I should do this calculation once myself to understand the mixing formula right. Then all debates about energy/momentum conservation and all this should be gone. I'm also pretty sure that this calculation must have been already done in the literature, and indeed there are a lot of papers with wave-packet ansatzes in QFT around, but all I've seen so far have strange arguments which seem to overcomplicate the subject, or do you have a good source about this? Perhaps such an analysis could also help to clarify what's really measured as "the electron-neutrino mass squared" in the various experiments described in Ehrlich's interesting paper.

 

[Orodruin]

I think, it's pretty easy, and I should do this calculation once myself to understand the mixing formula right. Then all debates about energy/momentum conservation and all this should be gone. I'm also pretty sure that this calculation must have been already done in the literature, and indeed there are a lot of papers with wave-packet ansatzes in QFT around, but all I've seen so far have strange arguments which seem to overcomplicate the subject, or do you have a good source about this?

Evgeny Akhmedov and Joachim Kopp discussed the QM wave-packet vs QFT approach in 2010: 10.1007/JHEP04(2010)008

 

[vanhees71]

Great! I've to read the paper carefully, but I think there all the issues are thoroughly discussed.