Negative Neutrino Mass Squared: Accepted Paper Analysis

[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 <\nu_e | m | \nu_e > = 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.

 

[Matterwave]

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.

I think you are forgetting that OPERA themselves issued a press conference on the matter. Sure they again stated during the press conference that they were asking for verification or non-verification of their results, but they knew the kind of sensationalism that the media would attribute to their results and yet they still issued a press conference. =/

 

[Vanadium 50]

I think you are forgetting that OPERA themselves issued a press conference on the matter

Where and when?

 

[OmCheeto]

Where and when?

That might be in reference to the following:

9/22/2011
Here is the msnbc story:
msnbc
It seems that the measurement team is asking for confirmation, so don't be too hasty.

9/22/2011
The researchers are now looking to the United States and Japan to confirm the results.

I'm currently watching the 9/23/2011 webcast, to see if I can confirm this.

ps. Have you ever seen their neutrino detector?
Check out slide #8.
Holy Cow!

 

[Vanadium 50]

I'm currently watching the 9/23/2011 webcast, to see if I can confirm this.

That's a CERN seminar, not a press conference. Matterwave said there was a press conference. I want to know where and when this was.

 

[Nugatory]

It may be just me, but I think that the handling of the OPERA debacle is fundamentally off-topic in this thread.

 

[Matterwave]

That's a CERN seminar, not a press conference. Matterwave said there was a press conference. I want to know where and when this was.

I was only told about the press conference. Because my advisor was quite annoyed about it at the time, and he was quite annoyed that CERN gave a press conference on the matter (he works in Neutrinos and so everyone was bothering him asking him if tachyonic neutrinos were possible). I basically just echoed his words on the matter lol.
Of course it's possible I misheard or misinterpreted what he said.

 

[Vanadium 50]

It may be just me, but I think that the handling of the OPERA debacle is fundamentally off-topic in this thread.

Feel free to split it off. If you really want to be adventurous, maybe you could find the original OPERA thread and graft it on to that.

I was only told about the press conference

I am unaware of one. There was a CERN seminar. CERN, not OPERA, did issue a press release after that.

 

[Matterwave]

I am unaware of one. There was a CERN seminar. CERN, not OPERA, did issue a press release after that.

I do recall now that it was CERN that my advisor was angry at. It's been a few years...cut me some slack. -.-

 

[Vanadium 50]

...cut me some slack. -.-

Hey, it was you who accused OPERA of doing this when they didn't. I'm just setting the record straight - they didn't do what you accused them of. (Which makes this even more off-topic)

 

[Larry Pendarvis]

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.

If there are tachyonic neutrinos, would there be some with a small enough absolute mass that their velocity is great enough to escape from inside an event horizon? And if we can detect them (which is the claim), then a tachyonic telescope could someday give us information back to the Big Bang and even earlier.