Philadelphia, PA

Dear Nihar, 

The papers in the following publication may prove of some use, especially the last of the group, p. 59ff:

https://arxiv.org/pdf/1510.05223.pdf

In any case, there seems to be a wealth of data available in this collection of papers based on observation. 

H.G.Callaway

Philadelphia, PA

Dear Nihar, 

Here is a suggestive passage from a recent summary report on neutrino physics:

The frequency of neutrino oscillations depends on the mass difference among the three different neutrino types. The NOvA experiment will soon begin to send neutrinos from Fermilab to Ash River, Minnesota, a distance of 810 kilometers. Scientists hope that the observation of the resulting oscillations will determine which type of neutrino is the heaviest and which is the lightest.

See:

http://www.symmetrymagazine.org/article/february-2013/neutrinos-the-standard-model-misfits

This may suggest the idea that the mass of highly accelerated neutrinos is very large in comparison to those of less accelerated neutrinos. If we think of high energy neutrinos as more massive because highly accelerated, then their mass differences might decline in comparison to the mass differences of low energy neutrinos? 

In any case, the linked article is an interest research summary. 

H.G. Callaway

Dear Mukta,

the simple reason is that they are massless at high temperatures, so there is no distinction among them in terms of gauge interactions. The same is true for charged leptons, by the way, at high enough temperatures.

Best regards,

Alexander

Philadelphia, PA

Dear Merle, 

Why would they be massless at high temperature if they start out with non-zero mass--which is what most theorists hold. Start with even a slight mass and subject it to relativistic accelerations, and you should get even more mass. Right?

If not, why no? 

H.G. Callaway

Dear Professors,

Thank you very much for the explanations.

If I am not wrong to think simply,  at high temperature or at extremely high energy (we can say) a particular symmetry was supposed to govern the system after the breaking of which only the particles (of the system say) are supposed to get mass.

Dear H.G. Callaway,

no, this is not quite right. As Mukta correctly points out, most particles are only massive at low temperatures. Neutrinos in particular get their mass either by a Dirac mass term (theoretically unlikely but not impossible) or by a Majorana mass term (which is ultimately either some form of the Weinberg operator or some more complicated Higgs-like coupling).

in *ALL* those cases, the neutrino mass is only generated after electroweak symmetry breaking, i.e., at low temperatures.

Best regards,

Alexander

Philadelphia, PA

Dear Merle & Nihar, 

It strikes me that the various theories about how neutrinos get their mass are weaker than the simply fact that they have some mass--which is a presupposition of their oscillations from one flavor to another. As a rule, we shouldn't impose an explanation of the relatively clear point that neutrinos have mass from the vantage point of relatively obscure, more doubtful theories about how they might obtain mass. Until and unless some theory of how neutrinos get their mass are confirmed, this is a relatively doubtful explanation of the variations of oscillations with temperature. Its a possible explanation based on an unconfirmed theoretical hypothesis. 

I take it that,

The frequency of neutrino oscillations depends on the mass difference among the three different neutrino types.

This is a point I quoted above from the Symmetry magazine article. My suggestion was that their mass differences diminishes with higher temperature. 

Zero mass at high temperature could explain lack of oscillation, The idea here is not to rule out a mere theoretical possibility. Instead it is a matter of comparative plausibilities. Given that neutrinos have some mass at low temperatures, then it stands to reason that their mass should increase with acceleration --as is generally the case with massive objects. But this is consistent with their mass differences being diminished, if the mass due to acceleration is very great in comparison with the low temperature masses. 

No one has yet explained the anomaly that low mass particles should become massless at high temperatures. That there is some breaking of a symmetry is unobjectionable--or that a critical temperature for oscillations is involved. 

I'm open to all possibilities but some seem less plausible in comparison. 

H.G. Callaway

Dear H.G. Callaway,

I am sorry, but this view is not correct. It is rather simple: we know all properties of neutrinos because we have *measured* them. For example, we do know how strongly they interact. The only unknown is their exact mass scale - we only know that at most one neutrino can be massless (but does not have to).

Given these properties, we know that any neutrino mass must to some extend involve the Higgs. This is clear from the neutrinos quantum numbers, but what we do not know exactly is how the Higgs contributes. There are more possibilities, all of which are possible, but we know that it has to contribute and that it has to develop a VEV, which it only does at low temperatures. Also the Higgs is experimentally verified, in fact with a striking precision in all channels accessible at LHC.

I don't know why you are claiming that "No one has yet explained the anomaly that low mass particles should become massless at high temperatures.". I suggest to really look into the literature available to understand what is known and what is not known, before making such unsolicited statements. One cannot simply discuss away experimental facts.

Best regards,

Alexander

Philadelphia, PA

Dear Merle, 

Many thanks for your very quick reply.

I certainly have no desire to ignore experimentally established facts, but as it happens, your proposed explanation of neutrino mass seems to have shifted a bit between your recent notes. Other proposed mechanisms were mentioned before, and now it is a matter of the Higgs mechanism. I have nothing against exploring theoretical possibilities; but such should not be presented dogmatically. I take it that what is "correct" and what is not is the very matter under debate? Or, do you hold that there can be no such debate or inquiry?  

In my admittedly limited experience, I am aware of few who doubt the confirmation of the Higgs particle at CERN. Perhaps you would care to explain how and why the Higgs can only contribute the the mass of neutrinos at low temperature? Also, of course, you have already claimed the possibility of other contributions to the mass of neutrinos. Why the sudden focus on the Higgs mechanism? 

I am claiming that no one on this thread has yet explained the anomaly that low mass particles should become massless at high temperatures. But that is your proposal. Of course, I would be pleased to see such an explanation here or even reference to relevant literature. 

You may be entirely right, of course, in your line of thought; but I am sorry to say that your approach on the present thread smacks of dogmatic pretense.

Perhaps you can do better?

H.G. Callaway 

Philadelphia, PA

Dear readers, 

I've come across what seems to be a very useful background piece for the present question. This is the "Scientific Background paper for the 2015 Nobel prize in Physics," on Neutrino Oscillation; and it is available from the Swedish Academy at the linked address below. There is much useful background and many references on the basics of the phenomenon. The article also serves to indicate just how specialized the present question is regarding high energy oscillation--in relation to the 2015 Nobel prize on the topic. Our question is on the very outer edge of contemporary theory. 

Here is a short passage from the paper:

Neutrino oscillation parameters

The experimental results are used to obtain the mass differences Δm 2 and the mixing angles θ. This is done using global fits including all available experimental data – observations of solar and atmospheric neutrinos, and neutrinos studied in reactor and accelerator experiments. The MSW effect is taken into account. Recent values of the parameters of the PMNS matrix based on a global analysis of all available oscillation data assuming a three-neutrino mixing scheme can be found in [36]. All entries, except Ue3, turn out to be large which is very different from the quark mixing matrix.

Why neutrino oscillations matter

Observation of the quantum mechanical phenomenon of neutrino oscillations implies that at least two neutrino species have non-zero mass. The mechanism which generates neutrino masses is still unknown, and the Standard Model must be extended to include this new physical reality. Although mass differences between neutrino flavours have been determined with precision, no one has yet succeeded in actually measuring the neutrino mass itself. The best upper limits derived from laboratory experiments give 17 € mν e < 2 eV (from tritium decay), while limits on the mass of the muon-neutrino and the tauneutrino (from pion and tauon decays) are considerably higher. Planned experiments should reach a sensitivity of ~ 0.20 eV.

---End quotation

See:

https://www.nobelprize.org/nobel_prizes/physics/laureates/2015/advanced-physicsprize2015.pdf

A couple of points here seems worth emphasizing in view of recent exchanges. According to this paper:

"The mechanism which generates neutrino masses is still unknown, and the Standard Model must be extended to include this new physical reality."

In consequence, here is little room for dogmatism here. What theoreticians do is evaluate the observational evidence in light of possible alternative accounts of the generation of neutrino masses. 

It seems that no one yet knows what explanation there may be for diminished neutrino oscillations at higher energies; and it is best to survey the plausible alternatives. Consulting this fine piece of exposition should benefit the undertaking. 

It would be helpful if Nahir would provide the sources for the presupposition of the question. 

H.G. Callaway

What is the reason of the fact that the three flavors of neutrino behave similarly at extremely high energy(

Dear H.G. Callaway,

ResearchGate is primarily a platform for researchers to echange, it is not an educational institution. This is why many researchers will be hesitant to go over what we consider as "textbook knowledge". I will nevertheless briefly comment on your points:

1. There are indeed people who doubt the Higgs discovery. But without any good arguments. They typically claim that a gold atom would have similar characteristics, which is however only true for the mass. A gold atom does not interact with other particles the way the Higgs does, which can already be derived from Rutherford's old scattering experiments.

We have found the Higgs because we have not only seen a particle of the correct mass, but we have also in about 5 channels measured the coupling of the Higgs to other particles. All these couplings match the Standard Model prediction *exactly*. In principle, they could be any number, but no, they exactly match the prediction. We have also measured other properties that match, like the spin.

Thus, whatever it is we have discovered, if it's not the Higgs then it's the perfect imposter. Or, as a scientist would put it, we have measured the Higgs but we do not know whether it's fundamental. It could still be something composed of other particles, but it is for sure something that behaves exactly as what we call Higgs at all energies we have been able to test it.

2. It is true that we do not know the mechanism behind the neutrino mass. However, we know for sure that at low energies this mechanism has in some way to be connected with the Higgs. Why? Because the properties of the neutrinos do not allow for any other options. This is really a binary thing, because we know the neutrinos quantum numbers and we know which possibilities this allows for.

Now, and this is technical, the Higgs *cannot* generate mass for anything else than itself for high enough tempratures. This has to do with how it's potential changes with temperatures. It's very complicated and the exact behaviour depends on which particles exist and on which values certain parameters have. However, the one thing that is known for sure is that the Higgs only developes what is called a "vacuum expectation value" for small enough temperatures. A temperatures somewhat larger than the Higgs mass, the ability of the Higgs to give masses to anything vanishes.

------------

This is the best I can do in simple words. In any case, I strongly suggest you to study the topic in detail before starting to doubt every bit of information you may not understand at first sight.

There are some things in physics we are really damn sure about. However, not all of them are easy to put into simple words. You may blame the physics community for not being able to explain these bits properly to you, but the truth is that Nature is rather complicated. So, if you want to truly discuss, you have to invest quite something in the first place. This is the only way to really understand the details.

Of course you can choose not to do that, but then you have to accept that at some point there is no way to explain things simpler than they are. Where this point is depends on you, however, and if you really want to give a good argument for why certain things should be wrong in physics, then it has to be thought-through and correct in every detail.

Best regards,

Alexander

Philadelphia, PA

Dear Merle, 

On my own view, it belongs to the purposes of philosophy of science to help make scientific results and endeavors more widely available to the educated public. This objective apparently goes somewhat beyond your comprehension. Its a project of philosophical research, whether you personally approve of it or not. 

In any case, I think we should be grateful for your little lecture on offer on the Higgs particle and the Higgs mechanism. It is not exactly clear that this was what was called for at this juncture, but in any case, it may prove useful. What seems to go missing is an explanation of why the Higgs mechanism should not generate mass at high temperatures--as contrasted with your assertion that such an explanation exists. But, as it happens, this was exactly where you were challenged. We still have no explanation on offer of the apparent anomaly of a loss of mass at high acceleration. 

It is not my custom of practice to "doubt everything" which I do not understand, or which remains unclear, as you suggest. Quite the contrary. Instead, the idea is to seek out well established theory and results. Here your rather amazing presumption seems to show again. Why should you presume to know what I have studied? Its curious. 

Typically, I find that the best work and achievements in physics come from people who can, indeed, explain their accomplishments and perspectives to the educated public. But I do not think this is a requirement of anyone working in physics. If many or most people in physics do not want to engaged in more general discussion that's o.k. by me. Its not easy. 

Its a false dichotomy to suppose that discussions of physical theory and results must either be unintelligibly technical or negligent and ignorant. Good arguments can arise out of informative and detailed exchanges. Its important to respond to questions such as the present one in good faith and in terms of the level of understanding of the typical participants. There is always better and worse in such discussions, if they are open, but perfection will only be sought in vain. 

H.G. Callaway  

Dear H.G. Callaway,

I can tell you exactly why the Higgs does not induce masses at high temperature: The reason is that its potential does, by quantum corrections, not have a non-trivial minimum (it has a parabolic shape instead of a Mexican-hat-like shape), implying that its vacuum expectation value vanishes and thus the Yukawa-couplings do not produce particle masses.

As I said, it is a technical aspect that I can put into one sentence, but not into one with simple words. Because it is not simple.

Again, I think you have to study the matters to truly understand. This is the only way to get into complicated things, and for everybody who has studied the Standard Model in detail, the above sentence will make sense.

Best regards,

Alexander

Isn't any particle set in the ultra-relativistic regime behaving like photons, irrespective of the particle rest mass energy and particle kind ?    Then at very high temperature only the total number of particles matters.

Philadelphia, PA

Dear Merle & readers,

Thanks for your further comments on the origin of the neutrino mass and its variation.

Readers of this thread my find the following brief introduction of interest, which goes into some detail on alternative theories of neutrino mass--including some theories assigning mass apart from the Higgs mechanism:

http://ctp.berkeley.edu/neutrino/neutrino5.html

The link goes to an excerpt, more directly relevant here, from a longer article on neutrino physics, which may also prove of interest.

H.G. Callaway

Philadelphia, PA

Dear Pfenniger, 

A usual explanation of why a massive object (or particle) cannot reach the speed of light, in relativity theory, is that as it approaches the speed of light, its mass increases, so that the calculated mass at c would be infinite. The faster it goes and the further into the domain of relativistic speeds, the more difficult it is to add any further acceleration. In consequence, by this reasoning, a particle with mass, including the neutrino presumably, could not reach the speed of light. In that way, it seems neutrinos are unlike photons. Photons have no mass.  

But on the other hand, the neutrino seems to be one of the least well understood particles of the Standard Model, and much about them seems to be up in the air. 

It remains unclear why you say, "at very high temperatures only the total number of particles matters." Matters for what? Matters in what way? 

Many thanks for your contribution. 

H.G. Callaway

From the well known equation E^2 = (pc)^2 + (m_0 c^2)^2, in the ultrarelativistic regime massive particles move *close* to the speed of light c, momentum p is then almost proportional to energy E, just like for photons for which the rest mass m_0 is zero.   So particles loose their identity when ultrarelativistic, only their number per unit volume matters.

It is why the tiny mass difference between the different neutrinos is irrelevant at very high temperature, because each particle contributes in average with the same energy in a fluid in thermodynamical equilibirum, where  the particle energy tends to be in equipartition.  For neutrinos this regime was established during the first seconds of the Big Bang.

Philadelphia, PA

Dear Pfenniger,

One way to go about the phenomenon of neutrino oscillations is by thinking in terms of waves and wave lengths. Neutrinos are thought to oscillate between the 3 "flavors," over longer distances, because their various (superimposed) wave-equivalents interfere, sometimes constructively and sometimes destructively. At higher energies, one would expect the wave-lengths to be very short; and this may suggest that the differences between such very short wave lengths are no longer of much consequence --do not result in significant destructive or constructive interference in comparison with the longer wave-length, lower energy states.

One of the curiosities, as I understand the photon, is that though it has no mass it does have momentum which is proportional to shorter wave-length. This point comes from Einstein's 1905 paper on the photoelectric effect and his application of the quantum idea to light. But if higher energy neutrinos have greater momentum, then, since they are massive particles, one would expect them to have greater mass corresponding to their higher energy.

My prior suggestion about the question above was the small mass differences between the neutrino flavors would be swamped by their relativistic masses at high energies, and that this might function to explain the reduced oscillations.

H.G. Callaway

One needs to study RGE evolution of PMNS matrix elements which will extrapolate mixing parameters to the1012 GeV scale. This will give an idea on whether neutrinos of different flavors act differently under the influence of weak interaction process at 1012 GeV. Perhaps you can see papers by Shivani Gupta in Researchgate.

https://www.researchgate.net/publication/263545317_Renormalization_Group_Evolution_of_Neutrino_Parameters_in_Presence_of_Seesaw_Threshold_Effects_and_Majorana_Phases

Article Renormalization Group Evolution of Neutrino Parameters in Pr...

Neutrinos? At high energy? They melt and become chocolate fudge.

Philadelphia, PA

Dear all, 

I wonder if we could get any comments on the suggested reading: 

Renormalization Group Evolution of Neutrino Parameters in Presence of Seesaw Threshold Effects and Majorana Phases

Shivani Gupta · Sin Kyu Kang · C. S. Kim

Abstract

We examine the renormalization group evolution (RGE) for different mixing scenarios in the presence of seesaw threshold effects from high energy scale (GUT) to the low electroweak (EW) scale in the Standard Model (SM) and the Minimal Supersymmetric Standard Model (MSSM). We consider four mixing scenarios namely Tri-Bimaximal Mixing, Bimaximal Mixing, Hexagonal Mixing and Golden Ratio Mixing which come from different flavor symmetries at the GUT scale. All these mixing scenarios give vanishing reactor angle ($\theta_{13}$) and maximal atmospheric mixing angle. The solar mixing angle has different value for all four cases. In the light of non zero value of $\theta_{13}$ it becomes interesting to study the present status of these symmetries, i.e. whether they can generate the current neutrino oscillation data at low energy scale or not. We find that the Majorana phases play an important role in the RGE running of these mixing patterns along with the seesaw threshold corrections. We present a comparative study of the RGE of all these mixing scenarios both with and without Majorana CP phases when seesaw threshold corrections are taken into consideration. We find that in the absence of these Majorana phases both the RGE running and seesaw effects may lead to $\theta_{13}< $5$^\circ$ at low energies both in the SM and the MSSM. However, if the Majorana phases are incorporated to the mixing matrix the running can be enhanced both in the SM and the MSSM. Even by incorporating non zero Majorana CP phases in the SM, we do not get $\theta_{13}$ in its present 3$\sigma$ range. The current values of the two mass squared differences and mixing angles including $\theta_{13}$ can be produced in the MSSM case with tan$\beta$ = 10 and non zero Majorana CP phases at low energy.

---End quotation

My general impression is that, though this is a quite competent paper and exploration of theoretical possibilities, it may be too technical for the present discussion without some considerable commentary and non-technical elucidation. 

"Supersymmetry" is a proposed extension of the standard model of particle physics, which proposes that the recognized particles of the standard model have super-symmetric corresponding particles --which have yet to be experimentally detected, so far as I know. This would require three additional neutrino-type particles with greater masses--as I recall?

I take it that this paper presents new results in mathematical physics (not experimental results) and that this involves some comparison with results involved in an alternative theory of "Majorana neutrinos."  A chief concern is whether some possible theoretical developments can meet the requirements of the data of observation regarding neutrino oscillations.  

H.G. Callaway

@ Mukta,

The answer to your question is straight forward.

The rest mass is very, very  small for each of the flavours of neutrino, electron, moun and tau neutrino, (but not completely massless). Clearly there will be a mass hierarchy with the tau neutrino being the heaviest. But most of the mass is relativistic, that is most of the mass derives form the near light speed velocity of the neutrino. Because of that the relative rest mass of each of the flavours of neutrino are very close. Hence neutrino oscillation is to be expected.

As greater the energy, as no  difference between their masses.