Talk:Neutrino oscillation/Archive 1

math typo
I changed


 * $$ \left| \nu_{a} \right\rangle = \sum_{a} U_{ai}^{*} \left| \nu_{i} \right\rangle\,$$

to


 * $$ \left| \nu_{a} \right\rangle = \sum_{i} U_{ai}^{*} \left| \nu_{i} \right\rangle\,$$

because the former was obviously wrong. Someone with more knowledge should check if this is now correct. 193.171.121.30 11:27, 7 February 2006 (UTC)


 * Thanks. That was the right fix. linas 01:54, 8 February 2006 (UTC)

Neutrino Parameters and Their Values
Can anybody define these parameters? I guess they correspond to the angles that the mass and flavor eigenvectors form but they are never mentioned in the text. Poszwa 02:48, 20 March 2006 (UTC)


 * They seem to be at least somewhat explained now. What do you think? Strait 22:35, 13 July 2006 (UTC)

Mixing Matrix Definition
I think the Mixing Matrix might be defined the wrong way round. U_{lk} is the co-efficient of mass state |v_{l}> in weak state |v_{k}>, not the other way round. Not so much wrong, as just different to the general convention I suppose.

I'm not sure how clearly I've put that, but hopefully it makes sense. Can an expert check this? (See, for instance, Author: Giunti, arXiv:hep-ph/0611125v1)

128.250.54.30 07:21, 3 July 2007 (UTC) Alex

Fermions are matterparticles?
The article states that fermions are "matter particles". I think this formulation is awkward, since combining two fermions creates a boson, which could still be a matter particle. I think that comment should be removed. Andersa 12:16, 11 April 2006 (UTC)


 * Then be bold and remove it! —Keenan Pepper 13:55, 11 April 2006 (UTC)

Neutrino interference compared to oscillation
I went through a long discussion on PhysicsForums with a student who was convinced that neutrino oscillation was incompatible with the rules of physics, specifically conservation of energy. His problem was that the flavor eigenstate neutrinos do not have well defined mass, so he concluded that the process could not have well defined energies.

I finally got him to at least agree that neutrino oscillation was compatible with the assumptions of QM by describing the situation from the point of view of the neutrino mass eigenstates. See post 47 in http://www.physicsforums.com/showthread.php?t=115360&page=4

When looked on in this way, while flavor eigenstate neutrinos oscillate, the mass eigenstate neutrinos interfere. That is, all three mass eigenstate neutrinos contribute to the combined process of decay (in the sun) and absorption (at the detector), and since the experiment cannot distinguish which of the neutrinos was involved (as their masses are so very small compared to the energies involved), the rules of QM say that one must add together the diagrams for all three masses before computing probabilities.

The result is that the three massive neutrinos interfere with each other in the same manner as a photon interferes with itself in the 2 slit experiment. It's a great illustration of how the rules of QM are used in QFT.

I think that this should be added to the discussion for two reasons. First, it illustrates a principle of QM and Feynman diagrams. Second, it resolves the confusion in the student as to where neutrinos that oscillate go. Unfortunately, while this is all very obvious, I can't find a reference that explains neutrino oscillation in this way. Does that make it incompatible with Wikipedia standards?

I'd type up a short description but I hate wasting my time. Any comments?

Carl


 * The notion of the student that the energy ( and momentum) of the neutrinos are not well defined (i.e. they are not energy/momentum eigenstates) is not wrong. The energy uncertainty of the initial state from which the neutrino is produced must be larger than the mass difference. With the uncertainty relations this translates to the condition that the initial state must be localized in a region of space smaller than the oscillation length, otherwise the oscillation pattern would be smeared out. This is also the reason, why there are no observed oscillations from electron to muon, which in principle also should be possible. Here the mass difference is much larger than the typical energy uncertainty in experiments while the oscillation length is much too small in order to be observable. A thorough treatment of neutrino oscillations actually should work with localized wave-packets of neutrinos. 212.66.146.131 (talk) 16:01, 9 February 2011 (UTC)


 * This is a good idea. I will eventually get around to writing it up if no one else does first. Strait 22:36, 13 July 2006 (UTC)


 * Ok, I have made a graphical guide to neutrino oscillations. I have not (yet?) attempted to tackle the subtle quantum mechanical points, though. Strait 02:59, 8 August 2006 (UTC)

Expert
I think that I have added enough to this page to warrant removing the expert tag. If you disagree, please put it back and say why you did so here. --Strait 18:26, 7 August 2006 (UTC)

Flavor and mass do not commute
How can we describe the mass of any neutrino flavor since they are not mass eigenstates? I ask because there is a flavor - mass table at neutrino, which would seem a contradiction in terms. --Michael C. Price talk 07:57, 23 August 2006 (UTC)


 * The mass of a flavor eigenstate such as the electron neutrino can be defined as a weighted average of the masses of the mass eigenstates of which it is composed. For example, if the electron neutrino is 70% ν1, 20% ν2 and 10% ν3, then the mass of the electron neutrino is 0.7m1 + 0.2m2 + 0.1m3.  I believe that this mass is the appropriate mass to consider when looking at direct measurements such as those gotten by observing the electron energy in beta decay.  However, I think that for some phenomena such as neutrinoless double beta decay, the flavor eigenstate's mass must be defined somewhat differently.  I will look into this and add information to the appropriate places when I get a chance.  --Strait 21:00, 31 August 2006 (UTC)

Oscillations in matter
"I have added the probabilities of oscillations through solar matter. I used Runge Kutta method in maple to solve the coupled equations. I'll add the theoretical discussions soon. Please comment."

Since we know that there are three neutrinos that participate in oscillation, and we know fairly well what the relevant parameters are, I would prefer that the three neutrino model be used for specific real-life cases like propagation through the sun. The two neutrino framework is all well and good when the discussion is pure theory, but it's not actually what happens.

Once you're done writing the new section on solar oscillations, the section near the top called "Solar neutrino oscillation" should be edited to reflect the addition. --Strait 22:16, 27 November 2006 (UTC)

Oh, also, if you have a good understanding of the MSW effect, you might try to improve that page. (I only just barely understand it myself, so I don't want to try.) --Strait 22:18, 27 November 2006 (UTC)

Importance
This article has been rated as being of "low" importance. I think that a phenomenon which stems directly from the (apparently) fundamental parameters which define the universe, and is the only known way of measuring those parameters, should be rated at least "mid" if not "high". I think that this page is not well described by "Subject is mainly of specialist interest." --Strait 21:34, 11 December 2006 (UTC)

Article length
Adding all the graphs has started to make the article a bit long, in my opinion. Pictures help readers understand the content, so we should leave them. I would rather see something more technical move away. General readers might look at this article after the recent publicity including a NOVA episode devoted to the subject. We could consider reseparating the Maki-Nakagawa-Sakata matrix because it contains all the numerical details unappealing to general readers. This could also discuss experiments that attempt to measure the values. Notice how the Cabibbo-Kobayashi-Maskawa matrix has its own article. Teply 03:33, 19 December 2006 (UTC)


 * Agree, if it can be done elegantly. If you start the process, I will be around to help.  --Strait 04:31, 19 December 2006 (UTC)

Indeed I did come to this page after viewing the Nova episode, "The Ghost Particle." The question in my mind--not resolved because I don't completely follow the math in the main article about mass and flavors not being congruent: since the masses of the three flavors of neutrino differ by more than six orders of magnitude (2.2 eV, ~170 KeV, ~15.5 MeV), oscillations among flavors, in order to conserve energy, must be accompanied by changes in velocity. Is this correct? At what fraction of the speed of light do solar neutrinos travel as electron neutrinos, and how much does this velocity decrease when they assume the other flavors? 21:08 PDT, 10 April 2008 —Preceding unsigned comment added by 67.161.40.124 (talk) 04:10, 11 April 2008 (UTC)

Is the neutrino flavor a "hidden variable"?
This isn't my field, and likely I'm misunderstanding - but what confuses me is that the neutrino seems only to be observed as one of three quantized flavors; yet it seems to know, internally, precisely at what point in its oscillation it is at at any given time. Given the source of the neutrino and approximate momentum it seems like you could come up with a better model of the neutrino's internal state (how likely it was to be a certain flavor and when it would turn into another) than you could actually measure. Does that make its oscillation state a "hidden variable" in the deprecated quantum mechanical sense? 70.15.116.59 (talk) 23:17, 9 December 2007 (UTC)

Removed reference to Nyquist theorem in context of Neutrino oscillation
As I understand it, neutrinos come in several varieties, such is the electron neutrion, the tau neutrion, and the muon neutrino. In simplest terms, take any one of these neutrinos and add a negative W Boson and you will get an electron, or a tau particle or a muon, accordingly. It is as if the neutrino is the "bucket" that can accept the quaunum of charge, and the boson is like the water that goes into a bucket. As such it is possible that neutrinos DO NOT OSCILLATE, but rather it may be that the sun gives off some muon neutrinos, and that while on the way to earth some muon neutrinos collide with free neutrinos that are drifting in the vacuum, in which case - there is an appropriate transfer of linear momentum from one particle kind to another. So the neutino game might simply be like a game of marbles, or billiards. In such a context; the Nyquist theorem would be irrelevant; since such neutrio oscillations would not imply that free neutrinos oscillate among types, but rather type exchange occurs freely because of interaction with the neutrios that are free in the presumed vacuum. —Preceding unsigned comment added by Lazarus666 (talk • contribs) 01:21, 9 August 2008 (UTC)

Conservation of energy and momentum
I have removed several edits from 88.68.XXX.XXX that has repeatedly stated that energy and momentum are not conserved by neutrino oscillations (as well as some personal opinions on the matter from the same source). As stated before on this talk page, neutrino oscillations occur because the mass eigenstates (which are the only ones that can possess definite energy and momentum) interfere with each other and that the flavor eigenstates produced in weak interactions are superpositions of these states. The theory is sound, completely analogous to that in the quark sector (although quarks possess properties that rules out any such interference - i.e., charge, large mass differences etc), and experimentally verfied. Of course, neutrinos are not plane waves, or produced with definite energy or momentum as the simplified derivation in the article suggests. However this is by far the easiest way of reasoning and it gives the correct result when compared to a full quantum field theoretical treatment in the ultrarelativistic limit. I would be happy to take any discussion on the theory of neutrino oscillations, but it should be kept here and not through vandalism of the article. --Blennow (talk) 09:17, 24 October 2008 (UTC)


 * Neutrino flavor states are not equivalent to the mass eigenstates, i.e., a flavor eigenstate does not have a definite mass. In addition, neutrinos are not actually produced in plane waves (no particles are), and thus, cannot have well defined energy or momenta. Rather, they will consist of superpositions of several different states of energy and momentum (this would be true even if the flavor states were the mass eigenstates). The different mass eigenstates will have well-defined relations between their energy and momenta, which is used in the derivation of the neutrino oscillation probabilities. However, since flavor eigenstate neutrinos are superpostions of the mass eigenstates, neutrino oscillations appear as interference between the mass eigenstates. There are several papers treating neutrino oscillations from a quantum field theoretical point of view, but I would say the content is not really suited for an encyclopedia. The result is essentially that the neutrino oscillation formulas obtained from the plane wave approximation are correct in the ultra relativistic limit. --Blennow (talk) 12:45, 24 October 2008 (UTC)


 * A single neutrino having a total energy E and a total momentum p which does not interact with any kind of matter or energy has a mass of
 * $$ m = \sqrt{\left({E/c^2}\right)^2 - \left(p/c\right)^2}.$$


 * Since E and p are conserved, the mass m is conserved as well. Therefore, the rest mass of the neutrino is conserved in neutrino oscillations or a fundamental law of physics is violated. --84.59.254.119 (talk) 12:54, 24 October 2008 (UTC)


 * Yes, that was your last edit. Feel free to point out which parts of my explanation that you find to be unclear. Bottom line is that the neutrino mass eigenstates obey that relation (although they are not states of definite energy or momentum, but rather superpositions of states with different energy and momenta - the only states which have definite momenta and energy are the plane waves, but those are not localized and fill all of space - this also holds for the charged leptons by the way) but they are not the states that actually interact (as in the quark sector, there is a misalignment between the states that couple to the W-boson and the states which are mass eigenstates - see CKM matrix). Because of the small mass squared difference, the mass eigenstates will interfere up to the point when the wave packets get separated enough to not overlap (precisely for the reason that different mass eigenstates have different masses). This is known as the correlation length, which is usually longer than the oscillation length and depends on both the creation and detection processes. The correlation length is usually defined as:
 * $$L_{\rm coh} = 2\sqrt{2} \frac{2\sigma_x E^2}{|\Delta m^2|},$$
 * where σx is the wave packet size. In general, it is not possible to separate the propagation from the creation and detection - however it is possible in the ultra relativistic limit, where it gives the result which is heuristically derived in the article. --Blennow (talk) 18:15, 24 October 2008 (UTC)


 * You mentioned an interesting point:


 * … this also holds for the charged leptons by the way …


 * So — why highly relativistic electrons do not oscillate and transform to myons? --88.68.120.100 (talk) 20:28, 24 October 2008 (UTC)


 * What we define as electrons are mass eigenstates. The reason we define the electrons, muons and taus to be the mass eigenstates is that the mass differences are so large that the mass eigenstate can be determined by measuring the kinematics of the reaction that produced it - or by measuring the q/m ratio. A more detailed discussion on why charged leptons do not oscillate was published by Evgeny Akhmedov in JHEP 0709(2007)116 (see arXiv version for preprint). Also low-energy neutrinos probably oscillate - although there is no experimental test of this so far - just that the simplistic derivation of the oscillation probabilities no longer gives the correct oscillation probabilities. Let me also note that, even if the mass differences were large enough to produce decoherence quickly, there would still be flavor transitions. This would simply come from the creation process creating different mass eigenstates with different probabilities. Each mass eigenstate produced then has a given probability to create a charged lepton of a certain flavor when interacting through a charged-current. Again, this would be completely analogous to what happens in the quark sector. However, there we have taken another approach since all the quarks are quite massive - we simply define the mass eigenstates as up, down, charm, strange, top, and bottom, which is what results in the up-coupling with the W of both the down and the strange quarks. If we would have had the same approach in the lepton sector, we would call the neutrino mass eigenstates certain (probably more elaborate than 1, 2, 3) things. However, because of the short-distance interference, it makes more sense to work with the interaction eigenstates. --Blennow (talk) 21:24, 24 October 2008 (UTC)


 * Sorry, that is a little too much to follow in detail. But, obviously there are some reasons why electrons cannot transform to myons, though their energy in accelerators may be extremely high compared to the rest mass. The question is now, why these arguments cannot be applied to neutrinos? --88.68.126.182 (talk) 08:20, 25 October 2008 (UTC)


 * Of course there are good reasons, why an electron cannot transform to a myon without interacting with other particles. The most obvious is the conversation of energy and momentum, because myon and electron have a different rest mass:


 * A single electron having a total energy E and a total momentum p which does not interact with any kind of matter or energy has a mass of
 * $$ m = \sqrt{\left({E/c^2}\right)^2 - \left(p/c\right)^2}$$


 * which is conserved as well. If, nevertheless an electron would transform to an myon such an oscillation would be observed certainly, since its path in an electric or magnetic field would change immediately. But, there is no experimental evidence for such a process. --88.68.118.88 (talk) 10:44, 25 October 2008 (UTC)


 * Here, again, the point is that the electron is defined as the mass eigenstate. The problem with neutrinos is that the mass eigenstates are not really the states that are the most convenient to work with. If we forget about neutrino flavor states for a short time: There are six leptons, three which are electromagnetically charged (let us just call them "charged leptons") and three which are not (let us call them "neutrinos") - they all have definite masses. In weak interaction, it is not certain that the charged leptons couple to only one of the neutrinos (just as in the quark sector where the up quark is coupled to both the down quark and the strange quark). Let us consider a process in which a charged lepton is produced along with a neutrino, which propagates and finally interacts with some matter producing yet another charged lepton. Let us also assume that we know which charged lepton (mass eigenstate) is produced in the first process. If the uncertainty in the momentum and energy of the charged lepton is low enough, then we will know exactly what neutrino mass eigenstate that was produced - the probability of creating a charged lepton of a given flavor in the final reaction will be given by the coupling between the neutrino and the different charged leptons. You have exactly the same type of situation in the quark sector, for example, the weak decay D+ → K0 + … is essentially due to the coupling between the c and s quarks, but the s quark also has a coupling to the u quark so the K0 can decay as K0 → π+ + ….


 * Now assume that the uncertainty in the initial charged lepton is not small enough to distinguish the neutrino mass eigenstates. If we then want to know what the probability is of producing a lepton of flavor β in the final reaction and a lepton of flavor α in the initial reaction, we must add the amplitudes of all of the intermediate neutrinos, which will lead to interference. This is what is known as neutrino oscillation (producing different lepton flavors in different ends of the experiment), the neutrino mass eigenstates never change, but the amplitudes to which they contribute will be subject to interference. The reason we define neutrino flavor states at all is that neutrinos are nearly massless, so the interference pattern between the mass eigenstates has a very long wavelength, but beware - they do not have definite mass, definite energy or definite momentum - so you cannot use the mass-energy relation for a neutrino flavor state. --Blennow (talk) 12:28, 25 October 2008 (UTC)


 * No doubt — neutrino oscillations violate energy or momentum conversion. --84.59.229.104 (talk) 14:57, 25 October 2008 (UTC)


 * They do not, not any more than weak decays of charmed mesons or baryons. As I have explained repeatedly, flavor eigenstates do not have definite mass and there is no dispersion relation of the form E2 = m2 + p2 for them. If you would tell me which part of the description you don't understand - instead of repeating a statement that I have repeatedly argued is false - I might be able to clarify that part. It is hard to explain something when you do not know the knowledge level of the person you are trying to explain it to. --Blennow (talk) 15:31, 25 October 2008 (UTC)

PMNS Matrix
I started a full article at Pontecorvo–Maki–Nakagawa–Sakata matrix. Review/Feedback/Expansion are appreciated.Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 14:11, 4 June 2009 (UTC)

Mixing with sterile neutrinos
It was stated that sterile neutrinos can oscillate with "normal" neutrinos. I'm trying to understand sterile neutrinos. I'm not clear whether "sterile" just means "right-handed". Are they synonymous for neutrinos (with the usual proviso that we switch left/right for particle/anti-particle)? If sterile neutrinos are just right handed neutrinos then it seems to me that they will have different weak hypercharge (0 for right-handed neutrinos, -1 for the left-handed neutrinos) and X charge. If so, wouldn't that prevent their mixing? --Michael C. Price talk 06:01, 21 November 2009 (UTC)
 * I think that "sterile neutrino" can refer to any fermion that doesn't interact by any of the Standard Model forces. Opposite-handed counterparts to the known neutrino fields are the most obvious candidates, but not necessarily the only ones. Left-handed and right-handed neutrinos would mix in the same way that other left-handed and right-handed fields mix—by the Higgs interaction. This conserves weak hypercharge because the Higgs also carries one unit of weak hypercharge. There's no evidence at this point that neutrinos are any different from the other SM fermion types, aside from happening to lack both electric and color charge. They seem different because their flavor basis is defined differently from the other fermions', but that's just convention. The same phenomenon that's called "neutrino oscillation" in the lepton sector is called "flavor-changing weak interactions" in the quark sector. -- BenRG (talk) 17:58, 21 November 2009 (UTC)

Thanks for the feedback. I was being a bit sloppy with my language. By "mixing" I meant the neutrino family oscillations e-mu-tau-e-mu-tau (which preserve quantum numbers), not the Higgs left-right-left-right flipping that give them mass (which, as you correctly observe, will change any quantum numbers carried away by the Higgs).--Michael C. Price talk 22:01, 21 November 2009 (UTC)

Justification for "Two neutrino case"
"These approximations are possible because the mixing angle θ13 is very small and because two of the mass states are very close in mass compared to the third." Please remove.. not justified. We do not know that much, there is also a model with a completely different mass hierarchy, that is not yet ruled out by experiment. This is simply a toy model and needs no justification. —Preceding unsigned comment added by 134.176.18.59 (talk) 16:59, 25 May 2010 (UTC)

Energy for "propagation and interference"
$$E_{i} = \sqrt{p_{i}^2 + m_{i}^2 }\simeq p_{i} + \frac{m_{i}^2}{2 p_{i}} \approx E + \frac{m_{i}^2}{2 E} $$, is a bit confusing when E is not specified. —Preceding unsigned comment added by 134.176.18.59 (talk) 16:26, 26 May 2010 (UTC)
 * Yes! I came here to the discussion page to mention the same thing. I looked for this calculation elsewhere and I found that something similar is done: in the calculation p is written directly instead of $$ p_{i} $$ for every i (when writing $$|v_{i}(t)> $$), but it does not say why.

--190.188.3.11 (talk) 14:40, 10 June 2010 (UTC)

Hey guys can you please mention in the article that when you write m_i, you are referring to m_*c^2, when you write p, you are referring to pc and finally, when you write L, you are referring to L/c^2?
 * Yep, somewhere the use of Natural units should be mentioned --134.176.18.59 (talk) 21:27, 16 October 2010 (UTC)

Reference
I think "propagation and interference" and "Two neutrino case" are very much like Chapter 5 of

Massive neutrinos in physics and astrophysics,Mohapatra, R.N. and Pal, P.B., 2004, Imperial College Pr

--134.176.18.59 (talk) 21:27, 16 October 2010 (UTC)

Error in formula?
In the central matrix in the matrix product under Classical analogue of neutrino oscillation (see http://upload.wikimedia.org/math/1/2/1/1214e944a130d2330f77074725ccee73.png) it appears that a minus sign and a plus sign have switched places in the upper row. Shouldn't that row read "g/La - k/m, [+]k/m"? - Episcophagus (talk) 16:23, 11 June 2011 (UTC)

Zambrano's hypotesis
User Hugozam has created this section and provided all content without any references. I've asked him/her for references, but haven't heard back. Does anybody know if the information is correct and/or have a reference? If not, I suggest we remove the section. — SkyLined (talk) 15:04, 14 November 2011 (UTC)
 * Section removed. There's no Zambrano hypothesis in established neutrino physics and for the looks of it, there will never be.Airsh —Preceding undated comment added 15:34, 15 November 2011 (UTC).

Thanks! — SkyLined (talk) 16:50, 16 November 2011 (UTC)