19 Mar 2010 8:35:43 UTC

Topic 194824

(moderation:

Just to increase the elementary particle zoo, a fourth neutrino version, which does not interact even weakly and is therefore called "sterile" makes its appearance. Could it be the "dark matter"?. You pays your money and you makes your choice.

sterile neutrino

Tullio

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## Sterile neutrino

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They want $8 for that one article??? Wow.

## RE: They want $8 for that

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I got it for free, I don't know why.I have no paid subscription.

Tullio

## Neutrinos are weird and hard

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Neutrinos are weird and hard to fathom sometimes. There is a subtle but important difference in how they are detected, due to their extremely low interaction rate with more 'ordinary' matter.

With say a high energy proton plowing through a cloud or bubble chamber ( pre solid-state detector days ) you'd see a track formed by successive collisions along some line ( or evident curve if a strong enough magnetic field present ). This track is actually a string of distinct expanding voids formed in the chamber's working fluid - just below a phase change ( near 'boiling' ), so local addition of energy by the proton causes expansion from a collision vertex - suitably photographed with the right timing delay and triggers. Too early after the proton's passage and the voids haven't grown to viewable size, too late and they get too big thus showing a 'thick' track. Think of a track as like a string of closely spaced beads. So a given track represents very many collisions, or put another way the interaction 'cross section' for protons with normal matter is quite high and thus very short distances separate collisions in the usual density of materials used.

Not so with neutrinos. It's like the order of a light year between collision vertices in say lead. As we don't have detectors of that dimension, or larger, we aren't ever going to see a given neutrino bounce off anything more than once in a typical detector. So they have an extraordinarily low 'cross section' for collisions. Cross section is a calculated quantity that reflects the probability of some interaction. It has the units of area - amusingly called 'barns' - and you can think of it like some target to hit. If the target is small then it's hard to hit, and vice versa. Can you hit a barn door with a neutrino ? ;-)

Anyhow neutrino detection isn't by tracks per se, but by deduction at single interaction vertices. So if a neutrino is 'born' in the Sun, say, that's one vertex ( that we never see of course ) and the other may be in a detector that we build. We find evidence with some events where momentum and/or energy doesn't balance sufficiently before and after collision points well enough, and we attribute the residual to the neutrino. Thus the neutrino 'appears' as a correction to keep our accounting neat. We like the general conservation laws, but that's OK to use that in this way. In a sense we have nominated a special account type, the neutrino ledger, for energy and momentum transport between places in the Universe. There's no neutrino 'track' visible in cloud chamber or bubble chamber photos ( solid state devices haven't really changed this aspect of neutrino detection, while improving many other measurement modes ).

So what's all the fuss with neutrino types, sterile or otherwise? Well you have to make some assumptions ( all are quite reasonable ) and work on large sets of data. So if I do neutrino detections at different distances from some known source ( like the Sun or an artificial nuclear reactor ) I'll find a waxing and a waning of the numbers in a rhythmic pattern. I deduce that the neutrino 'flavour' is changing with distance, as different detector setups ( one may be more sensitive to electron interactions, others with muons ) are used. What's generally been found found is that the total amount of neutrinos reduces in an acceptable way with distance from source ( like inverse square as you'd expect with an expanding shell of area ), but which type of lepton interaction ( electron/muon/tau ) is dominant at any given distance is what fluctuates.

The really queer bit is pure quantum mechanics. So just to annoy and confuse you, there is flavour mixing in addition to the flavour changing with distance as described above. While not absolutely necessary as an explanatory mechanism, it turns out the results of these type of studies make the simplest sense ( Occam if you like ) if one posits that : what is experimentally deemed to be an electron neutrino, or a muon neutrino, or a tau neutrino actually are each superpositions or mixtures of other 'base' types. These base types ( either three or four of them, you could label them as I, II, II and maybe IV if you like ) are not separately detected, but only mixtures thereof are. And these mixtures ( of I, II, III or IV ) are what we see as electron-type, muon-type, tau-type or sterile-type.

[ So it's a bit like like being told that 'Neopolitan' ice cream - you know, where strawberry ( yum ), chocolate and vanilla flavours are in distinct adjacent blocks/areas of a tub - are really each a superposition of three other ice cream types that you've never tasted separately. Nor will you ever know what I, II, III taste like alone. ]

The sterile neutrino is, by definition, not interacting ( even at the incredibly low cross section of neutrinos generally ) at all. So how can one say it exists if it doesn't interact? What's the accounting trick here? To a point this now depends on who you ask .... traditionally the idea has been that maybe we haven't accounted for all neutrinos by adding up the 'visible'/deducible electron/muon/tau types. Maybe a fourth, sterile type ( yet another mixture of I, II, II and now IV - as there has to be as many 'hidden'/base types as the number of distinct mixtures ) exists. So it's never detected per se, but the other types morph into/out-of it none the less. Sounds like the reserve bench for a footy game, there may be 18 guys out on the field ( Aussie Rules here ) playing at any one moment, but you can still swap to and from a pool of two extras on the sidelines. Ditto for basketball etc. I think/remember the key parameters being in the decay modes of certain things via neutrino production. The rates of decay depend on how many choices/pathways of doing that, which in turn depends on how many neutrino flavours ( 3 or 4 ) that you have.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## The neutrino: who ordered

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The neutrino: who ordered that? I think Wolfgang Pauli made the comment.

Tullio

## RE: The neutrino: who

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I don't want to nit-pick, but it seems it was Rabi speaking of the muon. At least that is what THE INTERNET says.

Michael

Team Linux Users Everywhere

## RE: RE: The neutrino: who

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You are probably right. But I know Pauli was skeptical about the neutrino.

## I think I.I.Rabi was the

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I think I.I.Rabi was the first to say that. When the particle 'zoo' started to appear with the 50's and 60's 'atom smasher' machines, and confusion reigned as new particles were just everywhere, many others copied the joke/comment.

He is perhaps less well known for his standard comment as a researcher in the Radiation Laboratory ( MIT, USA ) during WWII, upon seeing a new device or weapons design : "How many Germans will it kill?". Chilling to read now, but that was then. Different times.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## A further word on neutrino

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A further word on neutrino mixing, if you will bear it .....

Forget neutrinos for the moment and think of how you specify the location of something in 3D space. Normally you would construct 3 axes ( x, y and z ) converging at a point ( the origin ) and each lying at right angles to the other two ( orthogonal ). So if I have some object 'over there' somewhere I am going to start at the origin, and go along parallel to each axis in turn and remember the distances as I go, until I get to what I'm measuring. I'll get three numbers indicating the components of a vector from my co-ordinate origin to the point of interest.

Now suppose that you also have your own co-ordinate system - with the same origin as mine, and using the same length units ( metres say ) - but rotated in some fixed way with respect to mine. If you want to get a vector ( in your 'reference frame' ) to the very same physical point/object that I measured then you follow the same procedure that I did. Only going parallel to your axes, and not ( necessarily ) parallel to mine. You'll get another three numbers as components of a vector, but with respect to your system this time.

Unless there's some ( non-Euclidean ) funny business going on then we'll at least agree on the total length of each our vectors to the same object, despite that the respective components vary. The other constant b/w us is that we both need 3 sets of axes and components ( axis-parallel distances ). Nor will it matter in what order I went parallel to the x, y and z axes. I could go x, y then z. Or y then x then z. Or ..... etc. As long as I start at the origin, always move parallel to one given axis at a time, keep track of distances ( positive one way and negative the other ) ....

One can convert measurement in one system to the other if you know 3 angles : the ones b/w the respective axes in each system. Between x and x'. Between y and y'. Between z and z'. Where the prime ' means your axes, unprimed is mine. With some straightforward but none-the-less annoying trigonometry you can derive a method ( in matrix form is simplest actually ) to convert measurements ( the vector component values ).

In generic form ( tx, ty and tz are those angles between axes ):

x' = f(x, y, z, tx, ty, tz )

y' = g(x, y, z, tx, ty, tz )

z' = h(x, y, z, tx, ty, tz )

Where f,g and h are functions with sines and cosines and stuff. In particular, the axes of one system can be expressed as a mix of the axes of another. And vice versa. Because we like the idea that there isn't any one 'special' co-ordinate system then we could just as validly start with your components in your system and work towards mine :

x = f'(x', y', z', tx, ty, tz )

y = g'(x', y', z', tx, ty, tz )

z = h'(x', y', z', tx, ty, tz )

Either way we need those 3 angles to do it right [ there's other requirements eg. if I start in my system, convert to yours, and then convert back to mine : I should get back where I started with the initial component set. ]

Now let's broaden our thinking out of or beyond physical space now. Not by adding extra 'physical length' dimensions, but generalising the concept of 3 degrees of freedom. We could think of any 3 independent attributes of some problem. Like the engine capacity of Volvos, their number of passengers and the fuel economy .... :-)

Or a set of 3 things like, say, the quantum numbers that describe neutrino attributes. I can then plot each known neutrino type ( electron/muon/tau ) with respect to axes in this 'space'. So any neutrino is going to have three numbers representing 'distance' along each of these axes, I'll get three 'vectors' to each of the known electron/muon/tau neutrinos.

Now as the problem initially stood, each 'real' neutrino would be non-zero for one component but zero for the other two components. This means you could crawl parallel to one axis alone and get to an existing neutrino. None of the neutrino 'points' were lying off a particular single axis.

However .... you may have guessed the punchline by now ... you can rotate the axes that mark neutrino 'quantum numbers' such that each one no longer lies along the line of a distinct axis. 3 axes, 3 neutrinos, with each neutrino now specified ( in a new co-ordinate system ) by having non-zero component values for at least two of the components.

Call the first system of neutrino co-ordinate axes 'electron', 'muon' and 'tau' - with the second ( post rotation case ) axes I, II and III and you have the present description. Each detectable neutrino type - electron/muon/tau - is a mix of the other 'base' types - I, II and II. So why complicate matters by choosing a non-evident system where co-ordinates aren't simple? If there were only neutrinos in the world it wouldn't matter much I suppose, but for even more arcane reasons than presently discussed ( which I really can't follow myself, so I won't embarrass myself more by trying ) other matters in particle physics simplify dramatically by doing this.

This was cracked open by Mr Cabibbo, the first such angle of three was nominated as the 'Cabibbo angle' but as a group they are now called 'Cabibbo angles' or 'mixing angles'. They represent something ( who knows quite what yet ) fundamental about the universe. 3 detectable neutrino variants, 3 base neutrino types, 3 angles, 3 physical dimensions for that matter ..... who is for numerological co-incidences? :-) :-)

Or is it? A fourth neutrino, hence a fourth non-physical axis in our neutrino-quantum-number description? Call it the 'sterile' axis and the corresponding IV axis after to the 'rotation'? A four dimensional space now? Four Cabibbo angles?

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## AS an afterthought, Pauli was

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AS an afterthought, Pauli was indeed the first to advance the idea of a neutral particle to conserve energy and momentum in beta decay. It was Fermi who called it "neutrino" (little neutral one) to distinguish it from the bigger neutron discovered by Chadwick. But Pauli doubted that it could be detected by an experiment, and when Fred Reines and Cloyd Cowan did succeed in detecting one at Los Alamos in 1955 I think Pauli had to pay some ransom, maybe in liquid form (champagne, I believe). Now huge liquid neutrino detectors at the underground Gran Sasso laboratory have detected neutrinos coming from nuclear reactions in the core of the Earth (the Borexino experiment).

Tullio

## RE: A four dimensional

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Actually I think you need 6 angles for a 4D space ... yup, (4 * 3) / 2 = 6 as opposed to (3 * 2) / 2 = 3. Generally n(n-1)/2. Meaning the angles from one axis to each of the remainder, but don't double count as you iterate through them all.

Cheers, Mike.

( edit ) and I'm assuming this 'quantum number space' is at all Euclidean! :-)

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal