Monday, July 17, 2006

Neutrinos for Beginners

When I started my position at the University of Arizona, Keith suggested an interesting work about neutrinos to me. I didn't know very much about neutrino physics at this time (okay, I didn't know anything at all). However, I could immediately relate to these elusive particles with small masses that interact only weakly, and which have caused not little physicists to scratch their head.

During the following year, I learned a lot about neutrinos. Here, I'd like to give you a short and very basic introduction of what turned out to be a very fascinating and lively field of theoretical as well as experimental physics.

This is a three-step programme... today is for beginners.


When we were kids, my younger brother drove me crazy. Each time my grandma gave us 50 Pfennig, we would go to get ice cream. But when we arrived at the store, my brother could never made up his mind between vanilla and chocolate.

Thus, whenever we left home, I asked my brother what flavour he'd go for today. He'd start with a definite 'It's chocolate day', but after a minute he'd mumble something. Then it was 'Maybe vanilla', then 'No, chocolate', then again 'Better vanilla'... When we arrived at the store, he was caught somewhere between vanilla and chocolate. That is, until I'd yell at him to make up his mind before the queue behind us would just shove us away.

This I-scream issue was solved when the store got a new owner who introduced chocolate coating. So, my brother could get vanilla with chocolate and didn't have any more flavor problems.

Neutrinos come in three flavours. Each of them belongs to a charged fermion. There is the electron, the muon and the tau-neutrino. Neutrinos are produced in interactions (e.g. in the sun) and start their travel with one of these flavours. However, while time goes by, they can change from one flavor to another, and back, in a periodic process. Which flavor you find then depends on the time that passed after the neutrino was produced - or the distance it travelled during this time, respectively.

This is called neutrino oscillation. In his very readable introduction, John N. Bahcall refers to this as a 'multiple personality disorder'... ;-)

There are however mixtures of neutrino flavors which remain unchanged when you start with them, like the vanilla-with-chocolate choice. These time-independent choices have distinct masses, and are therefore called mass-eigenstates (there are also three of them). An important thing to know is that oscillations only take place when these masses are different. This implies that at least two of the masses have to be non-zero.

This is what makes neutrino-oscillations so interesting, because in the Standard-Model of particle physics, the neutrino masses are exactly zero. By examining the properties of the elusive neutrino however, we find that this can not be the case. We are therefore testing physics beyond the standard model - a challenge for every theoretical physicist, and a promising source for new insights.

The typical distance it takes for the neutrino to return to it's original state is the oscillation length. It depends on the energy of the neutrino. The larger the energy, the longer the oscillation length. It is also related to the differences of the squared masses. The smaller the difference, the larger the oscillation length. For zero difference, if would take forever for the oscillation to happen.

The second relevant quantity is the maximal fraction of flavor that can change into a different flavor. This is parametrized in the 'mixing angle', and measures how 'mixed up' the flavors are. An angle of Pi/4 refers to 'maximal mixing' at which one flavor can change completely into another.

The standard-model does not predict the number of flavors. In principle there could be more than three, but we know from experiments that - when equally light as the three known flavors - such additional particles are not produced in any reaction we have ever observed.

Such hypothetical extra neutrinos are therefore referred to as 'sterile', and would not be detected through the usually studied reactions. (They could, however, be detected indirectly as a missing signal, or from cosmological observations.)

By now, the properties of the neutrino-oscillations, mixing angles and squared mass differences, are measured very precisely. But for the theoretical physicist, the situation is a little unsatisfactory. Though one can calculate with the assumption of neutrino-oscillations, we don't know why the neutrino-masses are so small, how these masses are embedded in the standard model, or why the mixing between the flavors is so large. There is lots of stuff left to do...


During the last years, it has been confirmed with high precision that neutrino oscillation indeed happens. This is quite an impressive achievement as the mass-differences that have been measured are extremely small, less than 1 billion of the proton's mass.

The existence of neutrino-oscillations solves the puzzle of the solar neutrino deficit. Based on models of processes in the sun, one can compute how many electron neutrinos the earth should receive from the sun's nuclear fusion. However, far too little of the electron neutrinos were measured on earth, and it has been speculated that something is wrong with our understanding of the sun.

But eventually in 2002, the SNO-collaboration also measured the two other flavors, the muon- and tau-neutrinos by what is called a neutral-current interaction. Such, they were able show that the missing electron neutrinos indeed arrive - but with a different flavor. Since this total number measured is very close to what is expected from the sun's production of neutrinos, this also excludes substancial oscillation into sterile neutrinos (very small mixtures into sterile neutrinos are still not completely outruled).

Besides in the sun, neutrinos are also produced in the earth's atmosphere from cosmic rays. Here, it's a mixture of electron and muon neutrinos that one expects down on earth, with twice as many muon-neutrinos as electron neutrinos. These atmospheric neutrinos, which have a much higher energy than the solar neutrinos, have also been measured, and their behavior fits very good to the expectations from neutrino oscillations.

Besides this, neutrinos are in huge amounts produced in nuclear reactors, and in lesser amounts in natural radioactive decays in the earth's crust. Both of which are currently subject to intensive experimental studies.

Detecting a neutrino is not easy, because it interacts only very weakly. What one basically does it to take a large amount of something you know fairly well, and place detectors around it. And wait. Different experiments used e.g. solutions of cadmium chloride in water, chlorine containing fluids, heavy water, etc. Every once in a while, a neutrino will interact with one of the atom cores. This reaction produces charged secondary particles, traces of which can eventually be observed in the surrounding detectors. The larger the amount of stuff you place your detectors around, the larger the probability you actually see something.

I am always impressed by these experiments. My favourite detector is Super-Kamiokande. Here is a photo, where you see the large water tank (half filled) surrounded by the detectors. Isn't this beautiful?

(Click here for a different view of Super-K.)

Now that we have analysed the characteristics of neutrinos when they propagate, we can use them as a tool to further studies, e.g. about the properties of sun, or as messengers from far away places in the universe.


There are a huge number of neutrino experiments, a list of which you find here. The website of the Icecube experiment at the South Pole stands out not only with it's design, don't miss it.

Wow, I just noticed that the Wikipedia entry on neutrinos has been thoroughly cleaned up! (I read it on Friday, and thought that it provides a rather unbalanced view. It's much better now, but still very dominated by experiment.)

For a short theoretical introduction, check the above mentioned very nice article by John N. Bahcall. For some historical background, I recommend the short introduction at the Super-K website.

Via Quasar's nice post on nature's mysteries and surprises, I found more on John Bahcall and neutrinos, and the Nova introduction about The Ghost Particle.

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Updated on July 19th 2006


  1. Bee, I liked this post so much i ate it up like if it were strawberry yoghurt icecream.

    I've put a link to it from my blog
    hope that is ok! laters ... Q

  2. Correction, I haven't created a Link from your post

    I've placed a short cut to your post URL from my post. Maybe we'll start doing proper links on related articles soon.

    Have a nice day! Q

  3. I asked my brother what flavour he'd go for today...

    a great example of flavour oscillations with an enforced collapse at the end ;-)

    Best, Stefan

  4. waiting for Haagen Daaz to introduce the electron-tau swirl...

  5. Betelgeus will collapse into a supernova on 21 December 2012 local time. Neutrino telescopes will register a big fat correlated signal; LIGO will score; everybody will be cooked by

    Cl-37 + neutrino --> Ar-37 (ec) --> Cl-37 + gamma + 2 Auger electrons

    before they can get published. The universe is dedicated to stellar irony!

  6. Hi Uncle,

    I guess they just got scooped by you ;-) Best,


  7. Hi Stefan,

    flavour oscillations with an enforced collapse

    I thought the same thing... but didn't want to overstretch the analogy.

    btw, it's MUCH warmer here in Canada than in Santa Barbara.

    I think today is a chocolate day.

    Best, B.

  8. Hi Bee, thanks!
    I've just been brainstorming a comment at Plato's - and trying to absorve some of almost infinite data. I'll try and concise it into something that makes sense. laters ...

    PS icecream vendors here had their busiest day so far today. lol!
    PPS the super-k is beautiful

  9. A recent paper :

    has a very interesting overview, with historical and future reference's.

    I recall a paper sometime ago that made an interesting speculation as to the fact between the Sun and Earth, there is less dense matter, than, the Earth's Atmosphere and the Earth's surface ?

    The consensus reached was Neutrino oscilations may be releated to the density of local Matter (where detectors are located), and the density of Vacuum Space?

    Basically there is less matter and more "space" between the Sun and Earth ?

    Interestingly, a distance of say 3,000 miles on Earth, will be different for local detectors placed along the distance, than a detector placed anywhere along a 3,000 mile plane close to the Sun?

    Earth based experiments cannot replicate the output of the Sun with/and the vacuum (density) of space ?

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  11. Hi Bee,

    With your current post drawing my attention to this one, which you wrote some time back, I would first like to say it is certainly an excellent synopsis. Subsequently, it also has arisen in me a question, which I hope you will be kind enough to answer? I realize also you shouldn’t be expected to be the substitute for the public library and yet rather then to just leave this to my own ill considered speculations I thought I’d ask if you know.

    Recognizing that neutrinos do have a rest mass (unlike the photon), where high velocities are achieved with a small required energy, as this rest mass is so small. This realized, it is also understood that they are restricted to velocities less then C, since they do have such mass. As stated in your article that the period of oscillation relates to the energy of the neutrino; so I take that to be the energy that is in excess of rest mass. My question being then, what is the consequence of this in terms of the oscillation period if the neutrino were considered to have no such energy and is at rest, that is theoretically speaking? My guess (ill considered speculation) is that the neutrino would either have a infinitely small period of oscillation and in order avoid such that it would be restricted from being able to have zero velocity (be at rest). Is this then to be considered as simply to relate to QM, where zero velocity is not allowed for this forms to be a certainty. As a follow up question, are slow moving neutrinos allowed by theory and if so have they been observed.



  12. Hi Phil,

    I'm not entirely sure I understand the question. Neutrino oscillation isn't an effect of one neutrino with a mass. It is an effect of a neutrino that is produced in a flavor eigenstate which is *not* a mass (energy) eigenstate and subsequently mixes different flavors. If you start with a mass eigenstate (in whatever restframe) it will remain a mass-eigenstate and not mix.

    If the question is how long the oscillation period would be in a different rest-frame that is just a Lorentz-transformation. I.e. yes, we would think for the neutrino time runs slower. Slow moving neutrinos are allowed by theory, but 'slow' in itself is not meaningful, it is always only 'slow relative to'.



  13. Hi Bee,

    If the question is how long the oscillation period would be in a different rest-frame that is just a Lorentz-transformation. I.e. yes, we would think for the neutrino time runs slower. Slow moving neutrinos are allowed by theory, but 'slow' in itself is not meaningful, it is always only 'slow relative to'.

    Thanks for taking the time to answer and yes the question was what the oscillation period would be as it relates to rest frames. Now I will go back and consider the answer. Just as a point of clarification, a slow (relative) moving neutrino would have a considerably shortened oscillation period? That is to say that in the relative sense as an observer approached the speed of the neutrino (catching up) the period of oscillation would approach zero, as defined by limit. I guess what has me wondering is that if in matching the relative speed of a neutrino an observer would find it to have a oscillation period that was infinitely short. What if anything could this mean as it relates to its flavor; or is this hopeless novice again getting something confused?

    Whatever your answer if any, thanks once again for the effort and the time spent.



  14. I just read Sabine’s retweet of an article in titled: “A Proposal for a Neutrino Detection Array Spanning 200,000 Square Kilometers” that will attempt to detect air showers emanating from decaying tau neutrinos. This will be very interesting when this array is fully up and running as it can either confirm or refute aspects of the Standard Model as they pertain to neutrino behavior.


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