# Neutrino oscillation and Mass

1. Jan 1, 2009

### spidey

I have many doubts about neutrinos..can someone explain me?

1. All neutrinos and anti neutrinos have different masses..and if the neutrinos oscillate, how the difference in mass is justified? is there any violation of energy conservation?

2. If neutrinos which are leptons oscillate, then the other leptons electrons,muons and tau also oscillate?

3. What is the relation between oscillation and mass? why we say if neutrinos oscillate then it should have mass? then baryons also have mass, do they also oscillate?

4. what is actually changing in oscillation i.e. like charge, lepton number or what else is changing? how do we say that an electron neutrino is changed to muon or tau neutrino? is it by measuring their mass we predict their identity?

5. Do anti neutrinos also oscillate?

2. Jan 1, 2009

### malawi_glenn

1. See section "Propagation and interference" in http://en.wikipedia.org/wiki/Neutrino_oscillation

The hamiltonian will contain a mass term, and the hamiltonian is the generator of time evolution.

2. the MNS matrix (see the article) is conventionally chosen to be in the electrical neutral charged lepton sector, one could have it the charged lepton sector aswell-> Overall physics will be the same. But since one thought that neutrinos was massless, I think one choosed to have the MNS matrix with the neutrinos.

3. Baryons don't have this problem since they are first of all not elementary particles but composite systems. Oscillations are due to the nature of the weak interaction, so some hadrons oscillate, the most famous ones are the K^0 mesons.

4. No we measure the occurence of reactions. e.g we assume only electron neutrinos are produced in the sun/reactor (a VERY good assumption). Then we know that electron neutrinos produces electrons in inverse beta decay, muon neutrinos produces muons (etc) so in this way we can measure the amount of oscillations and from that deduce mass differences of the neutrinos.

5. Yes

3. Jan 1, 2009

### Xezlec

As usual, I will try to answer in a less technical way.

This is quantum physics. When we say the neutrinos oscillate, what we mean is that they are in a superposition of states that appears to oscillate due to interference between the wavefunctions of the different states. It's hard to speak about the momentum and mass-energy of the neutrino in a clear and definite way.

No.

Oscillation is a change in the state of the neutrino. If the neutrino is changing, it must experience time. Without time, there can be no concept of "change". According to special relativity, things that travel at the speed of light have no time, and things slower than slight have time. Therefore, neutrinos must travel slower than light. But also according to special relativity, things that travel slower than light must have mass. So neutrinos must have mass.

4. Jan 1, 2009

### hamster143

Perhaps I should elaborate.

We're familiar with quantum states called "electron", "muon" and "tauon" (charged leptons). Those are all by definition states of definite mass. Electrons are stable. Muons decay into an electron and a pair of neutrinos. Tau can decay into all sorts of things.

Weak interaction couples every charged lepton mass state to a superposition of neutrino mass states, and every neutrino mass state to a superposition of charged lepton mass states. We conventionally call the superposition that couples to the electron "electron neutrino", etc. It is an unfortunate archaism that goes back to the days before we knew that neutrinos had masses.

Problem is, pure mass states of charged leptons are easy to come by (just take electron, for example), and neutrinos are notoriously hard to work with. If you could somehow create a beam of neutrinos of a definite mass and shine it at a detector, you'd see a coherent superposition of e, mu and tau on the output. And then you could talk about charged lepton oscillation. But there's no such thing as a source of neutrinos of a definite mass.

Essentially all oscillation experiments consist of a source that involves charged lepton mass-states (a reactor, core of the Sun) and a sink that also involves charged lepton mass-states (perhaps a tank of chlorine or a block of ice). If they are spatially separated, we will see that the neutrino state that left the source is not identical to the state that arrives at the sink, because it's not a state of definite mass.

5. Jan 1, 2009

### Xezlec

Thanks for that explanation, hamster! That was not only more precise than my explanation, but also helped me understand things a little better than I did before.

6. Jan 1, 2009

### spidey

Thanks mates for clear explanation about neutrinos

7. Jan 2, 2009

### spidey

What does this mean "things that travel at the speed of light have no time".. what is no time?

8. Jan 2, 2009

### humanino

Proper time, which is the (minkowskian) length along the world-line, or to put it another way, how many oscillations counted by a perfect clock traveling along this line.

Neutrino mixing is quite a tricky topic.

TASI 2002 lectures on neutrinos
Neutrino physics overview

9. Jan 3, 2009

Staff Emeritus
The lecture notes by Grossman are quite good; I recommend them too.

There are two subtleties involved, one commonly mentioned, one implicit (and thus not as well known as the people doing the implying might think),

The common one is that it's not enough for neutrinos to be massive for them to mix. They have to have different masses. If two neutrinos have the same mass, I am free to relabel different mixes of $$\nu_1$$ and $$\nu_2$$ (I will use numeric subscripts to indicate mass eigenstates and lepton subscripts to indicate flavor eigenstates) and so I can define $$\nu_1 = \nu_e$$ and $$\nu_2 = \nu_\mu$$. So there are no longer any oscillations.

The less common one is very subtle. When most people are asked to describe how neutrinos oscillate in an accelerator experiment, they say something like this: "A beam of pions decays via $$\pi \rightarrow \mu + \nu_\mu$$. Of course, $$\nu_\mu$$ is actually a mix of $$\nu_1$$, $$\nu_2$$ and $$\nu_3$$, so one of those mass eigenstates is selected, it propagates to the detector, and then, since the detector detects flavor eigenstates, is projected back to the $$\nu_e$$, $$\nu_\mu$$ and $$\nu_\tau$$ basis. This is (observationally) wrong.

The above model predicts that the fraction of $$\nu_e$$'s that stay $$\nu_e$$'s is constant with flight distance, when in fact, it's a function of flight distance (actually L/E).

In fact, a mass eigenstate is not projected out. The $$\nu_\mu$$ evolves as a coherent mix of $$\nu_1$$, $$\nu_2$$ and $$\nu_3$$ and continues to oscillate between them until the detector projects out the flavor. This is quantum mechanics on a scale of hundreds of miles!

Last edited by a moderator: Jan 4, 2009
10. Jan 3, 2009

Staff Emeritus
Wow. The LaTeX sure got mangled.

11. Jan 3, 2009

### hamster143

And now the tricky part.

What happens when the neutrino is created with energy that is less than the mass of one or more of its constituents?

12. Jan 4, 2009

Staff Emeritus
What constituents? So fas as we know, neutrinos are elementary and have no constituents.

13. Jan 4, 2009

### humanino

Which is conserved in neutrinos oscillations : energy of momentum ?

14. Jan 4, 2009

Staff Emeritus
Both are. But that doesn't mean you are in an eigenstate of either. (This is a classic example of why it's important to study quantum mechanics before studying particle physics)

15. Jan 4, 2009

### hamster143

What I mean is, suppose that there are three different mass-states, and we have an interaction that could go through emission of a neutrino whose energy is lower than the mass of the heaviest mass-state.

16. Jan 4, 2009

### humanino

This is right, we are dealing here with elementary QM. Of course, the (academic) problem is that, if energy and momentum are fixed, mass must be fixed as well... As a matter of fact, the coherence length is related to the (energy and the) mass difference which itself is related to the wave-packet momentum spread.

Anyway, I got stuck for a while on this before finding out
When Do Neutrinos really oscillate ? Quantum mechanics of neutrino oscillations, PRD vol44 n11 (1991)
Quantum mechanics of neutrinos oscillations, PRD vol48 n9 (1993)

In any case, one should always look first at Neutrino mass, mixing, and flavor change (Particle Data Group)

Massive Neutrinos in Physics and Astrophysics, World Sci. Lect. Notes vol 72
Fundamentals of Neutrino and Astrophysics, Oxford UP.

17. Jan 4, 2009

### Xezlec

According to special relativity, if you get in a rocket and blast away at a very high speed, your time becomes different from our time. Time moves slower and slower for you as your speed approaches the speed of light. If you actually travel at the speed of light, you would be frozen in time. You would never move or get older.

What I was saying was that since neutrinos oscillate, something is changing. They are not frozen in time, so they must not move at the speed of light. Other people here are pointing out that this may not be the best way to think about things, but for me, talking about relativity is easier than talking about quantum mechanical wave functions.

The more complicated but probably more accurate way to look at it is that the oscillation is caused by interference between the wave functions for the different possible masses that the neutrino might have. If neutrinos didn't have different masses, then their wave functions would not be able to interfere in this way that changes the neutrino's flavor with time.

18. Jan 4, 2009

### Xezlec

I'm afraid we're hijacking the thread a little, but...

I'm a little out of my league here, but I sort of thought that when a particle is created with an amount of energy too small to account for its mass, then that means it's a "virtual particle" and is living on "borrowed time", so to speak. Would this also apply to a single mass-eigenstate component of a neutrino's wave-function? Does this just mean that the wave function can only have a tiny amount of that component, like that particular mass eigenstate could be thought of as "virtual" or something?