2 questions about Neutrino oscillations

Dmitry67

Two questions.

1. Different flavors have different mass. Look at it from the frame where neutrino is at rest. What’s about energy conservation? Are neutrinos oscillating so quickly that uncertainty principle plays role?
2. Why oscillations of neutral Kaons form 2 new “particles” (K-long and K-short) – why neutrinos don’t produce such mixtures?

phyzguy

This is incorrect. The point is that the flavor eigenstates do not have a definite mass - they are a mixture of different mass eigenstates. Likewise the mass eigenstates do not have a definite flavor - they are a mixture of different flavor eigenstates.

Bill_K

As phyzguy says, the flavor eigenstates in which neutrinos are produced are not the same as the mass eigenstates. Therefore it's not accurate to talk about, for example, the mass of the electron neutrino, because it is not an eigenstate of mass. The mass eigenstates are analogous to the K_L and K_S states we see in the kaon system.

Energy is exactly conserved. But in any reaction there is always a small spread in energy. What makes neutrinos unique is that their mass differences are so small that the process that produces them yields a coherent mixture of mass eigenstates.

Dmitry67

Thank you, it makes sense now.

But what is Feynman diagram for neutrino oscillation? For Kaons, W+/W- play role in changing quark contents, and for the neutrinos? It is just a line representing one flavor suddenly becomes the other flavor?

Bill_K

Let's take the OPERA experiment as an example. At CERN the production process is W → μ + neutrino. At Gran Sasso 730 km away the detection process is neutrino → W + τ. Conventionally we say "a muon neutrino was produced, and during its flight it mutated into a tau neutrino." Whereas in fact the unobserved neutrino is one of the three mass eigenstates, ν1, ν2, ν3. At the vertex in CERN there were three amplitudes W → μ + ν1, W → μ + ν2 and W → μ + ν3, and correspondingly at Gran Sasso there are three, ν1 → W + τ and so on. The three processes are coherent.

jtbell

In other words, the process isn't represented by a single Feynman diagram, but rather, by the sum of three Feynman diagrams.

Dmitry67

Thank you!

Dmitry67

Wait, still not clear...
"mass eigenstates do not have a definite flavor" - makes perfect sense.

regarding
"flavor eigenstates do not have a definite mass - they are a mixture of different mass eigenstates" - are they mixture of exactly 3 mass eigenstates, or, as flavor does not change only during very short time we don't have the exact mass just because of the uncertainty principle?

In another words, in Standard Model, extended to accomodate neutrino masses, how many NEW parameters are there for neutrino masses: 1 or 3?

Bill_K

Yes.
The model currently accepted is that there are simply three new mass parameters. The true nature of neutrinos is still being experimentally confirmed.
LA LA LA LA! Can't HEAR you!

Real physicists do not talk about the uncertainty principle. We talk instead about coherent states. A flavor state is a coherent superposition, |f> = a|v1> + b|v2> + c|v3>. The three mass states coexist coherently, like the two possible states of Schrodinger's cat. They are coherent because we have done nothing to distinguish them. If the energies of the particles in the reaction that created the neutrino were measured to within a millionth of an eV or whatever, we would know the mass of the neutrino state, and hence know which of the three eigenstates it was. The three eigenstates really do have different energies, but it's not from lack of energy conservation, or shortness of time, or the uncertainty principle.

The wavefunction of a state with energy E oscillates in time like e^iEt/ħ, and so if you wait long enough, the terms in a|v1> + b|v2> + c|v3> eventually get out of phase with each other. This alters the probability of its decay into a flavor state, and we see that effect as "neutrino oscillations."

Dmitry67

I see, and yes, I am not a real physicist :)
So currently we can't measure neutrino masses yet, but are there any constraints on ratios Mass(u neutrino)/Mass(e neutrino), Mtau/Mu?

jtbell

The constraints so far are not simple ratios of masses. Several schemes for the neutrino mass spectrum are consistent with current data on the mixing angles. See the following review from the Particle Data Group, in particular page 46:

http://pdg.lbl.gov/2012/reviews/rpp2...ino-mixing.pdf

mfb

Plus 4 mixing parameters, similar to quark mixing. They determine which superposition of mass eigenstates the flavour eigenstates are (and vice versa).

Bill_K

Yep thanks, I stand corrected. The array of mixing angles is called the MNS matrix, named for Maki, Nakagawa and Sakata.

Dmitry67

After reading the PDF, so the precision of the current experiments are at least one order above the precision, required to measure the neutrino mass?

mfb

If they are worse, their precision is lower, not higher.
The indirect measurements (difference of mass squared via mixing) cannot be used to calculate neutrino masses, but you can get an idea where they might be. And the current upper limits for direct mass measurements are still above that, right.

snorkack

What is measured is the differences in the squares of rest masses, right? And 2 such differences exist.

Is there any evidence that all 3 neutrino mass eigenstates possess rest mass? Existence of a massless particle is not contrary to general relativity (see photon)... so how about mixing of massless particle with 2 massive ones?

mfb

There are 3 differences (1<->2, 2<->3, 1<->3), and as (most?) mixing measurements are not sensitive to the signs all 3 are interesting on their own.

I did not see any. One neutrino could be massless, but that would be quite odd.