Neutrino Oscillation

[Kharakov]

Any theories in which quantized relative velocity of neutrinos determines flavor?

 

[repoman]

One thing that really makes me scratch my head is this: When the oscillations are happening and each of the masses are oscillating (m1, m2, m3) -- these masses, would they travel at different velocities during the oscillation? Yes, I know that it is one discrete neutrino, but its probability of being m1, m2 or m3 would seem to spread out because of relative velocity difference.

Also, kind of strange how they are oscillating both in flavor and mass.

 

[lpetrich]

I'll try to explain what causes neutrino oscillations.

Corresponding to each flavor of charged lepton is a flavor or weak-interaction state. It's the weak interaction that turns electrons into electron neutrinos and back again, and likewise for muons and tau leptons and their neutrinos.

But each flavor of neutrinos is a mixture of mass states, and each of them oscillates with a different frequency, because each one has a different mass. These oscillations turn a pure flavor into an oscillating mixture of flavors.

I'll try to explain it in the two-flavor case, because the math is easier than for the three-flavor case. I'll imagine only electron and muon neutrinos. They mix as follows:

(e-nu) = cos(θ) * (m1-nu) + sin(θ) * (m2-nu)
(μ-nu) = - sin(θ) * (m1-nu) + cos(θ) * (m2-nu)

The mass states can be found from the flavors as follows:

(m1-nu) = cos(θ) * (e-nu) - sin(θ) * (μ-nu)
(m2-nu) = sin(θ) * (e-nu) + cos(θ) * (μ-nu)

Now let them oscillate over time t, where (m1-nu) has energy E1 and (mu2-nu) has energy E2. The new mass states become

(m1-nu)' = (m1-nu) * exp(-i*E1*t)
(m2-nu)' = (m2-nu) * exp(-i*E2*t)

Then,

(e-nu)' = cos(θ) * (m1-nu)' + sin(θ) * (m2-nu)'
(μ-nu)' = - sin(θ) * (m1-nu)' + cos(θ) * (m2-nu)'

(e-nu)' = cos(θ) * (cos(θ) * (e-nu) - sin(θ) * (μ-nu))*exp(-i*E1*t) + sin(θ) * (sin(θ) * (e-nu) + cos(θ) * (μ-nu))*exp(-i*E2*t)
(μ-nu)' = - sin(θ) * (cos(θ) * (e-nu) - sin(θ) * (μ-nu))*exp(-i*E1*t) + cos(θ) * (sin(θ) * (e-nu) + cos(θ) * (μ-nu))*exp(-i*E2*t)

(e-nu)' = (cos²(θ)*exp(-i*E1*t) + sin²(θ)*exp(-i*E2*t)) * (e-nu) + (cos(θ)*sin(θ)*(exp(-i*E2*t) - exp(-i*E1*t)) * (μ-nu)
(μ-nu)' = (sin²(θ)*exp(-i*E1*t) + cos²(θ)*exp(-i*E2*t)) * (μ-nu) - (cos(θ)*sin(θ)*(exp(-i*E2*t) - exp(-i*E1*t)) * (e-nu)

Since the observed intensity is proportional to the absolute square of the wavefunction, we must take it.
|e-nu| -> |μ-nu|' = |μ-nu| -> |e-nu|' = T
|e-nu| -> |e-nu|' = |μ-nu| -> |μ-nu|' = 1 - T
where
T = 2*cos²(θ)*sin²(θ)*(1 - cos((E2-E1)*t))

Since neutrino masses are much smaller than most reaction energies, we get E2 - E1 = (m2² - m1²)/(2*E) to lowest order.

 Neutrino oscillation goes into a lot of technical detail for the three-flavor case.

 

[Kharakov]

Corresponding to each flavor of charged lepton is a flavor or weak-interaction state. It's the weak interaction that turns electrons into electron neutrinos and back again, and likewise for muons and tau leptons and their neutrinos.

AFAICT, in the Standard Model electrons don't turn into electron neutrinos..... muons don't turn into neutrinos, 2pi leptons don't turn into neutrinos. The various flavors are said to oscillate between one another (electron neutrino <--> muon neutrino <---> tau neutrino <--> electron nu .... ).


I'm interested in the effect of Quantized Relative Velocity on oscillation (indirectly, QRV's affect on the probability of detecting an oscillation), which is probably something we can't detect yet, so... nm.

 

[lpetrich]

AFAICT, in the Standard Model electrons don't turn into electron neutrinos..... muons don't turn into neutrinos, 2pi leptons don't turn into neutrinos. The various flavors are said to oscillate between one another (electron neutrino <--> muon neutrino <---> tau neutrino <--> electron nu .... ).

That's a terminology issue, using flavor = mass state instead of weak-interaction state.

 

[barbos]

Neutrino oscillation does look weird, but this is because people got used to talk about neutrino flavours as if it was something real. In reality it is just convenient way to dumb down reality. In reality it just happened that neutrino field has probably 3 distinct excitation (masses) and that's all. Neutrino flavours are linear combination of these 3 masses which couple to W boson along with electron of different masses (e, mu, tau) In other words, neutrino types do not really exist, what exists is a 3 by 3 matrix which mixes lepton fields with W.

 

[repoman]

Are there seasonal variations in the amount of each neutrino flavor detected from the sun? This would be from the difference between perihelion and aphelion after accounting for distance and flux.

 

[4321lynx]

Admit it.

Which one of you is Sheldon from *The Big Bang Theory*? And where are the others?
And most importantly where is Penny?

 

[repoman]

Admit it.

Which one of you is Sheldon from *The Big Bang Theory*? And where are the others?
And most importantly where is Penny?

This may add more mystery to the question:

 

[4321lynx]

I can almost understand that