3 ms·

A neutrino is born in a weak eigen state (e,mu,tau) and propagates as a mass eigen state (m1,m2,m3). The two bases are related by a rotation matrix of three an

A neutrino is born in a weak eigen state (e,mu,tau) and propagates as a mass eigen state (m1,m2,m3). The two bases are related by a rotation matrix of three angles and three phases of which one, the CP violation phase, can in principle be measured with long baseline neutrino experiments. The oscillation happens because each mass state propagates at a different frequency. So while a numu starts out with some fraction of m1, m2 and m3 states, it soon becomes a different mixture which is neither nue, numu nor nutau. Instead, when the neutrino interacts, it does so with some admixture probability of doing so in the form of each possible flavor.

qubex 9y ago
So it's basically a Markov Chain kind of process, but on continuum of time rather than in discrete steps?
- frumiousirc 9y ago
  I guess you could couch the concept in this way but I have not ran across this approach to do calculations. In vacuum the oscillation probability (ie, the vector holding probability amplitude saying how much of "e-ness", "mu-ness" and "tau-ness" the neutrino has over time) is analytic and almost trivial to apply. In the presence of matter, forward elastic interactions with electrons in the matter can "pop" or "reset" the neutrino back to a nue weak eigenstate. This is the so-called "matter effect". If the density is constant one can rewrite the oscillation probability formula into a form that is the same as the vacuum one. So, again, easy to calculate. When going through variable matter densities one must, to be proper, solve a differential equation. Computationally, this is done by stepping the equation, eg with Runge-Kutta. Happily for us humans doing experiments at home, if the matter in question is the Earth then the fact that its matter density is close to uniform in bands (crust, mantle, core) one can do a step-wise constant density approximation that's pretty close to a full solution and much faster.

qubex 9y ago

So it's basically a Markov Chain kind of process, but on continuum of time rather than in discrete steps?

frumiousirc 9y ago
I guess you could couch the concept in this way but I have not ran across this approach to do calculations. In vacuum the oscillation probability (ie, the vector holding probability amplitude saying how much of "e-ness", "mu-ness" and "tau-ness" the neutrino has over time) is analytic and almost trivial to apply. In the presence of matter, forward elastic interactions with electrons in the matter can "pop" or "reset" the neutrino back to a nue weak eigenstate. This is the so-called "matter effect". If the density is constant one can rewrite the oscillation probability formula into a form that is the same as the vacuum one. So, again, easy to calculate. When going through variable matter densities one must, to be proper, solve a differential equation. Computationally, this is done by stepping the equation, eg with Runge-Kutta. Happily for us humans doing experiments at home, if the matter in question is the Earth then the fact that its matter density is close to uniform in bands (crust, mantle, core) one can do a step-wise constant density approximation that's pretty close to a full solution and much faster.