Re: Questions about neutrino oscillation

Patrick,

A neutrino is a neutral spin-1/2 fundamental particle in the Standard Model of Particle Physics that is not affected by the electromagnetic or strong nuclear forces. It interacts extremely weakly with matter; right now there are 100 billion neutrinos from the Sun passing through your thumbnail every second and you never notice. The neutrino was postulated by Wolfgang Pauli in 1930 to explain the apparent non-conservation of energy and momentum in beta decay. Experimental confirmation of the elusive neutrino's existence only came 25 years later with the work of Cowan and Reines.

If neutrinos were massless, then there would be two consequences: they would always travel at the speed of light and they could not oscillate, that is, change "flavors" from electron type neutrino, to muon type neutrino, to tau type neutrino because traveling at the speed of light their internal clocks would be frozen. Recent experiments have shown that neutrinos do in fact oscillate. Therefore neutrinos must have some mass.

Neutrinos are always created and detected in a state of definite flavor (electron, muon, or tau) called a "flavor eigenstate". This quantum mechanical state does not, however, have a definite mass; the flavor eigenstate is a superposition of three distinct "mass eigenstates". And each mass eigenstate is a superposition of the three flavor eigenstates.

That may sound strange, and it is strange, but here is a rough analogy. In the card game Gin, one type of meld has a definite suit (flavor) but three different ranks (masses) for example 2, 3, and 4 of hearts. Another kind of meld has a definite rank (mass) but three different suits (flavors) for example 6 of hearts, 6 of clubs, and 6 of spades.

Each of the three different mass eigenstates propagates with a different frequency because the frequency depends on the energy and the energy depends on the mass. At a later time, the superposition of mass eigenstates will not be the same as at the neutrino's creation. This is how the different flavor states get mixed together.

You asked, "Over what time do neutrinos oscillate? How long does it take a neutrino to change from one state to another?" The answer depends on the energy of the neutrino and the square of the mass difference between the two mass eigenstates in which you are interested. The quantum mechanical phase difference is usually written in terms of distance L, but you can substitute L=c*t because the neutrinos are traveling at nearly the speed of light (only slightly less):

dphase = 2.54 * (dm)^2 * L / E

where dm is the mass difference in electron volts (eV); L is distance in kilometers; and E is energy in gigaelectron volts (GeV). You will notice the neutrino oscillation when the phase difference is around pi.

For example, for atmospheric neutrinos which are produced when cosmic rays collide with atoms in the upper atmosphere:
(dm)^2 = 2.5*10^-3 eV^2
E = 1 GeV
L = c*t = Pi*E/(2.54 dm^2) = 500 km

For solar neutrinos:
(dm)^2 = 7*10^-5 eV^2
E = .0005 GeV
L = c*t = Pi*E/(2.54 dm^2) = 9 km

Here are some resources to explore:

http://en.wikipedia.org/wiki/Neutrino_oscillation

http://en.wikipedia.org/wiki/Neutrino

http://www.pbs.org/wgbh/nova/neutrino/

http://www.cpepweb.org/cpep_sm_large.html

--Dr. Randall J. Scalise
http://www.phys.psu.edu/~scalise/