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Neutrino oscillation

From Biocrawler, the free encyclopedia.

Neutrino oscillation refers to the phenomenon of neutrinos oscillating between behaving like different flavors, in the sense that the flavor eigenstates are defined as the wavefunction that will produce a charged lepton of a particular type (electron, muon or tau lepton) when interacting with a W-boson, and a neutrino produced as one of these eigenstates will behave as a superposition of different flavor eigenstates with the ratio of proportions varying periodically. E.g. the standard Solar Model predicts that electron neutrinos are produced in the fusion reactions in the core. If these neutrinos interact with a W-boson immediately, they will produce electrons 100% of the time. However, a short while later, they may produce muons 50% of the time and electrons 50% of the time (due to the inherently statistical nature of quantum interactions). Later still, these neutrinos may come back to being purely electron neutrinos, and will produce electrons with 100% certainty. (These numbers are not particularly accurate!)

The period of this oscillation is quite small, but since neutrinos are generally produced travelling close to the speed of light, the distance over which they travel during one period can be quite large.

Contents

1 Evidence For Neutrino Oscillations

2 Neutrino Masses

3 Origins Of Neutrino Mass

4 See also

5 External links

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Evidence For Neutrino Oscillations

The discrepancy between the amount of electron neutrinos predicted to reach Earth from the Sun by models of Solar fusion and the actual amount detected (see Solar neutrino problem) was the initial experimental evidence for neutrino oscillations. Further evidence was also provided by experiments measuring the neutrino flux from the upper atmosphere (where they are produced by cosmic rays), nuclear reactors and particle accelerators.

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Neutrino Masses

It is widely accepted in the Particle Physics community that the oscillations are due to the different flavors of neutrino having different masses. If a neutrino is produced as a flavor eigenstate, and that flavor eigenstate is not a mass eigenstate, then we may write the wavefunction as a superposition of mass eigenstates:

$\left| \nu \right\rangle = \sum_{i} \left| \nu_{i} \right\rangle$

where the : $\left| \nu_{i} \right\rangle$ are mass eigenstates (i.e. obey Einstein's relativistic energy-momentum equation), and so can be written as plane wave solutions, : $\exp( -2 \pi i ( E t - \vec{p}.\vec{x}) / h )$ .

If this neutrino is created with a definite 3-dimensional momentum, then the energy each mass eigenstate in the superposition will be given by:

$E^2 - |\vec{p} \,|^2 c^2 = m^2 c^4$

If the mass eigenstates have different masses, then the will have different energies, and thus different frequencies (as the frequency is the coefficient of time in the plane-wave function). If they have different frequencies, then they will interfere in a manner that will produce different ratios of mass eigenfunctions in the superposition, which will correspond to the wavefunction being a superposition of flavor eigenstates as well, which in turn will produce the behavior described above.

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Origins Of Neutrino Mass

The question of how these masses arise has not been answered conclusively. In the Standard Model of particle physics, fermions ("matter particles") only have mass because of interactions with the Higgs field (see Higgs boson). These interactions involve both left- and right-handed versions of the fermion (see Chirality (physics)). Neutrinos are special, since as electrically-neutral particles they may have another source of mass, Majorana mass (which cannot work for electrically-charged particles since it would allow particles to turn into anti-particles which would violate conservation of electric charge). Neutrinos are also special because only left-handed neutrinos have been observed.

Physicists like to modify successful theories (like the Standard Model) as little as possible, so the smallest modification to the Standard Model, which only has left-handed neutrinos, is to allow these left-handed neutrinos Majorana masses. The problem with this is that the neutrino masses are implausibly smaller than the rest of the known particles (at least 500000 times smaller than the mass of an electron), which, while it does not invalidate the theory, is not very satisfactory. The next simplest addition would be to add right-handed neutrinos into the Standard Model, which interact with the left-handed neutrinos and the Higgs field in an analogous way to the rest of the fermions. These new neutrinos would interact with the other fermions solely in this way, so are not phenomenologically excluded. Still, the problem of the disparity of the mass scales remains.

The most popular solution currently is the "see-saw" model, where right-handed neutrinos with very large Majorana masses are added. If the right-handed neutrinos are very heavy, they induce a very small mass for the left-handed neutrinos, which is proportional to the inverse of the heavy mass. If it is assumed that the neutrinos interact with the Higgs field with approximately the same strength as electrons do (which is quite reasonable as neutrinos and electrons/muons/tau leptons are associated with each other in the same way as up and down quarks are associated with each other), the heavy mass should be very close to the GUT scale.

There are other ideas for the origin of neutrino mass, such as R-parity violating supersymmetry, which proposes that the masses for the neutrinos come from interactions with squarks and sleptons, rather than the Higgs field. However, these interactions are normally excluded from theories as they come from a class of interactions that lead to unacceptably rapid proton decay (if they are all included). Still, these theories have not been ruled out yet.

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