Type 1 Seesaw
This model produces a light neutrino, corresponding to the three known neutrino flavors, and a very heavy neutrino, which has yet to be observed.
The mathematics behind the seesaw mechanism is the following fact: the 2×2 matrix
where is much larger than, has the following eigenvalues:
The larger eigenvalue, λ+, is approximately equal to while the smaller eigenvalue is approximately equal to
More precisely, |M| is the geometric mean of λ+ and −λ−. In other words, the determinant equals λ+λ− = −M2. If one of the eigenvalues goes up, the other goes down, and vice versa. This is the reason why the name seesaw was given to the mechanism.
This mechanism is used to explain why the neutrino masses are so small.
The matrix A is essentially the mass matrix for the right-handed neutrino. The Majorana mass is comparable to the GUT scale and M, the Dirac mass, is of order of the electroweak scale. The smaller eigenvalue then leads to a very small neutrino mass comparable to 1 eV which qualitatively agrees with the experiments. Such an agreement may be interpreted as an experimentally confirmed qualitative prediction of Grand Unified Theories.
Read more about this topic: Seesaw Mechanism
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