Seesaw mechanism
In theoretical physics, the seesaw mechanism is a mechanism to generate very small numbers from "reasonable numbers" and very large numbers. Mathematics behind the seesaw mechanism is the following fact: the 2 by 2 matrix
:
where is big and is of intermediate size has the following eigenvalues:
:
The larger eigenvalue is approximately equal to while the smaller eigenvalue is approximately equal to
:
Therefore, is the geometric mean of and , up to the sign. This mechanism is used to explain why the neutrino masses are so small. The matrix A is essentially the mass matrix for the neutrino. , the Majorana mass, is comparable to the GUT scale and , 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. See neutrino oscillation
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