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In theoretical physics, in the area of quantum field theory, the seesaw mechanism is a mechanism to generate very small numbers from "reasonable numbers" and very large numbers. The mechanism is commonly seen in grand unification theory, and in particular in theories of neutrino masses and neutrino oscillation. This model produces a light neutrino, corresponding to the three known neutrino flavors, and a very heavy, undiscovered sterile neutrino.

The mathematics behind the seesaw mechanism is the following fact: the 2 by 2 matrix

<math>A = \begin{pmatrix}0&M\\M&B\end{pmatrix}</math>

where <math>B</math> is big and <math>M</math> is of intermediate size has the following eigenvalues:

<math>\lambda_\pm = \frac{B\pm \sqrt{B^2+4M^2}}{2}.</math>

The larger eigenvalue is approximately equal to <math>B</math> while the smaller eigenvalue is approximately equal to

<math>\lambda_- \approx -\frac{M^2}B</math>

Therefore, <math>M</math> is the geometric mean of <math>B</math> and <math>\lambda_-</math>, up to the sign. In other words, the determinant equals <math>\lambda_+\lambda_- = -M^2</math>. 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. <math>B</math>, the Majorana mass, is comparable to the GUT scale and <math>M</math>, 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 predictions of Grand Unified Theories.