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In theoretical physics
Theoretical physics

Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world....
, in the area of quantum field theory
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
, 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
Grand unification theory

Grand Unification, grand unified theory, or GUT refers to any of several very similar unified field theory or models in physics that predicts that at extremely high energies , the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field....
, and in particular in theories of neutrino
Neutrino

Neutrinos are elementary particles that travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect....
 masses and neutrino oscillation
Neutrino oscillation

Neutrino oscillation is a quantum mechanics phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor can later be Quantum measurement to have a different flavor....
. This model produces a light neutrino, corresponding to the three known neutrino flavors, and a very heavy, undiscovered sterile neutrino
Sterile neutrino

A sterile neutrino is a hypothetical neutrino that does not interact via any of the fundamental interactions of the Standard Model except gravity ....
.

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

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
 where is much larger than , has the following eigenvalues: The larger eigenvalue is approximately equal to while the smaller eigenvalue is approximately equal to Therefore, is the geometric mean
Geometric mean

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, which is what most people think of with the word "average," except that instead of adding the set of numbers and then dividing the sum by the count of numbers in the...
 of and , up to the sign.






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In theoretical physics
Theoretical physics

Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world....
, in the area of quantum field theory
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
, 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
Grand unification theory

Grand Unification, grand unified theory, or GUT refers to any of several very similar unified field theory or models in physics that predicts that at extremely high energies , the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field....
, and in particular in theories of neutrino
Neutrino

Neutrinos are elementary particles that travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect....
 masses and neutrino oscillation
Neutrino oscillation

Neutrino oscillation is a quantum mechanics phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor can later be Quantum measurement to have a different flavor....
. This model produces a light neutrino, corresponding to the three known neutrino flavors, and a very heavy, undiscovered sterile neutrino
Sterile neutrino

A sterile neutrino is a hypothetical neutrino that does not interact via any of the fundamental interactions of the Standard Model except gravity ....
.

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

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
 where is much larger than , has the following eigenvalues: The larger eigenvalue is approximately equal to while the smaller eigenvalue is approximately equal to Therefore, is the geometric mean
Geometric mean

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, which is what most people think of with the word "average," except that instead of adding the set of numbers and then dividing the sum by the count of numbers in the...
 of and , up to the sign. In other words, the determinant
Determinant

In algebra, a determinant is a function depending on n that associates a scalar , det, to an n?n square matrix A. The fundamental geometric meaning of a determinant is a scale factor for measure when A is regarded as a linear transformation....
 equals . If one of the eigenvalues "goes up", the other "goes down", and vice versa. This is the reason why the name seesaw
Seesaw

A seesaw is a long, narrow board suspended in the middle so that, as one end goes up, the other goes down.In a playground setting, the board is balanced in the exact center....
 was given to the mechanism.

This mechanism is used to explain why the neutrino
Neutrino

Neutrinos are elementary particles that travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect....
 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 , the Dirac
Dirac spinor

In quantum field theory, Dirac spinor is the bispinor in the Plane wave solutionof the free Dirac equation,where is a relativistic spin-1/2 Field ,...
 mass, is of order of the electroweak scale
Electroweak scale

In particle physics, the electroweak scale is the energy scale around 246 GeV, a typical energy of processes described by the electroweak theory. The particular number 246 GeV is taken to be the vacuum expectation value of the Higgs field ....
. The smaller eigenvalue then leads to a very small neutrino mass comparable to 1 eV
EV

eV may mean:* Electronvolt, a unit of energye. V. may mean:* Eingetragener Verein, a registered club in GermanyEV may mean:...
 which qualitatively agrees with the experiments. Such an agreement may be interpreted as an experimentally confirmed qualitative predictions of Grand Unified Theories.

See also

  • Majoron
    Majoron

    In particle physics, majorons are a hypothetical type of Goldstone bosons that are theorized to mediate the neutrino mass violation of lepton number or B-L in certain high energy collisions such as...
  • Sterile neutrino
    Sterile neutrino

    A sterile neutrino is a hypothetical neutrino that does not interact via any of the fundamental interactions of the Standard Model except gravity ....
  • Spinor
    Spinor

    In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector and tensor....


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