In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of the order of eV, compared to those of quarks and charged leptons, which are millions of times heavier.
The name of the seesaw mechanism was given by Tsutomu Yanagida in a Tokyo conference in 1981.
The simplest version, "Type 1", extends the Standard Model by assuming two or more additional right-handed neutrino fields inert under the electroweak interaction,[a] and the existence of a very large mass scale.
The simple mathematical principle behind the seesaw mechanism is the following property of any 2×2 matrix of the form It has two eigenvalues: and The geometric mean of
while the smaller eigenvalue is approximately equal to This mechanism serves to explain why the neutrino masses are so small.
is comparable to the GUT scale and violates lepton number conservation; while the Dirac mass components
are of order of the much smaller electroweak scale, called the VEV or vacuum expectation value below.
then leads to a very small neutrino mass, comparable to 1 eV, which is in qualitative accord with experiments—sometimes regarded as supportive evidence for the framework of Grand Unified Theories.
The 2×2 matrix A arises in a natural manner within the standard model by considering the most general mass matrix allowed by gauge invariance of the standard model action, and the corresponding charges of the lepton- and neutrino fields.
Call the neutrino part of a Weyl spinor
a part of a left-handed lepton weak isospin doublet; the other part is the left-handed charged lepton
as it is present in the minimal standard model with neutrino masses omitted, and let
There are now three ways to form Lorentz covariant mass terms, giving either and their complex conjugates, which can be written as a quadratic form, Since the right-handed neutrino spinor is uncharged under all standard model gauge symmetries, B is a free parameter which can in principle take any arbitrary value.
The parameter M is forbidden by electroweak gauge symmetry, and can only appear after the symmetry has been spontaneously broken by a Higgs mechanism, like the Dirac masses of the charged leptons.
In particular, since χ ∈ L has weak isospin 1/2 like the Higgs field H, and
has weak isospin 0, the mass parameter M can be generated from Yukawa interactions with the Higgs field, in the conventional standard model fashion, This means that M is naturally of the order of the vacuum expectation value of the standard model Higgs field, if the dimensionless Yukawa coupling is of order
It can be chosen smaller consistently, but extreme values
on the other hand, is forbidden, since no renormalizable singlet under weak hypercharge and isospin can be formed using these doublet components – only a nonrenormalizable, dimension 5 term is allowed.
This is the origin of the pattern and hierarchy of scales of the mass matrix
The large size of B can be motivated in the context of grand unification.
In such models, enlarged gauge symmetries may be present, which initially force
in the unbroken phase, but generate a large, non-vanishing value
A huge scale has thus induced a dramatically small neutrino mass for the eigenvector